‘Tape II, Summary of experimental data on H:-. This table gives the band designation which we use in the present review (Bands

ee

”). For each author, listed in the first column, we give the nomenclature he used for a given band (e.g., “Series I,” “‘strong”)

and also the final state in which the band was observed (e.g., X1,*, b H,*), and the energy of the first resonance, in eV.

Possible equivalence*

t

rr

fg?

Band designation al “” “e “ar e “pr fg
Kuyatt et al. (1966) “strong” xe “weak”
(transmission) 11,28 11.46
Comer and Read (1971a) _ X*B,*(o) X1E,t XD ,H(o)
(7>8)
11.30 10.93! 11.19"
Weingartshofer et al. “Series I” “Series I” “Series II”
(1970) X1D,t, bt BY BY Cn.
11.30 11.30 11.50 13.63
Sanche and Schulz (trans- 11.32 x 11.43 13.66 15.09
mission) (1972)
Width, r (eV) <0.016 (H:)® 0.08 <0.016¢ 0.08
0.03 (D2)
Symmetry 2+ yt 25+; Ty "HI, (?) "Zt
Observed in Hz, HD, Dz H H:, HD, Ds H Hr Hs,D: He, Dz
R. (A)* 0.9740.01 1.1750.01 0.97
a (eV)ed 0.34540.015 0.190.015 0.345
b (evyed 0.013540.003 0.005+0.003 0.0135
Ey (eV) ed 11.40 11.41 11.40

* The arrows indicate that band ‘‘a” could be identical to band “d” and that band “‘c” may be identical to band “e.” See text.

» From Weingartshofer et al, (1970).
© From Comer and Read (1971a).
4 Defined by the equation E=Fpta(v+4) —b(v+4)*.

° The symbol X indicates that band “‘b” is observable only in the high vibrational states (v>8) of the 1Z,*state and thus cannot be

observed in transmission experiments.
* Extrapolated to v=0; see Appendix I.
* From Joyez, Comer, and Read (1973).

citation (v=0—1; j=1—3) is similar to the cross sec-
tion for vibrational excitation alone (vx=0—1; Aj=0)
and thus both processes seem to be dominated by the
22u* resonance. Angular distribution measurements by
Ehrhardt and Linder (1968) and by Linder (1969)
(Fig. 8), shows that pure vibrational excitation exhib-
its a po-wave dependence, i.e., the scattered electrons
exhibit a minimum at 90 degrees. These observations
are in agreement with the theory which predicts an
approximate angular distribution of the form (1+
2 cos’@). [See Bardsley and Read (1968), Ehrhardt,
Langhans, Linder, and Taylor (1968), and O’Malley
and Taylor (1968). ]

When rotational levels are excited in addition to vi-
brational levels, a flat (isotropic) angular distribution
is observed. Figure 8 shows the results for the transi-
tion Aj=2, Av=1. The ratio of the vibrational cross
section without rotational excitation to that with rota-

tional excitation, ¢(Aj=0; Av=1)/o(3-1; Av=1) is
shown in Fig. 9 in comparison with the theories of
Abram and Herzenberg (1969), of Henry (1970), and
of Henry and Chang (1972). The theory of Abram
and Herzenberg is based on the quantum mechanical
impulse approximation and neglects the kinetic energy
of rotation of the molecule during the collision. The
work of Henry and Chang uses the theory of frame
transformation as developed by Chang and Fano
(1972). The p-wave nature of the ratio is obvious
from the figure.

As far as pure rotational excitation, in which the
vibrational quantum number does not change, is con-
cerned, there are available the experimental data of
Ehrhardt and Linder (1968) and the improved data
of Linder and Schmidt (1971a). It is the latter data
that are shown in comparison with theory in Fig. 10.

As pointed out most recently by Linder and Schmidt


Fic. 24. Energy dependence of 23.5
cross section at 0° and 72°. The solid
Tines are from the close-coupling
theory of Burke, Cooper, and
Ormonde (1966). The dashed curves
are experimental: The 72° data are

° (0)
0,12
Let2

_ZE Xp. (Ref. 3)

°

from Schulz and Philbrick (1964) and
the 0° data from Chamberlain and
Heideman (1965). The first peak in
the cross section curves is attributed
to the #P resonance and the second to
the *D resonance. [From Burke,
Cooper, and Ormonde (1966).]

© (0,E) (7703 /Ster.)

(b)

19.8 20.0

energy range 19,5-20.3 eV. We should note that the
last of these structures coincides in energy with the
broad 2*P shape resonance discussed in the following
section.

4. 20.3-20.45 eV (2P)

The total cross section for excitation of the 2°S state
exhibits a maximum at about 0.5 eV above threshold as
shown in Fig. 23. It has been pointed out by Baranger
and Gerjuoy (1957) that such behavior can best be
explained by considering that the inelastic process
proceeds via a compound state. By fitting the total 28S
cross section with a Breit-Wigner one-level formula,
they obtained a very good fit to the experimental
cross section for metastable production (2%5-+-2!S)
of Schulz and Fox (1957). The parameters that resulted
in the best fit located the position of the resonance
at 20.2 eV with a width of about 1.0 eV. More detailed
theoretical considerations by Burke, Cooper, and
Ormonde (1966), using the close-coupling approach,
confirmed these ideas. Burke ef al. found that the
major peak of the 2°S cross section occurs within the
range of the p-wave resonance, which they calculate to
occur at 20.2 eV with a width of 0.52 eV. Another
smaller peak at the *D resonance (21.0 eV) is also
found in this calculation. These considerations then lead
us to associate experimentally determined maxima of
the 2°S cross section with the existence of compound
states.

If the width of the p-wave resonance is anywhere near
the value quoted by Burke ef al. (0.52 eV), it is not
surprising that the observed location of this maximum
varies depending on angle and the mode of observation.
Whereas the total 2°5 cross section peaks at 20.3-20.35
eV, (see, for example, Schulz and Fox, 1957; Pichanick

20.4 21.2

20.8
ELECTRON ENERGY (ev)

21.6 22.0

and Simpson, 1968) the differential cross section peaks
near 20.45 eV (Chamberlain, 1967; Ehrhardt and
Willmann, 1967; Ehrhardt, Langhans, and Linder,
1968). It is doubtful that this discrepancy, of the order
of 100 meV, is instrumental. In fact, the “shifting” of
the peak is dramatically demonstrated in Fig. 24, due
to Burke et al., which shows a shift in the location of the
peak in the 28S cross section by almost 200 meV
between an angle of observation of 0° and 72°. Thus it is
impossible to define, without a detailed analysis, the
exact center of this resonance.

Ebrhardt and Willmann (1967) find that the
angular distribution of the scattered electrons which
have excited the 235 state around 20.45 eV (see Fig. 25)
exhibits a p-wave character, so that the designation of
this resonance as 2?P seems established.

5. Effects near the Thresholds of the 2S and 2S
Excitation Cross Section

The differential cross sections for both the 28S and the
215 states exhibit a small peak within 150 meV of
threshold. This behavior has been observed in two
independent experiments, one performed by Chamber-
lain and Heideman (1965), who analyzed the inelas-
tically scattered electrons in the forward direction, and
the other by Ehrhardt and Willmann (1967) and by
Ehrhardt, Langhans, and Linder (1968) , who observed
inelastically scattered electrons at 10-90°. The latter
experiments show that the angular dependences of the
structures near both the 2°S and the 24.5 thresholds are
isotropic, indicating an s wave. The peaks occur at
19.95 eV (140 meV above the 2°S threshold) and just
above 20.6 eV, respectively.

The results of Ehrhardt ef al. (1968) are shown in


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CODEN: NSRDAP

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observing elastically scattered electrons. These struc-
tures were confirmed by Golden and Bandel (1965) in
a Ramsauer-type experiment for both Hz and D2.
Menendez and Holt (1966) found the structure in the
excitation of the »=1 and v=2 vibrational states of
the ground electronic state, Hp(X 'Z,+), thus indicat-
ing a decay of the resonances into vibrational states.
Heideman, Kuyatt, and Chamberlain (1966) were the
first to observe the decay of these compound states into
electronically excited states of Hz by studying the en-
ergy dependence of the »=0 and »=1 vibrational
states of the B1Z,+ state of Hy. Also, it was understood
both theoretically (Eliezer e¢ al, 1967) and experi-
mentally (Kuyatt e¢ al., 1966) that more than one
compound state contributes to the observed structure,
and that the isotopes HD and Dz exhibit a set of simi-
lar structures but that they show differences in the
relative strength of the series,

Experimentally, five series of resonances have been
definitely identified, and as many as seven can be in-
voked to explain the experimental data. Comer and
Read (1971a) have suggested a classification scheme,

af 3h
E=1beV Lt Eeteev
7 eet te I
a
EG ab
Zz! weet
a 1
a oe 14
<°o 30 60 30 10 0 30 60 90 120
Zz .
fe)
53h. 3k oe
PS . E=23eV E=2heV
a
wo 2b ° 2r
3? . .
& Se eeel Seeee
= ak ab I
y
B
< 0 n 1 1 1 9 n 1 1 1
w°o 30 60 90 120 0 30 60 90 120
a
<
= 3b
27° -
s t « E=29eV E-38eV
&
2 . 2°
a . .
. .
1 ween] le .
* eee!
pL a1 1 1g poy 4
030 60 90 120 % 30 60 90 120
SCATTERING ANGLE (deg.)
Fic. 28. Angular dependence of “elastically” scattered elec-

trons at various fixed electron energies #. A common scale is used
for all curves. [From Ehrhardt and Wilimann (1967).

65

v8
i

V6,

VS

3.

V-2

DIFFERENTIAL CRQSS SECTION (ARB. UNITS)

va

is

without gas

10 2.0 3.0 40

ELECTRON ENERGY (eV)
Fie. 29. Energy dependence of the vibrational excitation in Nz
at a scattering angle of 20°. Excitation to eight vibrational states

{o=1—8) is Observed nthe region of the i, compound state
From Ehrhardt and Willmann (1967) .]

which was later adopted by Sanche and Schulz (1972),
and which is followed in the present review. We desig-
nate the different bands with the letters “a” to “g.”
Table II provides a listing of the bands and indicates
the names given to the bands by different authors,
the decay channel in which the bands were observed,
and the energy of the first feature. The table is pre-
sented to provide a “dictionary” which is helpful in
reading the original literature.

It should be noted that series “a” and ‘“d” have the
same starting energy and the same spacing. The need
for postulating two separate series with similar molec-
ular parameters is brought about by angular distribu-
tion measurements (Comer and Read, 1970). Series
“a” is of the Z-type and thus is expected to exhibit an
isotropic behavior. Weingartshofer et al. (1970) observe
structure in the B1Z, state at the positions of the
resonances in series “‘a.”” However, the angular distri-
bution in this channel of decay is not isotropic. There-
fore, Comer and Read find it necessary to postulate a
state of II symmetry around 11.40 eV. They have
considered the possibility that the observed anisotropy


40 1 1 T 7
. Exol? 4
2. v=2 J
“3.0 4
2°0 1
erg
ans
Z20b 4
ef ;
z q
Zo 4
2 ob e=50° +
BOL 4
° “Shae J

10 15 20 25 30 35 40
ELECTRON ENERGY, (eV)

Fic. 45. Energy dependence of the differential cross section
for vibrational excitation to »=2 in Ne for three angles of observa
tion. The energy range is 15 to 30 eV. The peak in the vibrational
cross section possibly indicates the existence of a high density of
overlapping compound states around 20 eV. The curves for 2=1
and 2=3 are similar to that shown. [From Pavlovic, Boness,
Herzenberg, and Schulz (1972).

problem. However, the early theoretical approaches,
although correct in principle, could not reproduce un-
ambiguously these properties (Herzenberg and Mandl,
1962; Chen, 1964; Hasted and Awan, 1969).

It was pointed out by Herzenberg (1968) that it is
essential to consider the variation of the width ' with

Tapue V. Derived properties of the 11.48-eV core-excited
Feshbach resonance in Nav."

Symmetry 23,
Parent ED,

R. (A) 1.115:£0.01
a (eV) 0.27040.02
5 (eV) 0.002320.002
r (ev) 6x10

Es (eV) 11.345

* The quantities ¢ and b are the Morse parameters of the poten-
tial curve defined so that the energy E of the vibrational level v,
with respect to the »=0 level of the ground state, is given by E=
Eo+a(v+4)—b(v+4)*. Re is the equilibrium internuclear
separation. [From Comer and Read (1971).]

internuclear separation. Such a variation is expected
from the dependence of the penetrability of the cen-
trifugal barrier with the energy of the emitted electron,
which varies with R. Without allowing for such a vari-
ation, theory cannot reproduce the simplicity and regu-
larity of the experimental results (see Fig. 32), and it
certainly cannot reproduce the simple shift in peaks
shown in Fig. 31.

Birtwistle and Herzenberg (1971) used a variable T
in their theory and obtained excellent agreement with
experiment, as shown in Fig. 33.

| |
v=2 | | |
| | | Fic. 46. Combined angular and energy
dependence of the differential cross sec-
i i
| Wj j tion for vibrational excitation to »=2 in
Bi 1. 20 Nz. The energy dependence of the process
= nS 4 AAA observed depends on the angle of ob-
SS 28/1079 Zo servation. The complexity of the curves
we WY, makes it probable that a superposition of
~o4 OX ho many compound states is involved.
Zz” [Erom Pavlovic, Boness, Herzenberg,
5 20 | ho D> and Schulz (1972).]
x Y/ ev
Se
e
5 12 V fro &
Z VW, EF
Zz 0.8) | 1 > ‘80 e
% >
£ 0.4) | J 4 90
a

1% 20 22 24 «26 28
ELECTRON ENERGY (eV)

76


H Theory: H Experiment
1 3 1 3 1 H”
13.0K s Ss P P D
>
o
s tf
Fic. 9. Energy level dia- 3
for compound states —— 1235
in atomic hydrogen, con- =g n=3 12.23
structed from the results of c 12.037 12.048 1216
theory and experiment. The 212.0;-- — nas —— 206
theoretical values are taken ° — nsig_ |——— nao
from Burke (1968). Values (5 1733 n764 SN 77
below then =2 level are also — hes (!
listed in Appendix I =x 5 ('s)
(marked ccc) in comparison o r
with other results. The >
experimental values listed  _§
in the figure are those of  &
Sanche and Burrow (1972) TOF
for the lowest three reso- a .
nances and of McGowan 2
et al. (1965, 1969) for the >
remainder. iG SHAPE RES. (7,)2 10.65 (9)
+ 10.45
a2 Woi7e_ 10.202 10.222 10200, 4 125 10.29 (hy
7015 10177. 10.190 101
10.0- 350 28 ('D)
974 3
956 —— 9.738 (3p)
q —— 9.558 ('s)
Energy Levels of HTM

2P states of hydrogen produces, at large distances, an
r~ potential. This potential is sufficiently attractive to
support an infinite number of bound states (5, P, D)
in the absence of coupling to the ground state of
hydrogen.

The state marked (2p)? in Fig. 9 is a *P state, but
with even parity whereas all the other states in the ®P
column are of odd parity. If LS coupling is a good
approximation, the (2p)? state does not participate in
elastic scattering, nor does it decay to the ground state.
The value quoted for the (2p)? state has been calculated
by Drake (1970) by Holgien (1960).

Just above the n=2 state of hydrogen, Taylor and
Burke (1967) find a core-excited shape resonance !P.
Using a three-state plus twenty correlation term
approximation, the energy is found to be 10.22204 eV
and the width '=0.0151 eV. This width is unusually
narrow for a shape resonance. As is common for shape
resonances, the mechanism for the 'P resonance is
provided by the angular momentum barrier, together
with the short-range nuclear attraction. Because the
resonance lies so close to the n=2 state, the barrier is
very thick, and the penetrability very low. As pointed
out in Sec. I, such circumstances lead to a narrow
width. The existence of such a resonance close to the
threshold of an inelastic process dominates the behavior
of the inelastic cross section near threshold.

The tabulated data of Taylor and Burke (1967)

12

show that the ‘P resonance exhibits itself by a peak in
the elastic cross section near 10.222 eV. This peak,
being only 1.3% of the elastic cross section would be
difficult to observe experimentally. Nevertheless, this
peak in the elastic cross section provides an example of
the decay of a core-excited shape resonance into the
elastic decay channel.

The six higher states of H- (near »=3) shown in
Fig. 9 are the result of a close-coupling calculation in-
volving the 1s, 2s, 2p, 3s, 3p, and 3d states (Burke
et al., 1966, 1967). The energies and the widths for these
states have been obtained by Macek and Burke (1967)
and are also discussed by Burke (1968).

A. Resonances in the Elastic Cross Section

As previously mentioned, experiments with mono-
chromatic electrons in atomic hydrogen are among the
most difficult. The first confirmation of the theoretical
considerations was the experiment of Schulz (1964a)
who found a peak in the unscattered electron current
transmitted through atomic hydrogen at an electron.
energy of 9.70+-0.15 eV. For various technical reasons,
the electron energy distribution in this early experi-
ment was insufficient to resolve the 1S and the *P
resonances. Very recently, Sanche and Burrow (1972)
succeeded in resolving these states in a transmission
experiment which uses many improvements developed


energy with series “a,” Comer and Read suggest that
the compound state is not the same since series “a”
involves a *Z,+ state. However, Black and Lane (1971)
have recently pointed out that angular distributions
are not a simple guide to the assignment of symmetries
because different rotational transitions may be domi-
nant in various decay channels. Thus Black and Lane
show that the rotational transition j=0—-j=1 domi-
nates in the process e+H,(X !2,+)—Hy-(e+C 'Il,)—>
H,(B 12,+)-+e. If such mechanisms are present, angular
distributions will have to be analyzed in more detail.

5. Band “e”

Under the heading of band “‘e” we list the measure-
ment of Weingartshofer e¢ al. (1970) who observed
inelastically scattered electrons having excited the
B'2,* state.

No (J=1->3)

ENGELHARDT et al.

i tuul

CROSS SECTION (em?)
sul

wv Luu

ELECTRON ENERGY (eV)

Fic. 37. Pure rotational excitation (J=1-3) in the region
of the*II, compound state in Nz. Shown are the theoretical results
of Oksyuk (1966) ,Burke and Sinfailam (1970), and Chen (1966b) ,
and the momentum transfer cross section of Engelhardt, Phelps,
and Risk (1964).

Comer and Read advocate such a separation because
of a discrepancy in the energy scale, but there is a good
possibility that band “e” may be the same progression
as band “c”.

6. Band “f”

Band “f” extends from approximately 13.5 to 16 eV
in Hz and from 13.5 to 14.5 eV in Ds. This band corre-
sponds to the 13.63-eV progression found by Ehrhardt
and Weingartshofer (1969) in the C "II, decay channel
of Hp. It has also been observed by Golden (1971) ina
transmission experiment using a derivative technique
similar to that of Sanche and Schulz (1972). In trans-
mission experiments, band “f” exhibits a width of about
90 meV in both H; and Dz, in good agreement with the
natural width of 80 meV estimated by Ehrdhardt et al.
(1969). The #2,+ symmetry for band “f” was assigned
by these authors.

Band “f” shows peculiar characteristics: it decays

71

transmitted current (arb. units)

L

io

_ 5 120
incident electron energy eV

Fic. 38. Transmission of electrons by Ne, showing a sharp
“window’-type resonance at 11.48-0.05 eV. ‘The zero of current
has been displaced. Additional structure occurs at 11.75 and
11.87 eV. The latter is partly due to an inelastic threshold
(£33,*). The nitrogen pressure was ~0.04 Torr. [From Heide-
man, Kuyatt, and Chamberlain (1966a).]

5 130

preferentially to identical vibrational levels of the
CM, state, ive., in the decay process the vibrational
quantum number does not change (Weingartshofer ef
aj,, 1970). This is clearly evident from Figs. 23 and
24, It is therefore likely that the potential energy curve
responsible for band “f’”? has the same shape and the
same equilibrium internuclear separation as the C "I,
or DI, states.

ne A
Ti tition
40°

FA

= ROE et tng
85°

Fae ae a ee
Wo NS 12.0 125
Collision energy

Fic. 39. Energy dependence of the differential elastic cross
section for Nz at 40° and 85°. The largest structure shown occurs
at 11.48 eV and is coincident in energy with the transmission
peak shown in Fig. 38. The designation is 22,*. The energies of
the other structures are listed in Appendix V. [From Comer and
Read (1971b).]


Intensity

Relative

Fic. 35. Total metastable cross
section for neon vs electron energy.
Curve (a) is from Pichanick and Simp-
son (1968) with 50-meV resolution;
curve (b) is the detail in the 18-19-eV
range by the same authors, with 35-
meV resolution; curve (c) is from
Olmsted et al. (1965). [From
Pichanick and Simpson (1968).

| L 1

| L }

16.0 17.0 18.0 19.0

Impact Energy (eV)

approaches confirm the above assignment. Eliezer and
Pan (1970) use the stabilization method to calculate
the position of the 2s*2p and 252? states and Nicolaides
(1972) uses a variational principle applied to the
projection method with correlation included. Both
theoretical methods give good agreement with the
energies observed experimentally (see Appendix IV)
and thus the assignment of the leading term (2s*2p
and 2s2*) for the two resonances seems well estab-
lished. In fact, Nicolaides (private communication)
finds that the 2s?2p configuration contributes 73% to
the square of the wave function of the *P resonance,
with the remainder in terms like 24? and 2s2pnd. For
the *D resonance, the leading term, 2529”, contributes
83%, with the remainder in terms such as 2s’nd and
2p'nd.

Figure 31 shows an energy level diagram in the
region 57-60 eV. The ?P and *D resonances can decay
by the emission of a single electron into various excited
states of helium. Decay into the 2°S, 24S, and 2'P
states has been studied by Simpson, Menendez, and
Mielczarek (1966) whose data are shown in Fig. 32.

The same resonances can also decay by the emission of
two electrons, yielding Het+ 2e. This type of decay has
been found by Burrow and Schulz (1969) by studying
the interference of zero-energy electrons produced in
the two-electron decay. The trapped-electron method
was used for these studies. This two-electron decay

29

20.0 21.0

also causes structure when one observes the energy
dependence of the formation of He*, as was done by
Grissom, Compton, and Garrett (1969). Quéméner,
Paquet, and Marmet (1971) have improved the sensi-
tivity for the detection of structure in positive ion
curves by several orders of magnitude. Their results
are shown in Fig. 33. An analysis of the peak shapes
yields, for the *P state, T=0.045-+0.007 eV (q=
—0.75+0.12) and, for the *D state, '=0.0254-0.010 eV
(q= —0.95+0.25). Here, T is the width of the state and
q is the “line profile index” (see Sec. I).

An unusual feature has been recently observed in the
28S excitation cross section near 50 eV by Crooks et al.
(1972). When the energy dependence of the differential
cross section for the electrons having excited the 2°5
state is examined around 90 degrees, a precipitous dip in
the cross section is observed near 50 eV. Such behavior is
reminiscent of interference phenomena, and calculations
show (Macek and Wooten, unpublished) that the
s and d waves exhibit interference. When the differen-
tial cross sections for excitation to the 2°S state are
integrated, the resulting total cross section exhibits a
peak near 50 eV, which is 15 eV wide. Crooks et al.
interpret this peak in terms of a p-wave resonance. It
therefore appears that near 50 eV in helium, there is
interference of partial waves and, in addition, a broad
resonance.

The resonance itself could be understood by con-


formed by the addition of a single 3s, electron to the
O:*(a4II,) core, thus forming “II and II Rydberg
states. These states lie at 12.50 eV (*II) and 12.24 eV
(SII), respectively, and the observed progression lies
about 0.6 eV below the ‘II state. Since a value of 0.6 eV
is a reasonable value for the electron affinity, Sanche
and Schulz (1972) consider this a further confirmation
that the *°II states of O: are the parents of band “a”.
Again, the “binding” of the two 3so, electrons to the
grandparent is about 4.4 eV.

The quantum number of each vibrational level
listed in Appendix XI is determined by fitting the
Franck-Condon probabilities of the O2 ion to those of
the O:+ ion. The zeroth level of the O:- progression
cannot be observed because its Franck-Condon
probability is small.

2, Band “b”

Another band of O;- states (band “b’’) consisting
of a progression of four vibrational members has been
observed above ionization (Sanche and Schulz, 1972)
and is listed in Appendix XI. In this case the vibrational
spacings are close to those of the b?Z- state of O*.
The #2, state which lies 0.210 eV above the zeroth
level of band “b” and constitutes the lowest Rydberg
excited state belonging to the 6 42,~ state of the positive
ion system is the suggested parent for this progression.

VII. CONCLUSIONS

In this section we summarize some of the features
discussed in the text, not by molecular species, but by
the process involved.

A. Shape Resonances

All molecules discussed in this review exhibit shape
resonances associated with the ground electronic state.
These can be understood by referring to Table VIII.
Listed are the molecular orbital configurations of the
ground state of the respective molecule; the designation
of the ground state; the lowest vacant orbital into
which the electron attaches to form the shape reso-
nance; the designation of the compound state; and the
dominant electron partial wave responsible for forming
the compound state.

The angular distribution measurements and the
widths of compound states can be understood in terms
of the partial wave which is dominant. In homonuclear
diatomic molecules, having a center of symmetry, the
allowed values of the angular momentum in the partial
wave are either all even or all odd. Therefore it is un-
likely that higher allowed partial waves, beyond those
indicated, provide a significant contribution. In
heteronuclear diatomic molecules, where there is no
center of symmetry, one has to consider mixtures of
partial waves. The dominant mixtures are indicated in
Table VIII. For those molecules for which the lifetime
of the compound state is short compared to the rotation

time (all listed molecules except Oz), the angular dis-
tribution: measurements show the behavior charac-
teristic of the partial waves indicated. In heteronuclear
molecules, the admixture of the two components must
be adjusted properly in order to obtain agreement with
the: experiments, as has been done by Read (1968)
for CO. Read (1968) has shown that “pure” partial
waves, i.e., po, pr, do, dr, and dé exhibit the charac-
teristic shapes for p waves and d waves, in the sense
that a minimum exists at 90° for the po and px waves
and a maximum exists at 90° for the do, dx, and dé
waves. However, the detailed shape is somewhat
different from that of p and d waves: the po and pr
waves do not lead to zero cross sections at 90°, and
neither do the do, dx, and dé waves show a zero near 60°.

When the lifetime of the compound state is com-
parable to or long compared to the rotational time,
then the angular distribution becomes nearly isotropic,
as is the case in Oz, and little information can be gained
from angular distribution measurements, beyond the
lifetime considerations.

The mixture of partial waves which one has to con-
sider in the case of CO and NO contains -wave com-
ponents in the partial wave. Because the p-wave com-
ponent leads to a much lower barrier than a d wave, the
decay via the -wave barrier is favored over escape via
the d-wave barrier. Although d waves may be more
important in the interior of the molecule, the p wave
may dominate the decay and thus be responsible for
the angular distribution and lifetime. These considera-
tions explain the shorter lifetimes of the compound
states in CO and NO, compared to Ne and Os.

B. Core-Excited Shape Resonances

Singly or doubly excited states of molecules also can
bind an extra electron by the centrifugal barrier, thus
forming shape resonances. The most extensive study
has been made for the case of Nz, in which the singly
excited valence states, A#Z,* and BIl,, have as-
sociated shape resonances. The progression of vibra-
tional levels of these shape resonances are often long,
exhibiting up to 18 vibrational states. These core-
excited shape resonances have properties which are very
similar to shape resonances associated with the ground
state,

Core-excited resonances consisting of a doubly
excited core plus an electron also have been postulated,
for example in Ne near 22-eV energy.

Although other molecules have not been studied in
sufficient detail, it can be expected that core-excited
shape resonances are the rule rather than the exception
and that future energy level diagrams of negative
molecular ions will show a fantastic number of com-
pound states.

It should be noted that repulsive states of molecules
also can have associated shape resonances, as is the
case in Hy.

100


Since the electrons are ejected from a moving O-
particle, the measured electron energy must be cor-
rected, and the “unshifted” energy must be determined.
The energies indicated above the peaks of Fig. 48 refer
to these corrected, “unshifted” values. Edwards ef al.
calibrate their energy scale by observing the reactions
O-+H; and O--++Ar. In the former reaction, electrons
resulting from compound states H~(1D) at 10.13 eV
and from H-(1S) and H-(3P) were observed, although
the latter two states could not be clearly resolved. In
the reaction O-+Ar, the two low-lying resonances of
Ar could be observed, and in fact the observed splitting
(173 meV) is in agreement with other experiments (see
Table II). These calibration experiments establish the
reliability of the observations in oxygen. The energy
level diagram of Fig. 49 shows schematically the con-
figuration suggested by Edwards et al. to interpret their
observations.

In order to test the results of the above experiment,
Ormonde, Smith, Torres, and Davies (1973) performed
a multi-configuration close-coupling calculation. They
calculate elastic and inelastic cross sections and
search for resonances. The *P and *D terms, which are
possible parents for resonances are retained in the
theory. A single resonance is found at 10.38 eV (0.25 eV
above the experimental value quoted above), with a
width of 20 meV. The discrepancy between theory and
experiment in the energy of the resonance is attributed
by Ormonde e¢ al. (1973) to limitations of the theory.
The assignment of the resonance given by Edwards
et al. (1971) does not appear to be altered by the results
of the theory.

A search for the higher-lying resonance (12.115 eV)
found experimentally by Edwards et al. was also under-
taken by Ormonde et al. (1973) using the close-coupling
theory. No sharp resonances were found, but a shape
resonance in the 2P° partial wave was found near 11.5
eV, with a width about 1 eV. This shape resonance is
probably in addition to the sharp structure at 12.115
eV found by Edwards et al.

Very recently, Matese, Rountree, and Henry (1973)
undertook a configuration-interaction study of doublet
resonances in atomic oxygen. They calculate the follow-
ing levels of O-:

2p*(45)353p(2P) at 9.50 eV,
2p°(?D°)3s*(?D®) at 12.05 eV,
2p (?P?)3s°(2P%) at 13.65 eV,
2p*(45°)3p?(2P%) at 10.87 eV.
A reasonable estimate of possible errors in the above-
quoted energies is +0.1 eV. Matese et al. suggest that
the 12.115-eV peak observed experimentally by

Edwards, Risley, and Geballe corresponds to the
2p*(2D°)3s*(2D°) state, thus confirming the original

36

IE fe} o
2p%(?D)3s
———" 12.539
2p3(2 2(2
9°(70)382(0) 1 15
lab
>
o
>
oO
a
us
2
Ww
We
3/4,
27°(48)30 14 749
34 2 (2)
2p>(48)3p2(7P) 1 0
10-

Fic. 49. Energy level diagram for O and O-, invoked by
Edwards et al. (1971) to interpret the data of Fig. 48. The two
states of O are considered to be parents of the compound states
(O-) indicated. Energies are given in eV. The interpretation must
be considered preliminary.

assignment for the upper state of Edwards e¢ al., as
plotted on Fig. 49.

ACKNOWLEDGMENTS

The author is very grateful to U. Fano, F. Linder, L.
J. Kieffer, C. E. Kuyatt, A. V. Phelps, and H. S.
Taylor, all of whom read portions of the manuscript and
generously supplied many comments and corrections. A
portion of this review was written at JILA, University
of Colorado, Boulder and the author is grateful for the
hospitality of the JILA staff, and for the excellent
editorial services rendered by Mrs. Lorraine Volsky
and her staff. The author also wishes to acknowledge
the support he received, at various stages, from the
Westinghouse Research Laboratories, the National
Science Foundation, the Army Research Office, and the
Office of Naval Research. To his colleagues at Yale,
particularly to A. Herzenberg, P. D. Burrow, M. J. W.
Boness, and L. Sanche go thanks for many stimulating
discussions and for help in unravelling the many effects
described in this paper. To his wife, Rose, go thanks for
her acquiescence that resonances should take precedence
over a lot of other things.


He He He
16 —
i 1 3p By
al. c'n, 'n, *s%
=
| f=
ax =
I2;—
10}—
> L (wy
3
8 a
2
BE
6K
WW
t- 10
4 9 | H+H
|g -
8 H+H
tL 6
5
eae 4
3
t- 2
1
oL_

Fic. 23. A schematic summary of the decay of five energetically distinct compound states into various decay channels. In the middle
of the figure we show the positions of bands “a” through “g,” and on the left and right we show states of Hy. The arrows point to those
decays that have been experimentally determined, but not all decay channels could be given on the figure. Band““f” seems to decay into
the C11, state without change of vibrational quantum number, and this is propertly recorded on the figure. Band “‘b” seems to decay
only into high vibrational states of the X 12,* ground state. Decay into H-+HTM (dissociative attachment) is also indicated.

energy the cross section becomes very large due to
Langevin spiralling arising from long-range polariza-
tion (Herzenberg, 1967); the compound state is essen-
tial for an understanding of the process; the Hz produced
in the reaction is highly excited (Herzenberg, 1967;
Chen and Peacher, 1968b) and an inverted population
may result.

Experimentally, the reaction H-++-H—H?+¢ has not
yet been studied using ion beams because of the diffi-
culties associated with this type of experiment. How-
ever, similar reactions

(e.g., O-+CO>CO-CO2+e;
O-+H:—>H,0-—H,0+e)

have been studied both in swarm experiments (see,
e.g., Ferguson, 1968, Moruzzi et al., 1968) and in beam
experiments (Mauer and Schulz, 1973). In both these

61

reactions, a compound state is involved. In the case of
CO; the state is *M, (Claydon, Segal, and Taylor,
1970; Krauss and Neumann, 1972), and in the case of
H,-, the state is *2,+ and has been previously discussed.
The CO;-(7II,) state has a lifetime which is somewhat
longer (Burrow and Sanche, 1972, give a width,
T=0.13-0.26 eV) than the compound state in H2
(T~1 eV).

The experiments of Mauer and Schulz (1972) show
that at very low energies, the cross section is given by
a 1/v functional form, where » is the relative velocity.
Thus polarization dominates, consistent with previous
swarm experiments (Moruzzi ef a/., 1968; Ferguson,
1970), Because Mauer and Schulz used a beam experi-
ment, they could extend the range of incident ion
energies; they find that at higher energies (e.g., 1.5 eV
in the center of mass for the reaction O-+CO) the
cross section rises and exhibits a maximum, as shown


1000h . 200
800
H +150
Fic. 43. Total cross section for scatter- i
ing of electrons by sodium. Full curve— “go H
theory of Moores and Norcross (1972);  @ 600 1
X—experiment of Brode (1928) divided r \ . 3
by two; O-—experiment of erel, -
Englander, and Bederson (1962) nor. © Z #100
malized to theory at 5 eV. [From Moores i
and Norcross (1972).] 400 H
i
1
! 50
200 \
H
H
i N \ Nl
° 1 2 3 4 5

periments (Andrick and Ehrhardt, 1966). The informa-
tion in these rare gases is more limited than in the case
of He, since information on the excitation of elec-
tronically excited states of these gases is only now
becoming available (Swanson ef al., 1971, 1973).
Optical experiments with a good energy resolution in the
electron beam are also very sparse [Sharpton ef al,
(1970) observe a sharp structure in photon emission at
18.6 eV in neon.]

Figures 34-36 show the experimental evidence for
resonances in neon, and Fig. 37 shows an energy level
diagram of Ne with the resonances included. Appendix
V gives a comparison between the available experi-
ments in tabulated form. A clearcut assignment of the
higher-lying compound states is not yet available. The
characteristics of Ar, Kr, and Xe are similar to those of
neon. Energy level diagrams are shown in Figs. 38-40
and the energy values are listed in Appendixes VI~
VIII.

B. Resonances above the Ionization Potential

Above the ionization potential of Ne, Ar, Kr, and Xe,
a number of features have been detected, some of which
are undoubtedly resonances associated with singly
excited states of the neutral atom. The energy range
of these features spans the regions 42-50 eV in Ne,
24-32 eV in Ar, 22-27 eV in Kr, and 18-20 eV in Xe.
These features are discussed in connection with the
transmission experiment by Sanche and Schulz (1972),
in connection with the trapped-electron method by
Grissom, Garrett, and Compton (1969), and in con-
nection with positive ion detection by Bolduc, Qué-
méner, and Marmet (1972). The reader is referred to
these papers for an up-to-date discussion and for a list
of previous references. One of the difficulties inherent

32

E, ev

in these studies lies in distinguishing between reso-
nances and the onset of highly excited autoionizing
states of the neutral atom. Thus one has to rely heavily
on measurements of the structure in the photoionization
continuum, which provides the location of optically
allowed transitions to highly excited states (see, e.g.,
Ederer, 1971). Some of the energies at which resonances
are believed to occur in Ne and Ar are listed in Ap-
pendix IX.

V. LITHIUM AND SODIUM

Electron scattering in alkali atoms has been of
considerable interest in the past years (Bederson
and Kieffer, 1971), but high-resolution experiments
with monochromatic electron beams have only recently
become available. Thus much of our knowledge re-
garding resonances in these atoms comes from theory.
There is general agreement that at low energies (~0.15
eV) the spin exchange cross section in both Li and Na
has a sharp rise (Karule, 1965; Burke and Taylor,
1969; Norcross, 1971; Moores and Norcross, 1972).
This sharp rise is attributed to the existence of a *P
compound state at about 0.15 eV. The width of this
resonance is believed to be relatively large (>0.1 eV).
The *P resonance also affects the phase shift of the
elastic cross section (Moores and Norcross, 1972).
The elastic cross section calculated from these phase
shifts agrees with the cross section measured by Rubin
et al. (unpublished).

In the vicinity of the (1s°2p)*P state of lithium, two
resonances, 1D and 'P, are postulated (Burke and
Taylor, 1969). For reasons which are not entirely clear,
Fung and Matese (1972) do not find these states using
their multiconfiguration Hartree-Fock method; possibly
the width of these states is too large. However Fung and


30

=~ PY YD
BON 8 OD

TOTAL SCATTERING CROSS SECTION (A2)
a

rtitotitivistititititils
10 18 26 3A 42
ELECTRON ENERGY (eV)

5,0

Fic. 26. The absolute total cross section for scattering of
electrons on Ne, as obtained using a modified Ramsauer technique.
‘The total cross section includes elastic and inelastic components.
The structure above 1.8 eV is indicative of the pseudovibrations
of the *1, compound state. The structure below 1.8 eV has not
been substantiated by other experiments, although attempts at
confirming it have been made. The structure below 1.8 eV must
beconsidered in doubt at the present time. [From Golden (1966)..]

et al, (1965). These results are shown in Fig. 15. Similar
considerations as those discussed in Sec. IIA4 also
apply here. In fact, Bardsley, Herzenberg, and Mandl
(1966b) have obtained a good theoretical fit to the
curves of Fig. 15, and they point out that decay of the
2y,+ state of H;- to the *2,* excited state is more prob-
able than decay to the ground state. The overlap is
more favorable when the compound state can decay
into its parent (*Z,+) state. This may explain why
it has not been possible to detect the decay of the
Hy-(*2,+) state to the ground electronic state. The
total width of the *2,+ state is estimated to be '=0.8
eV and the entry width from the ground electronic
state is 0.004 eV.

The potential energy curves for the *Z,,*+ and the *2,+
states, derived by Bardsley ef al. (19662) and by Chen
and Peacher (19682), have already been discussed in
connection with Fig. 6. Also shown are the imaginary
parts of the potential curves, i.e, the width T, as a
function of internuclear separation. The potential en-
ergy curves of Eliezer ef al. (1967) are shown in
Fig. 25(b).

The H- formation via the *2,+ state extends well

64

into the 11-12 eV region, in which a multitude of reso-
nances are observed in elastic and inelastic scattering
(see Sec. IIC). It is therefore not surprising that high-
resolution experiments on negative ion formation would
show structure in the 11-12 eV region. The decay of
bound compound states into the dissociative attach-
ment channel was observed by Dowell and Sharp
(1968) and is shown in Fig. 16. The mechanisms for
this coupling have been discussed by Eliezer et al.
(1967) in terms of a radiationless intramolecular tran-
sition.

The structure shown in Fig. 16 is further discussed
in Sec. IIC,

C. Core-Excited Resonances in the 11~15 eV Region

Resonances of the core-excited (Feshbach) type in
Hz were discovered by Kuyatt, Mielczarek, and Simp-
son (1964) in the energy range 11.62 to 13.31 eV by

DIFFERENTIAL CROSS SECTION (ARB. UNITS)

without gas

1 n >
29 v 0
ELECTRON ENERGY (eV)

rn
10

Fic. 27. Energy dependence of the “elastic” cross section in
Ne at various angles of observations. The experiment uses an
electrostatic monochromator and an electrostatic analyzer, which
accepts only “elastically” scattered electrons. Since the resolution
is not sufficiently good to resolve rotational states, all rotational
transitions are included in the measurement. [From Ehrhardt
and Willmann (1967).]


C. Binding of Rydberg Resonances

A recurrent theme throughout this review is the
observation that most core-excited Feshbach resonances
are associated with Rydberg excited states of the
molecule. These states can be considered as being
formed by the attachment of two electrons in Rydberg
orbitals to the positive ion core, which we call the
“grandparent.” The lowest configuration that is possible
contains the positive ion core plus two 3se, electrons.
Table X lists the “binding energy” of these two elec-
trons to the various positive ion cores of Hz, NO, CO,
Na, and O2. The “binding energy” is determined by
taking the difference between the energy of a particular
state of the positive ion and the experimentally ob-
served energy of a particular resonance which we
associate with this positive ion core. The association
between the positive ion core and the resonance comes
from a comparison of the vibrational spacings and
Franck~Condon factors. The data used for constructing
Table X are taken from Sanche and Schulz (1972) and
are fully discussed in the body of this review.

It is obvious from Table X that all the molecules
listed have binding energies for the two 3sc, electrons
of about 4 eV.

Taste X. “Binding” energy of two 3sc, electrons to

grandparents.
Positive ion Associated
resonance “Binding”
Energy Energy —_—energy
Molecule State ev ev ev
H XW,t 15.42 11.32 41
N Xt 15.51 11.48 4.03
Aly 16.62 12.64 3.98
co x°mt 14.1 10.04 44
Am 16.6 13.95 se
NO x1nt 9.27 5.04 4,23
on 16.56 12.36 4.20
AM 18.32 14.19 4.23
BAL 21.72 17.51 4.21
O xX", 12.06 8.04 4.02
aly 16.10 11.698 4.4
bE" 18.16 14.27% 3.9

* The level »=0is not observed. The value given is an extrapola-
tion.
» The assignment as »=0 is uncertain.

D. Thresholds of Inelastic Cross Sections

It is pointed out in Sec. IIIB2 that the threshold
behavior of inelastic cross sections is often dominated
by nearby resonances. Both core-excited shape reso-
nances (which lie above the electronic state) and
Feshbach resonances (which lie below their parent)
are important. Sometimes, the influence of these two
types of resonances can be distinguished and energy
ranges can be specified which are dominated by the
influence of one or the other resonance. This is the case
for the 2S excitation function of helium. In other
cases, the threshold is dominated only by a nearby
shape resonance (E*X,+ state in Ne). In still other
cases the threshold behavior is dominated by a Fesh-
bach resonance lying below the respective excited state
(5 *2* state in CO). The.width of the Feshbach reso-
nance appears to be a dominant factor.

ACKNOWLEDGMENTS

The author is indebted to many people and to many
agencies who made possible his participation, over the
past eighteen years, in the exciting developments
partially described in this report. Support for this work
came at various stages from the Westinghouse Research
Laboratories (1954-1966), from the National Science
Foundation, the Defense Atomic Support Agency, the
Advanced Research Projects Agency, and the Army
Research Office, Durham. To these agencies go the
thanks of the author for providing the funds which
enabled him and his colleagues to participate in the
progress of this field. Needless to say, many other
advances, not reported in this survey, resulted from the
above-mentioned support.

The scientists from whom the author learned about
atomic collision processes along the way include U.
Fano, E. Gerjuoy, A. Herzenberg, A. V. Phelps, H. S.
Taylor, and many others.

The author received comments, suggestions, and
corrections from J. Comer, U. Fano, E. Ferguson,
F. Linder, C. Kuyatt, C. Lineberger, P. D. Burrow, A.
Herzenberg, A. V. Phelps, H. S. Taylor, and M. J. W.
Boness and wishes to express his thanks to them for
reading portions of the manuscript.

A portion of this review was written while the author
enjoyed the hospitality of JILA and special thanks go to
L. J. Kieffer for his interest in this review, for carefully
reading the whole manuscript, and for suggesting many
changes and corrections. Mrs. L. H. Volsky of JILA
and Mrs. M. R. Harrison of Yale provided editorial as-
sistance. Lastly, the author is greatly indebted to his
wive, Rose, whoselflessly tended to the problems of life,
the family, and the home, and gave up a great many
things for the cause of science.

101


Appendix VIIJ—Continued

Optical excitation experiments* (Kisker, 1972c)

4624 A 4671 & 4079 & 4583 A 4734.8
11.02-11.05
11.12-11.15 11.11- 11.16-11.20
11.22-11.31 11.27
11.40-11.46 11.39-11.45
11.53-11.58 11.51-11.55
11.61-11.65
11.83-11.90 11. 75-11.87 11.81-11.95
12.03-12.09 12.03-12.10
12.13-12.23 12.19-12.28 12,20-12.27 12.20

* In this table, the first energy corresponds to an observed maximum, the second energy value on the same line
corresponds to an observed minimum.

APPENDIX Ix

Suggested resonances in Ne and Ar.

Energy
eV Method Observer Designation

Neon

41.98 Transmission. Sanche and Schulz (1972)

42.1 Trapped electrons Grissom et al. (1969)

43.05 Transmission Sanche and Schulz (1972)

44.35 Transmission Sanche and Schulz (1972)

44.25 Trapped electrons Grissom et al. (1969)

47.6 Transmission Sanche and Schulz (1972)

47.57 Trapped electrons Grissom et al. (1969)
Argon

24.44 Art Bolduc et al. (1972) 3s3p%4s? 2S

24.53 Transmission Sanche and Schulz (1972)

26.87 Transmission Sanche and Schulz (1972)

27.91 Transmission Sanche and Schulz (1972)

28.9 Transmission Sanche and Schulz (1972)

42


resonance 5 lies at 12.64 eV, only 20 meV above the
estimated position (Sanche and Schulz, 1972). The
parent of these structures can be the F "IL, state lying
at 12.75 eV. This state has a *II,, core with an extra
3se, electron attached. Mazeau et al. (1972b) suggest
that the G(*Il,) state at 12.8 eV could be admixed,

Structures 5 and 6 are also replicated in the differen-
tial cross section of the E*Z,+ (v=0) state and these
structures appear at 12.54 and 12.78 eV, respectively,
as shown in Fig. 44(B) and in Appendix IV. Structures
5 and 6 are not visible in the E*Z,* (v=1) decay
channel.

4. Bands “c” and “d”

Two short bands (“c” and “d”) in the 13-15 eV
energy range are shown in Fig. 42. They start at 13.00
and 13.88+:0.05, respectively. Here the overlap be-
tween the different resonances makes an accurate read-
ing of the spacing between the vibrational members of
each band difficult. Nevertheless, the average spacing
of 230-5 meV for band “c” and 2255 meV for band
“d” lies close to the value of 228 meV for the corre-
sponding average spacings of the vibrational levels of
the A *II, state of N;*+ which is the suggested grand-
parent for the two bands. Mazeau et al. (1972b) suggest
that the parent of band “‘c” is the state H which they
have recently discovered. The state H is a triplet, and
its v=0 level lies at 13.15+0.01 eV. The spacing of the
two lowest vibrational levels is 240 meV.

The band “‘c’” has been observed in the decay chan-
nels E#Z,+ (v=0, v= 1), a” 12,+ (v=0), and also CII,
by Mazeau et al. (1972b). The energies of bands ‘“‘c”
and “d” are listed in Appendix IV.

C. Bands “a” and “a’”: Core-Excited
Shape Resonances

At lower energies (7-11 eV) other structures are
visible in the total scattering cross section of N2. These
structures are clearly seen in derivative transmission
spectra for N2 shown in Fig. 43. The progression of
dips between 7 and 9 eV in the transmission spectrum
is interpreted predominantly as the excitation of vibra-
tional levels of the B*II, valence state of Nz and indi-
cates that the cross section for excitation of the B
state rises sharply at threshold. This finding confirms
similar conclusions derived from studies using the
trapped-electron method (Brongersma and Oosterhoff,
1969, 1967; Hall et al., 1970).

The next structures (band “a” in Fig. 43) form a
very well-developed progression of 18 vibrational levels
which extends from 9 to 11 eV. The energy of each
structure and the corresponding spacings are given in
Appendix V. When one attempts to correlate the ener-
gies of this progression with vibrational energy levels
of the known states in this energy region, namely the
By, a2, a, and WA, valence excited
states, it is found that none of these states nor any

84

combination of them could reproduce the spacing of
band “‘a” (Sanche and Schulz, 1972).

Structures at the same energies as band “a” have
also been observed, superimposed on a continuum, in
the excitation function to various vibrational states
(v=1—5) of the B ‘II, valence state of nitrogen. This
is shown in Fig, 44D,

We are dealing here with a vibrational progression
of core-excited shape resonances, similar to those exist-
ing near 2.3 eV in Na, ie., the "II, state of No-. Many
of the features of band “a”, when ‘observed in the
decay into the B*II, parent state are reminiscent of
the features already discussed in connection with the
2.3-eV shape resonance in Ng. The position on the en-
ergy scale of the peaks observed in different vibrational
decay channels of the B*II, state shift. This can be
clearly seen in Fig 44D and in Appendix V, where
the energy values are tabulated. The shifting of the
peaks is reminiscent of a similar effect already dis-
cussed in connection with the 2.3-eV shape resonance
in nitrogen (see Figs. 31 and 33), and the Boomerang
model (Fig. 34) developed by Herzenberg (1968) and
by Birtwistle and Herzenberg (1971). A band similar
to band “a” is also associated with the A *2,*+ state,
as evidenced by the structure in the cross section to
various vibrational states of the A *Z,,* final state, in
the energy range 8.22-9.57 eV (Fig. 44E). As in the
case of band “a”, the locations of the peaks shift on
the energy scale. The parent of this band is the 4 *2,*+
state. Appendix V gives the energies of the structures,
as observed in the v=2-6 states of the A *Z,* elec-
tronic state.

The energy level diagram, Fig. 44F, indicates sche-
matically some of the decay channels. The core-excited
shape resonance associated with the A *Z,+ state is
marked ‘“‘a’”,

D. Resonances above the Ionization Potential in No

Pavlovic et al, (1972) have observed vibrational ex-
citation for the levels v=1, 2, 3 in Ne in the energy
range 20-24 eV. They also observed the angular dis-
tribution of electrons having excited these states and
found that the angular distribution depends strongly on
the incident energy, and in fact the shape of the energy
dependence depends on the angle of observation. These
anomalies in the angular distribution, coupled with the
large size of the observed cross section, led Pavlovic
et al. to prefer an interpretation in terms of resonances
associated with doubly excited states of the nitrogen
molecule rather than singly excited Rydberg states.
Further experimental work will, however, be needed
before this model is reliably proved.

Resonances associated with doubly excited states of
atoms (e.g., 2s°2p in the case of He) are well known.
In the case of small systems such as helium, one expects
these resonances to be spaced well apart compared to
their width, whereas in systems with more electrons
(e.g., Ne) there is the possibility of many doubly ex-


ELECTRON
MONOCHROMATOR

COLLISION
CHAMBER

3—

MEASURED
CROSS SECTION

Y

[> ELASTIC

}—> visraTionaL

[> _ ELECTRONIC

ELECTRON ENERGY

8 LOSS ANALYZER

TRANSMISSION = [-——> TOTAL

TRAPPED
ELECTRONS [> INELASTIC
‘METASTABLE

DETECTOR f—> “METASTABLE
PHOTONS > opricat
mass F—> POSITIVE ION
‘SPECTROMETER

[—> NEGATIVE ION

Fic. 3. Schematic overview of experiments which are useful for the study of resonances in atoms and molecules.

coaxial cylindrical “mirror” configurations, the 127°
cylindrical electrostatic, and the 180° concentric
spherical configurations. For production of very slow
(<1 eV) monochromatic electrons, one can use the
time-of-flight spectrometer. Monochromatic electrons
can also be produced by ionization, using monochro-
matic photons. Electron monochromators can also be
used in series to further improve the energy resolution.
It appears that, at the present time, the most widely
used monochromators for experiments in which a
magnetically field-free region is desired are the 127°
cylindrical and 180° concentric electrostatic configura-
tions.

When an axial magnetic field is desired, one can use
the retarding-potential difference method. The
retarding-potential-difference method relies on the
chopping of the electron distribution and thus is not a
true monochromator. Although important advances
have been made by use of this method, it has been made
obsolete by the trochoidal monochromator. Also note-
worthy are the 180° magnetic selector and the crossed
electric and magnetic selector (Wien filter).

Figure 3 gives an overview of the experiments which
are used for the measurement of resonances. The elec-
tron monochromator and the collision chamber are
common to all experimental arrangements. The detec-
tion methods, however, differ widely, and are listed in
Fig. 3. Below we discuss the various methods in slightly
more detail, without giving credit to the inventors and

users of the methods. Such credit would only duplicate
the much more detailed credit given in the subsequent
chapters (and in the following paper) when the actual
accomplishments are discussed.

Differential Cross Section Measurements using
Electrostatic Monochromators and Analyzers

A typical arrangement used for the measurement of
structure in the differential elastic or inelastic cross
section is shown in Fig. 4. This type of apparatus is
typical of many instruments used in various labora-
tories to obtain the results discussed in subsequent
sections. It is capable of measuring differential elastic
or inelastic cross sections and usually it is possible to
alter the angle between the monochromator and the
analyzer, so that angular distributions of the scattered
electrons can be obtained.

Electrons emitted from the filament are focussed,
using electrostatic lenses (1-6) on a hole in plate 7,
which serves as the input aperture for the mono-
chromator. The monochromator itself may consist either
of coaxial cylinders (127°) or concentric hemispheres
(180°). Either of these devices should give an energy
distribution with a full width at half-maximum of
0.02-0.06 eV. The electrons are focussed onto a molecu-
lar beam by the three-element lens system (10, 11, 12).
Electrons scattered from the molecular beam pass
through the electron optics of the analyzer, through the
analyzer proper, and finally impinge on a multiplier and


Contents

Page
Foreword 2.0.00... cece cee eee cece eee eee eee eee e eee e et eneeees iii
Preface 6... eee eee ne en eee nen n eben tenn tenes iv
Resonances in Electron Impact on Atoms
George J. Schulz....... 60.0.0. e cece eect een eet eee ene 1
Resonances in Electron Impact on Diatomic Molecules
George J. Schulz. .... 0.0.6. c cece cece eee nee eee nent e eens 47


APPENDIX Ula

Larger structures in the optical excitation functions of He.

Preliminary data.
Wavelength Wavelength
Energy of observation. Possible Energy of observation Possible
eV (A) Ref. designation eV (A) Ref. designation
22.96 7065 (a) 45 4713 (c)
23.12 7065 (a) 24.0 4472 (a)
23.25 7065 (a) 4922 (a)
23.31 7065 (a) 3188 (b)
23.47-23 .62 3889 (b) 2P(?) 24.08 5047 (a)
23.41 5876 (a) 4713 (a)
23.50 5876 Transition  3°S-28P 3°D-28P 4°D-2P 4\D-21P
23.86 5876 (a) Wavelength 7065 5876 4472 4922
4472 (a) (B)
4922 (a)
23.94 5876 (a) Transition 4'S-21P 48$-23P | 3*P-2S 48P-285
4472 (a) 3S Wavelength 5047 4713 3889 3188
5047 (c) (A)

= Kurepa and Heddle (1972).
» Kisker (1972b).
¢ Heddle, Keesing, and Kurepa (1973).

The data have been arbitrarily selected by the author
to indicate the main peaks observed in optical spectra.
Many more, smaller structures have been reported. This
table must therefore be considered preliminary, subject

to change. This does not apply to the structures for
which the wavelength is underlined. These are large and
well-defined. The structure for which the wavelength is
doubly underlined is “enormous”.

APPENDIX IV

Position of resonances above the ionization potential in He.

Authors (22p)2P—(2s2p2)2D Authors (2s°2p)2P — (282*)*D
Experiments Quéméner ef al. (1971) 57.1520.04 58.2320.04
Kuyatt et al. (1965) 57.1%0.1  58.240.1 Grissom ef al. (1969) 57.21 58.31
Golden and Zecca (1970) 56.7/56.93 57.87/58.08 Theories
Eliezer and Pan (1970) 57.3 58.3
Burrow and Schulz 56.9340.1 58.04:0.1 (stabilization)
1969
(1909) Nicolaides (1972) 57.3 58.4
Sanche and Schulz 57.1640.05 58.25+0.05 (projection and cor-
(1972) relation)

39


x1o"'8

110
10.0
90
80
70
6.0
5.0
40
3.0
2.0
10
0.0

2

ENGELHARDT
PHELPS &
RISK

Cross Section, cm

20

05 10 is
Electron Energy, eV

Fie. 35. Excitation function for v=1 in Nz near threshold.
Shown are the results of Engelhardt, Phelps, and Risk (1964)
obtained from an analysis of swarm experiments, the double
electrostatic analyzer measurements of Schulz (1964), and the

slope near threshold obtained using the trapped- electron method
(TEM) by Burrow and Schulz (1969). The low-energy portion
of the theoretical cross section (Chen, 1964a) is identical to that
of Engelhardt, Phelps, and Risk below 1.2 eV. [From Burrow and
Schulz (1969).]

25

for band “b” and suggested that the new resonance
has the configuration (o,1s)(ou1s)?*2,+, representing
an electron bound to the B1Z,* excited state of Hy.
This band has not been observed in any transmission
experiment. The assignment is still in doubt, especially
since the potential energy curve for the (a,1s)(ouls)?
compound state should have a larger equilibrium inter-
nuclear separation than the parent B'Z,* state (H. S.
Taylor, private communication). In order to interpret
their experiment, Comer and Read (1971a) must as-
sign a smaller equilibrium internuclear separation to
the (o,1s)(c,1s)? state compared to the parent B1Z,+
state, as shown in Fig. 25(a).

3. Band “c”

Band “c” has been observed in the transmission ex-
periments of Kuyatt et al. (1966) and of Sanche and
Schulz (1972) in both H; and D2. In their early work,
Comer and Read (1971a) observed band “c” only in
De and not in Hy. They assign to band “‘c” the con-
figuration (c,1s) (742p)(o,2s)?II,. Recently, however,
Joyez, Comer, and Read (1973) were able to observe
band “c’” in a high resolution experiment in Hy. Their
value for the width is ['<16 meV and the starting
energy is about 11.19 eV, with subsequent values
at 11.50, 11.80, and 12.07 eV. If the starting value of
11.19 for band “c” is substantiated, then the quantum.
numbers for band “c” as assigned by the other investi-

70

gators listed in Appendix I will have to be incremented
by unity.

As pointed out previously, band “c”
in vacuum uv emission.

The calculated progression of Eliezer e¢ al. (1967)
for the configuration *2,+(og1s)(.2p)(wu2p’) agrees
well with most of the experimental energy positions, as
shown in Appendix I. However, there is a problem in
understanding the angular dependences found by Comer
et al.

The detailed understanding of bands “‘c” and “‘e” is
still missing and the above considerations must be con-
sidered as preliminary.

appears strongly

4. Band “‘d”

This band was postulated by Comer and Read (1971a)
froth an analysis of the results of Weingartshofer e¢ al.
(1970). On the basis of the angular distribution of elec-
trons observed by Weingartshofer e¢ al, in the B1Z,
exit channel, Comer and Read suggest that the com-
pound state involved must have “II, symmetry. Al-
though the results of Weingartshofer are coincident in

.
BE
re . Vs3
50- E=2)ev
r00or * vet .
Fa EBev 25 te ee Pe]
Z 75+
. . 0
2 0 30 60 90 120
< 50+ oy
.
z . ]
oo ve 30F v=3
5 ° E=a1ev
Pd .
mob 2 4 20
g"o 30 60 90 120 o Lote
9 fee
& rob
2
<
=
gior* °9 30 60 90 120
4 vet
z E=28eV
© ask
= 75 75f
. Vs5
sor 50 E=22ev
.
L Loe
25 25| ogee te]
0 a a ee oe oe
0 30 6 90 12 0 30 6 90 12

SCATTERING ANGLE (deg)

£16. 36. Angular dependence of the cross section for vibra-
tional excitation to »=1, 3, and 5 in Nz. The electron energy is
indicated. The subsidiary ‘peaks near 90° result_from d-wave
scattering. [From Ehrhardt and Willman (1967).]


T T T T T
x RAPP & BRIGLIA
~~ CHANTRY
=Stamatovic& +

Schulz

Arb. Units

Fic. 53. Formation of O- from CO by
dissociative attachment. Shown are the
curves of Stamatovie and Schulz 1970
(points) and their calibration against the
onset of Xe*. Also shown are the results
of Chantry (1968) by the dashed line
and of Rapp and Briglia (1965) by the
crosses. The structure near 10 eV on the
curve by Stamatovic and Schulz is caused
by the #2* resonance existing at 10.04 eV.
{From Stamatovic and Schulz (1970).]

lon Current,

11.00 12.00 13.00
Electron Energy, eV
1
TT TTT
co @=20°

cross section in CO. The
exit channels are the v=0
and 2=1 vibrational states
of the ground electronic
state. The positions of the
resonances are listed in Ap-
pendix VI. [From Comer
and Read (1971c).] (b)
Energy dependence of the
elastic cross section in the
vicinity of the *D* res-
onance at 10.04 eV at di
ferent angles of observat
The shape is characteristic
of an s-wave resonance.
[From Pavlovic (to be pub-
lished).]

Fic. 54. (a) Energy de- : Maat 2.5%]
pendence of the differential :

Differential cross section

y Scattered Current, (Arb. Units)

bonsai tiviat biiisit
10.0 10.5 110 1S 9.6 10.0 104
Collision energy (eV) Electron Energy, eV

(a) (b)

ro oe oo or eet

79


Resonances in Electron Impact on
Atoms and Diatomic Molecules

George J. Schulz

Department of Engineering and Applied Science
Yale University
New Haven, Connecticut 06520

Reprinted from
Reviews of Modern Physics
Vol. 45, No. 3, pp. 378-486, July 1973

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary
NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued October 1973


APPENDIX V—Continued

Energies of shape resonances connected with the A *Z,* state.
A *%,* decay channel (Mazeau et al., 1972c)4

v=2 3 4 5 6

8.225 (15)
8.315 (15) 8.307 (10)
8.415 (10) 8.415 (10) 8.395 (10)
8.515 (10) 8.522 (10) 8.503 (5)
8.610 (10) 8.620 (10) 8.595 (5) 8.603 (5) 8.553 (5)
8.705 (10) 8.715 (5) 8.690 (15) 8.698 (5) 8.653 (10)
8.800 (10) 8.800 (10) 8.778 (15) 8.785 (5) 8.745 (10)
8.880 (5) 8.878 (15) 8.870 (5) 8.837 (10)
8.960 (10) 8.950 (15) 8.958 (5) 8.925 (5)
9.040 (5) 9.030 (15) 9.040 (5) 9.008 (5)
9.120 (10) 9.110 (15) 9.115 (5) 9.088 (5)
9.195 (10) 9.178 (15) 9.183 (10) 9.168 (5)
9.263 (10) 9.245 (15) 9.250 (5) 9.238 (5)
9.312 (15) 9.315 (5) 9.300 (5)
9.375 (15) 9.373 (5) 9.358 (5)
9.428 (15) 9.430 (10) 9.418 (5)
9.480 (10) 9.482 (10) 9.468 (5)
9.538 (10) 9.515 (5)
9.575 (10) 9.562 (10)

* Absolute error of the energy is +0.05 eV. Relative error +0.003 eV.
> The spacings are given to the nearest 5 meV.

¢ Error approximately +10 meV (see Mazeau et al., 1972c).

4In parentheses are given the probable errors, in meV.

APPENDIX VI
Energies of features in CO (10-15 eV).

Differential
Comer and Read
Transmission (1971c) Mazeau et al.
Feature Sanche and Schula —-—-————————__ (1972a)
number (1972) v=1 v=2 b3E+,v=0* Designation
1-1’ 9.98-10.04 10.02 10.02 10.04> 2zt v=0
2-2’ 10.24-10.29 10.28 v=1
3 10.42 10.38 10.46
44/ 10.65-10.72 10.80 10.7 "11
5 11.27 11.3
6 12.17 12.2
Band “a” 13.95
14.155
14.345
14.530
14.705
14.870

* The threshold for the 6 *E+ state is 10.39 eV.
> Determined from elastic scattering at 90°. The calibration is performed against the (152s*)*S resonance in
helium which the authors locate at 19.350.02 eV. [Sanche and Schulz find 19.34+0.02 eV.]

105


Preface

The publication philosophy of the National Standard Reference Data System recognizes that
data compilations will be most useful if all available channels of publishing and disseminating the
information are employed. Selection of a specific channel—Government Printing Office, a scientific
journal, or a commercial publishing house—is determined by the circumstances for the individual
document concerned. The goal is to reach all of the appropriate audience most readily at minimum
expense.

The two compilations which follow were first published in Reviews of Modern Physics. Since they
represent a substantial collection of reference data, it appeared desirable to make them available in a
form suitable for distribution to interested users of this type of information. With the generous per-
mission of the editors of Reviews of Modern Physics, and the approval of the author, the Office
of Standard Reference Data has undertaken to reprint the articles as a part of the National Standard
Reference Data System-National Bureau of Standards series.


APPENDIX VII

Comparison of vibrational spacings and Franck-Condon probabilities observed for four bands of NO~ with
appropriate values for NO+(X 12+) Sanche and Schulz (1972).

Vibrational spacings (meV)

NO- band* NOt(X 13+)
Av “a” “b? “o? “aq”? Experimental Theoretical
O-1 286 290 292 282 290
1-2 286 290 288 284 287
2-3 282 284 286 275 283
34 275 278
45 275 273
Franck-Condon probabilities
NO~ band* NOt(X 45+)
v “a? “b” “c? “a” Experimental Theoretical
0 0.84 0.57 see 0.66 0.7 0.48
1 1 1 tee 1 1 1
2 0.62 0.64 ee 0.7 0.7 0.92
3 0.16 0.24 see 0.19 0.5 0.49

* “a?! “bh”, “c”’, “d” represent designations of bands, which start at 5.04, 5.41, 5.46, and 6.44-40.05 eV, respec-
tively.
APPENDIX VII APPENDIX Ix

Resonances in NO and their grandparents (12-18 eV) Spacing of vibrational states of O;- X(*I,) in meV.*
(Sanche and Schulz, 1972).

Spence and Linder and Gray

Grandparent Vibrational Schulz Schmidt et al.
NOt transition (1970) (1971b) (1971)
Resonance*
NO- Energy _ Binding 445 117 125 128
energy eV Designation eV eV 56 113 123 125
67 110 120 121
12.36(v=0) 6 16.56 4.20 7-8 108 119 118
12.57(v=1) 8-9 106 117 115
12.73(s) 9-10 115 113
12.94(s) 10-11 113 109
14.19(0=0) AM 18.32, 4.13 tae to 105
14.52(s) 13-14 107
eee cm 20.46 wee 14-15 104
17.51(v=0) BM 21.72 4.21 ton io
17.94(s) 17-18 99
5.04(0=0) XlEt 9.27 4.23 Extrapolated:
0-1 135 135 140

* The features marked (v=0) are interpreted as the
lowest states of core-excited Feshbach resonances. The ® The state v’=8 is located near 569 meV (Linder and
features marked (s) are interpreted as core-excited Schmidt, 1971b) and it is nearly coincident with the
shape resonances. v=3 state of O2 (Spence and Schulz, 1970).

106


30° 30°

s7UV 58.2) eV.
° PA.
IN
IN

i

71) 158.2 eV

30°].

COLLECTOR CURRENT (ARB. UNITS)

iy

5° 40°

10° 45°

15 /

50°

5714 58.2)

ELECTRON ENERGY (eV)

Fic. 32. Typical line shapes of the 57.1- and 58.2-eV resonances
(2s*2p and 252%), as observed in*S, 1S, and ‘P inelastic channels.
The angles of observation are indicated on the figure. The ordinate
is in arbitrary units and the zeros are displaced. The energy scale
is accurate to about 0.2 eV. [From Simpson, Menendez, and
Mielczarek (1966) .]

57.1} 58.2)

20.7 eV, which probably results from the *D resonance.
The position of the peak resulting from the 7D reso-
nance shifts to lower energies (i.e., from 21.0 eV to 20.7
eV) as the angle of observation is decreased (Linder,
private communication). In view of the large width of
this resonance and the possibility for interference,
such a shift is not unusual.

2S excitation: The *D resonance at 21.0 eV is also
prominent in the 24S excitation, as reported by Ehr-
hardt, Langhans, and Linder (1968) particularly at
small angles of observation (10°~50°) and in forward
scattering (Chamberlain, 1967).

In the total metastable excitation, which measures
the sum of the 28S and 21S excitation, a peak occurs
at 21.0 eV. This peak can be attributed, in retrospect,
to the *D state.

The theoretical work on the *D state appears fairly
consistent. Burke et al. place the D state at 21.0 eV,
and ascribe to it a width of 0.4 eV. The stabilization
technique of Taylor gives a value of 20.3 eV (Eliezer
and Pan, 1970). Also, the 2D state is prominent in the
calculated cross section for electron excitation of the
21S state from the 28S state (Burke et al., 1967). The
theory of Burke ef al. (1969) shows that both the elastic

27

and inelastic cross sections for electron impact on the
low-lying metastable states in helium are dominated by
the presence of the *P and *D resonances.

8. 22.42-24 eV (PS, #P, etc.) Optical
Excitation Functions

The data of Fig. 21 show many partially overlapping
structures starting near 22.42 eV and extending to the
ionization potential of helium. The lowest of these
structures have been studied in the differential inelastic
cross sections and are shown in Fig. 28. The values of
the energies are listed, together with the suggested
designations, in Appendix IIIa.

Very recently optical excitation functions have been
studied using monochromatic electrons. Kurepa and
Heddle (1972) have studied the following excitation
functions: 4°S2'P (4713 A); #5—2P (5047 A);
38S—2P (7065 A); “D—2P (4922 3); 44D—2P
(4472 A); 3*D—2»P (5876 A). Heddle, Keesing, and
Kurepa (1973) have further analyzed the 4S and 4°5
excitations. Kisker (1972) has reported data on the
3®P-+28S (3889 A) and the 4*P—»28S5 (3188 A) lines.

Kurepa and Heddle (1972) detected seventeen
structures, many of which appeared rather small, in the
energy range 22.80-24.08 eV. Appendix Ila lists the
more prominent structures observed in this work. Also,
Appendix IIIa lists large structures observed by Kisker
(1972) in the 3°P excitation and 4°P excitation func-
tions.

Most of the observations on structures in the optical
excitation functions have not yet been analyzed in
sufficient detail, so that any assignment is preliminary.

ION COUNT
(in million)

598

597} :
te (2s?2p)*P
57 59

ELECTRON ENERGY (eV)

Fic. 33. Formation of Het by electron impact on He. The
background ion formation is subtracted so that only the structure
remains, representing ~0.8% of the total Het signal. The count
rate is indicated. The structure results from the decay of the
(25%2p) and (2529%) resonances by two-electron emission. [From
Quémenér, Paquet, and Marmet (1971).]

(2s2p?)?p
58



A fairly good, but not perfect, fit to the experimental
curves was obtained by O’Malley and Taylor (1968)
whose theory gives the angular distribution in the form
(1+7 cos’#). The deviation between this expression
and the experiment is of the order of 10%. Read (1968)
was able to improve the fit to the angular distribution of
inelastically scattered electrons in CO, using a mixture
of px and dw waves. The mixing of the pr and dx
waves is left as a parameter and the mixing parameters
are adjusted until a good fit to the experimental angular
distribution is obtained.

B. Dissociative Attachment (9.65-12 eV)

Dissociative attachment in CO leads to the formation
of O- via the reactions (Chantry, 1968)

e+CO0-+C(*P) [9.62 eV]
and
e+CO0-+C(1D) [10.88 eV].

A much smaller cross section (~6X10- cm?) exists
for the reaction (Stamatovic and Schulz, 1970)

e+CO—-0+C~-(4S) [10,20 eV].

Whereas the experimentally observed appearance
potentials for the reaction leading to O-+C, given in
brackets above, occur at the expected position for these
reactions, the formation of O+C- is “delayed” by
about 360 meV from the energetically lowest value that
can give the reaction (9.84 eV). A hypothetical poten-
tial energy diagram showing some of the observed
features is shown in Fig. 52.

Figure 53 shows the dissociative attachment cross
section for O- formation as measured by Stamatovic
and Schulz (1970), by Chantry (1968), and by Rapp
and Briglia (1965). Stamatovic and Schulz detect
structure in the dissociative attachment curve near
10 eV, which can be interpreted by the presence of the
23+ core-excited resonance (to be discussed in the
following section) interacting with the potential energy
curve responsible for O- formation.

C. Core-Excited Resonances in the 10-15 eV Region

Core-excited resonances in CO strongly resemble
those of Nz. Just as in Ns, the lowest Rydberg state of
CO, 6#S*, can support a strong core-excited resonance
of the Feshbach type. This resonance, discovered in a
transmission experiment by Sanche and Schulz (1971a),
was further studied by Comer and Read (1971c), by
Swanson et al. (1971, 1972) and by Mazeau et al.
(1972a). Uniform agreement exists on the location of
this resonance as measured by Sanche and Schulz,
ie., 10.04-+0.03 eV, with a width about 45 meV.
Angular distribution measurements (Mazeau ef al.,
1972a; Pavlovic et al., 1973) show that the resonance
exhibits itself in the s wave and thus the symmetry
is *E*,

86

‘Figure 54(a) shows the energy dependence of the
differential cross section for the v=0 and v=1 exit
channels of the ground electronic state at angles of 80
and 60 degrees, respectively, and Fig. 54(b) shows the
elastic differential cross section at other angles of ob-
servation, The transmission experiment of Sanche and
Schulz is shown in Fig. 55(A). The features are num-
bered and the positions of the features are listed in
Appendix VI in comparison with the features observed
by Comer and Read (1971c) and Mazeau et al. (1972a).

The principal decay channels are indicated on the
energy level diagram [Fig. 55(B)], mostly based on the
work of Mazeau ef al. (1972a), Swanson et al. (1972),
and Comer and Read (1971c). The excitation function
of electronically excited states at different angles of
observation is shown in Figs. 55(C) and 55(D).

The features observed in CO are discussed in greater
detail below.

1. #E+ Resonances (10.04 eV, 10.28 eV)

Structures (1-1’) to (4-4’) in the derivative trans-
mission spectrum of CO, shown in Fig. 55(A), exhibit
a remarkable resemblance to the structures (1-1’) to
(4-4’) in Ne and can be interpreted similarly. Structures
1-1’ (10.04 eV) and 2-2’ (10.28 eV) can be identified
as two members of a vibrational sequence of Feshbach
resonances whose parents are the 6*Z+ and Bzt+
states of CO at 10.39 and 10.77 eV, respectively. The
grandparent is the X *Z+ ground state of CO+ and the
resonance itself has a symmetry *2+. The binding of the
two 3se, electrons with respect to the grandparent
state is 4,1 eV, similar to other cases studied (see
summary, Table X).

The *Z* resonance at 10.04 eV also influences dis-
sociative attachment as has been discussed by Sanche
and Schulz (1972), who reinterpreted the dissociative
attachment experiments of Stamatovic and Schulz
(1970) and pointed out that the structure near 10 eV
in the O~ production from CO may be due to the *2+
resonance, Also, the formation of C~ from CO can be
interpreted in terms of this resonance.

Although compound state formation is expected to be
similar in the isoelectronic molecules N2 and CO, the
*Z+ resonance in CO has a natural width (T~40 meV)
which is almost two orders of magnitude greater than
that found for the *2,+ resonance at 11.48 eV in Ne
(T=0.6 meV). The larger width in CO probably
results from the partial decay of the ?2+ resonance into
the O-(?P)+C(8P) channel. In Ne dissociative proc-
esses are not observed and the potential energy curve
corresponding to the one leading to O-+C in CO
could occur at a different energy where it would not
interact with the *2,+ state of No. Thus the natural
width of the *2,+ state in Nz would be small since this
state decays predominantly to the ground state of the
molecule.

The decay of the *2*+ resonance has been studied by


differential cross section

1 | 1 | 1 —>

12 13

electron energy (eV)

IMPACT ENERGY, @V
3: Threshold Behavior of the Cross Section to v=1

The “direct” component of the vibrational cross sec-
tion in Ny is small and therefore the onset of an appreci-
able cross section for vibrational excitation is delayed.
This can be seen in Fig. 35, which compares three
measurements in the threshold region. The small cross

81

Fic. 55. (D) Differential excitation function of the
B13+ y=0 level at 40°. Arrows indicate Feshbach res-
onances at 11.3 and 12.2 eV. [From Mazeau et al.
(1972a).] (E) Differential cross sections at 40° and 80°
scattering angles for elastic scattering and for vibrational
excitation to the v=1 state in CO. The top two curves are
experimental elastic cross sections at 40° and 80°. The
appropriate cross section scale for these two curves is read
on the right; all other curves are read on the left. The two
curves marked “40° exp” and “80° exp” are experimental
vibrational cross sections at 40° and 80°, respectively, for
v=0—1. (Note peak near 20 eV.) ‘Also shown’ are
theoretical results for 40° and 80° using the polarized Born
approximation ‘based on the potentials of Takayanagi and

itman, 1965 (TG) ; Sampson and Mjolsness, 1965 (SM) ;
71 (CD). [From Chutjian et al.

Crawford and Dalgarno, 1
(4972).]

section near threshold may be due to direct excitation
or to the residual effect of the compound state.

4. Angular Distributions
It has already been pointed out that angular distribu-

tion measurements are a powerful tool for the deter-


| PUMP OUT I
Sp PRESSURE
DROPPING

mae
Sy

asin
canane S <A
Sq

\

COLLECTOR

Fic. 6. Schematic arrangement of a modified Ramsauer ap-
aratus for the measurement of total scattering cross section.
Eitrom Golden and Bandel (1965).]

at a constant energy. In this kind of selector, two
parameters define the electron energy. One is the
magnetic field strength and the other is the accelerating
voltage. This coupling of the energy to two experimental
parameters leads to the fact that the electron energy is
usually not continuously variable. Since the energy
spread is a function of the electron energy, the study of
resonance effects is quite tedious, but resonances have
been measured using this method. The advantage of this
method lies in the fact that it yields the absolute magni-
tude of the total cross section at and near the resonance.

Inelastic Cross Section Measurements using the
Trapped-Electron Method

The trapped-electron method has been used for the
past 15 years for the measurement of inelastic cross
sections, particularly near the threshold of excitation.
Basically, the method consists of establishing an
electrostatic potential well in which low-energy elec-
trons, resulting from inelastic collisions, are trapped and
subsequently collected with a very high efficiency.

Figure 7 shows a schematic diagram of the tube and
the variation of potential along the axis. An electron
beam collimated by a magnetic field is accelerated into
the collision chamber with voltage V4. The collision
chamber consists of two end plates and a grid. A
cylindrical (or parallel plane) outer collector surrounds
the collision chamber. By applying a positive voltage to
this collector, with respect to the collision chamber, an
electrostatic well, having a depth W (in volts), can be
produced along the axis of the tube.

An electron making an inelastic collision just above
the threshold for an inelastic process loses most of its
energy and is trapped in the well. It spirals back and
forth following the magnetic field lines and eventually
makes enough elastic collisions to diffuse across the
magnetic field to the trapped-electron collector. At an
electron energy that exceeds the threshold of an in-
elastic process by the amount W, the electrons have

enough energy remaining to escape over the potential
barrier at the end of the collision chamber, and the
trapped-electron current vanishes. Therefore, as a
function of accelerating voltage, the trapped-electron
current is zero below an inelastic threshold, and then
grows to a peak which is proportional to the magnitude
of the cross section at an electron energy that exceeds
the threshold by W.

The well depth can be determined by applying a
negative voltage to the trapped-electron collector
relative to the collision chamber, thus creating a
potential barrier in the path of the electron beam.

The shift in the electron-beam retarding curve for
different values of the applied voltage measures the
size of the barrier, which is the well depth with reversed
polarity. Other methods for establishing the well depth
also exist.

Using the trapped-electron method, sometimes in
conjunction with a modulation of the well depth, it is
possible to measure an excitation function for several eV
above the onset.

A method very similar in concept to the trapped-
electron method is the “SF, scavenger technique.”
This technique takes advantage of the fact that SFy
has a very large attachment cross section for zero-
energy electrons, and a very small cross section for all
other energies. Thus one admixes a small amount of
SF, to the gas under study and whenever an inelastic
collision takes place, it leads, near threshold, to zero-
energy electrons which promptly attach to SFy. By

TRAPPED-ELECTRON
CURRENT

ee naar
t= he

ELECTRON

>

s
mi

<— POTENTIAL
POS. o NEG

Fic. 7. Schematic diagram of a trapped-electron experiment
and potential distribution at the axis of the tube. F is the filament,
Py is the retarding electrode, G is the cylindrical grid forming
the collision chamber, M is the cylinder for collection of trapped
electrons, E is the electron beam collector, Va is the accelerating
voltage, and W is the depth of the well. The double line in (b)
indicates the energy of the electron beam and the arrow indicates
the energy lost by an electron in an inelastic collision, The electron
energy a the collision chamber is (Va-+W). [From Schulz
(1959).


CROSS SECTION (10°'® cm?)

Fre. 8. Curve A: Angular distributions
for pure vibrational excitation «(v=

E-15ev

0-1; Aj=0). Curve B: Angular distribu-
tion for rotational-vibrational excitation,
o(v=0—11; j=1-43). Points are experi-
mental (Linder and Schmidt, 1971a) and
lines are theoretical. [From’ Henry and
Chang (1972).]

CROSS SECTION (10°'cm?)

4 1 L

paper), into two major categories depending on the
state of the target molecule to which the incident elec-
tron attaches. Table I may serve as a helpful guide to
the semantics of compound states.

When the incident electron is trapped in the potential
connected with the ground electronic state, we speak
of shape resonances or single particle resonances. The
two terms are synonymous. In this case, the centrifugal,
polarization, and exchange forces combine to create a
potential with a penetrable barrier. Thus, it is the shape
of the potential which is responsible for the trapping
of the particle and for the resonance. Shape resonances
associated with the ground electronic state have been
substantiated in all diatomic molecules studied to date
(Hz, Dz, HD, O2, N2, NO, CO). They occur at low ener-
gies (0-4 eV), exhibit a lifetime in the range 10- sec
to 10~" sec or even longer, and decay into vibrational
and rotational levels of molecules and sometimes into
negative ions by dissociative attachment. In all cases
described in this review, vibrational excitation proceeds
predominantly via shape resonances; resonances also
play an important role in rotational excitation. Thus
shape resonances are very important in our understand-
ing of low-energy impact on molecules,

51

60 80 too 120
SCATTERING ANGLE 6°

140 160 180

Since typical vibrational times are ~10- sec, shape
resonances may be short-lived, long-lived, or compara-
ble to vibration times. When the lifetime is short (e.g.,
Hy), the energy dependence of the vibrational cross
section exhibits a broad peak; when the lifetime is long
(e.g., O2), the compound state itself can vibrate and
the energy dependence of the cross section to a given
final vibrational state exhibits a series of spikes at the
location of the vibrational levels of the compound state.
When the lifetime of the compound state is comparable
to typical vibration times (e.g., Nz, CO) an intermedi-
ate situation prevails. In such a case, the compound
state may perform about one vibration before decaying
and the cross section to the final vibrational state will
exhibit several broadened spikes.

The location on the energy scale and the particular
properties of shape resonances are described under a
separate heading for each molecule.

Core-excited resonances are associated with an elec-
tronically excited state of the molecule, which is called
the “parent.” Core-excited resonances thus consist of
a “hole” in one of the orbitals normally occupied by an
electron, and of two “particles”, i.e., electrons in nor-
mally unoccupied orbitals. We can also visualize reso-


When the backward extrapolation is performed and
terminated at the electron affinity of 0.44 eV, one ob-
tains a value of 132 meV (Spence and Schulz, 1972) or
135 meV (Linder and Schmidt, 1971b) or 140 meV
(Gray et al., 1971) for the spacing of the lowest vibra-
tional states, i.e., v'=O—0'=1 of O:-. These values
compare to a value of 135 meV deduced by Holzer
ef al. (1968) from Raman spectroscopy of alkali
halide crystals in which O;- is trapped. The agreement
between all these values appears to be good.

A high-resolution (10 meV) transmission experiment
by Land and Raith (1973) shows that the »’=4 peak is
split by spin-orbit coupling into "Ms and *I1j. com-
ponents, separated by 20-2 meV. The center of the
v'=4 state is determined to be at 91-5 meV.

2. Vibrational Excitation of Oz at Low Energy
(0-1.0 eV)

The vibrational cross section in Oz should consist of a
“direct” component and a “compound-state” com-
ponent at the position of the compound state, Os.

@ +02 X°Zstv20) —> o7T,) —

— e+0, PEM

V0 (elastic)

intensity (arb. units] ———>

0; 7T1,{¢r) E=0.680¢V

—— ‘rotational states of compound
system included

‘smn slow rotation approximation

vz0-~1

v=0-~2

25

s ~ v
6 in E

Gitterential cross section [arb.units]

2
a

1 1
60 90 120°
scattering angle ————_____

Fic. 66. Angular distribution of electrons having excited the
v=1 and 9=2 vibrational states in O;. The points are experimental
(error ~10%). The lines represent theoretical models with and
without rotational states of the compound state. The curves have
been normalized at or near 90°, [From Linder and Schmidt
(1971b).]

1

0 1
30

This model was invoked by Hake and Phelps (1967)
and by Schulz and Dowell (1962) to explain swarm and
trapped-electron experiments, respectively.

Recent trapped-electron experiments by Spence and
Schulz (1970) led to the conclusion that the vibrational
cross sections in Oz consist of series of spikes at the
position of the compound state which had been pre-
viously established from elastic scatterings. This finding
is corroborated by the differential cross section meas-
urements of Linder and Schmidt (1971), whose data
are shown in Fig. 65.

The trapped-electron method possesses a high sensi-
tivity for detecting when a level of Oz and a level of O2-
occur accidentally at the same energy. Spence and
Schulz find that the o’=8 level of Os~ is coincident in

05 10 15

collision energy[eV]——>

Fic. 65. Measured vibrational cross sections to v=1, 2, 3, 4
of Oz. The horizontal line at each curve indicates the zero line
of the stored signal. Two runs of the energy dependence of elastic
scattering are also shown in the upper part of the figure. The
scattering angle is 60° for all curves. The vertical lines indicate
the energy position of the resonance peaks. The threshold onsets
of the excitation functions are marked by small arrows. Energy-
integrated cross sections in absolute units are listed in Appendix X.
[From Linder and Schmidt (1971b).]

energy with the o=3 level of Os, thus fixing the relative
positions of the vibrational levels of the two systems.
This coincidence has been confirmed by Linder and
Schmidt, who find that the coincidence between these
two levels is within 1 meV, as well as by Land and
Raith (1973).

In order to obtain an absolute magnitude from their
differential cross section, Linder and Schmidt have to
know the angular distribution of the scattered elec-
trons, Figure 66 shows that the experimentally ob-

93


Differential cross sections

vs3
xl0

Collision energy

Fic. 40. Energy dependence of the differential vibrational
cross sections for scattering of electrons from Nz. The exit channels
are vibrational levels of the electronic ground state and the
scattering angle is 70°. The curves do not have the same cross
section scale but the peak intensities can be obtained from Table
i ne aa lines are shown broken. [From Comer and Read

1971).

7. Band “g”

Figure 17 shows that band “f” appears perturbed
by the presence of other structures. This new band is
labelled “g” and tabulated in Appendix I. It appears
much more clearly in Dz where bands “f” and “g” do
not overlap. Three features around 16 eV in the data
of Golden (1971) in H: which he attributed to auto-
ionization could be members of band “g.”

Il. NITROGEN

A. Resonance at Low Energy (1.74 eV) "II,

The earliest experiments on the total cross section in
Ne showed a broad peak in the region around 2.3 eV
in N; (Ramsauer and Kollath, 1931), but it was not
until the early 1960’s that an understanding of this
effect became available, largely as a result of improved
experimental techniques and the pioneering theoretical
contribution of Herzenberg and Mandl (1962). From
an experimental viewpoint one obtains the most de-
tailed information on the nature of the compound state
involved by studying structure in the elastic and vibra-

tional cross sections vs energy and by studying angular
distributions of the scattered electrons. It should be
recalled that, in the case of Hg, the dissociative attach-
ment decay channel provided valuable understanding.
However, since no stable N- ion exists, such a study
is not feasible in No.

The history of this discovery has been well reviewed
by Massey and Burhop (1969), by Chen (1969), by
Birtwistle and Herzenberg (1971), and by Bardsley
and Mandl (1968). Following the total cross section
measurements by Ramsauer and Kollath (1931), Haas
(1957) established that the vibrational cross section
exhibits a peak in the 2.3-eV energy range and that a
temporary negative ion is involved. Schulz (1959) con-
firmed these observations using the trapped-electron
method, but not until he used double electrostatic
analyzers (Schulz 1962a, 1964a, 1966) could he estab-
lish the details of the resonance process.

The nitrogen molecule has the configuration (c,1s)?
(ouls)?(og2s)?(ou2s)*(m.2p)*(o,2p)?. The first unfilled
orbital is 7,2p (=3dz, in the united-molecule notation)
and the incident low-energy electron temporarily occu-
pies this orbital. As the electron escapes, it encounters
a d-wave barrier through which it must tunnel. This
shape resonance has a symmetry *II, and it is centered
around 2.3 eV. It dominates the low-energy electron
impact cross sections in Ns, as shall be discussed in the
following sections. A summary of shape resonances in
other molecules is given in Sec, VII.

1. Elastic Cross Section via "I,

The energy dependence of the total scattering cross
section, obtained by Golden (1966) using a modified
Ramsauer apparatus, is shown in Fig. 26, The struc-
ture in the cross section above 1.8 eV is clearly visible.
This structure can be observed in a Ramsauer-type
apparatus when the energy distribution of the electrons

Differential cross section Carbitrary units)

30 60 90°

Scattering angle
Fic. 41. Angular distribution for the two resonant peaks

observed in the v= 1 exit channel (see Fig. 40). [From Comer and
Read (1971b).]

72


Fic. 44. Differential experimental
cross section for elastic scattering of elec-

trons on sodium. The angle of observa-
tion is indicated. Scales (b) and (c) are
expanded with respect to scale (a) by
factors of 3.7 and 25, respectively.
[From Andrick, Eyb, and Hofmann
(1972).

(a) 60 (b)
g
i 20°
3 75°
5 30°
° 145°
45
¥6 Fa 25 "6 2 25
Energy (eV) Energy (eV)
90° Ce)
s
8
Fy
5
2 105°
5
é
6 120° ae
16 24 25

Energy (eV)

Matese find three compound states lying below the
(15*3s)2S state and four states below the (15°3p)?P
state of Li. A schematic diagram, constructed from the
results discussed above is shown in Fig. 41.

In sodium, an analogous situation prevails (Moores
and Norcross, 1972) and the appropriate energy level
diagram is shown in Fig. 42. Fung and Matese find only
a single compound state in the 3-eV region of Na.

The existence of the 1P and ‘D resonances just below
the threshold of the first electronic state should domi-
nate the excitation function to that state, and it appears
that this is the case in Na (Enemark and Gallagher,
1972; Moores and Norcross, 1972).

The energy dependence of the total elastic and the

differential elastic cross section in sodium exhibit a
dramatic cusp at the energy of the *P state at 2.1 eV.
This cusp is shown in Fig. 43 for the total cross section,
as derived from the close-coupling theory of Moores
and Norcross. The experimental results of Andrick,
Eyb, and Hofmann (1972) for the differential elastic
cross section are shown in Fig. 44. The close-coupling
theory of Moores and Norcross is in very good agree-
ment with the experiment. The structure shown in
Figs. 43 and 44 is strongly influenced by the presence of
the !P and 1D states near 2 eV (Norcross and Moores,
1972).

It is noteworthy that the calculated cross sections for
photodetachment of electrons from Li- and NaTM in


Phys. Rev. A 7, 560.

Schulz, G. J., 1959, Phys. Rev. 116, 1141.

Schulz, G. J., 1963, Phys. Rev. Lett. 10, 104.

Schulz, G. J., 1964a, Phys. Rev. Lett. 13, 583.

Schulz, G. J., 1964b, Phys. Rev. 136, A650.

‘Schulz, G. J., and R. E. Fox, 1957, Phys. Rev. 106, 1179.

Schulz, G. J., and J. W. Philbrick, 1964, Phys. Rev. Lett.
13, 477.

Sharpton, F. A., R. M. St. John, C. C. Lin, and F. E. Fajen,
1970, Phys. Rev. A 2, 1305.

Shore, B. W., 1967, Rev. Mod. Phys. 39, 439. .

Simpson, J. A., 1964, Rev. Sci. Instrum. 35, 1698.

Simpson, J. A.; 1967, Rev. Sci. Instrum. 38, 103.

Simpson, J. A., afid U. Fano, 1963, Phys. Rev. Lett. 11, 158.

Simpson, J. A., M. G. Menendez, and S. R. Mielczarek, 1966,
Phys. Rev. 150, 76. .

Sinfailam, A. L., and R. K. Nesbet, 1972, Phys. Rev. A
6, 2118.

Smit, C., and H. M. Fijnaut, 1965, Phys. Lett. 19, 121.

Smith, K., 1966, Rep. Prog. Phys. 29, 373.

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Taylor, A. J., and P. G. Burke, 1967, Proc. Phys. Soc. Lond.
92, 336.

Taylor, H. S., 1970, Adv. Chem. Phys. 18, 91.

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A 5, 1663.

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3, L148.

Weiss, A. W., 1968, Phys. Rev. 166, 70.

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Zapesochnyi, I. P., and O. B. Shpenik, 1966, Sov. Phys.-JETP
23, 592.


a
5 \ —-— Bardsley et al. + 6
\| ——— Chen & Peacher 3 T T T T
> 4 a = —— Bardsley et al.
e Se \ ag Chen & Peacher
eS 3 a x
~ sz
> s
sr 3*
Bab g
Hf 53
5° g
B-ab 2?
S
= 2
5-2} 1
3 =)
dal z,
0 10 20 30 40 50 60
4 Internuclear separation, R, ag
-5 js ee ee ee ee
0 10 20 30 40 5.0 60 7.0

Internuclear separation, R, ag

Fic. 6. The real and imaginary parts of the potential energy curves for the *2,* and *2,* states of Har. On the left-hand side are
shown the potential energy curves for Hz (—), and the potential energy curves for Hi~ derived by Bardsley et al. (1966a) and by Chen
and Peacher (1968a). The dotted curve indicates the real part of the potential curve for the ?2,* state which is needed to obtain agree-
ment with the vibrational cross section of Ehrhardt, ef al. (1968). The repulsive curve for Hy" (*2,*) of Chen and Peacher (1968a) is
in very good agreement with the curve derived by Eliezer, Taylor, and Williams (1967), which is shown in Fig. 25(a). The potential
energy curves for the lowest states of Hz(#2,* and *2,*) are taken from Kolos and Wolnicwicz (1965). The right-hand side of the figure
shows the calculated widths of the *2,* and *2,* states. [From Chen 1969.]

compound states, namely,
o(£)« | A+(TinTout)!?/(E—-Eo+3iP) PY,

then the term A, representing the direct contribution
to scattering, is small compared to the resonance term.
in inelastic processes. Above, Tin is the partial width
for decay into the ground state, Tou: is the partial width
for decay into the excited state, and I’ is the total
width, related to the partial widths by F=Ti.+Tout.
£y is the resonant energy.

Other review papers have recently appeared: Taylor
et al. (1966), Bardsley and Mandl (1968), Burke
(1968), Massey and Burhop (1969), Chen (1969),
Herzenberg (1970, 1971), Taylor (1970). The nomen-
clature and general approach used in this review have
been strongly influenced by these papers. Phelps (1968)
has recently reviewed vibrational and rotational cross
sections; Takayanagi and Itikawa (1970) have reviewed
rotational cross sections. Golden, Lane, Temkin, and
Gerjuoy (1971) have reviewed low-energy scattering ex-
periments and rotational excitation and have given a
review of experimental techniques. The aim of the
present review is the tabulation and discussion of ex-
perimental values for compound states: their positions,
widths, and classifications, Theoretical considerations

50

are brought in only in those cases where they are needed
for the discussions, but no attempt is made to include
the bulk of theoretical considerations. Experimental
methods are briefly discussed in the paper immediately
preceding, which deals with compound states in atoms.

A. Classification of Compound States

We can classify compound states in molecules, in an
analogous manner to that in atoms (see preceding

5

203

Ps

ry

im 0.2

S

fr]

a

B O4

°o

$ fe

o Lt 1 ! 1 n n
° 2 3 4 5 6 7
E (ev)

Fic. 7. Curve A: Energy dependence of pure vibrational cross
section, o(v=0-—1, Aj=0). Curve B: Energy dependence of
rotational-vibrational cross section, o(0=0—>1, j=1-»3). Points
are experimental (Linder and Schmidt, 1971a), ines are theoret-
cal (Henry and Chang, 1972). [From Henry and Chang (1972).]




= 2
(ae) 'AOU3Na

=

2

0%

“sopumuoser yDeqyse,| 94 Jo siueredpuesS ay) 9yROIPUT $978IS UOT
aansod ay 07 Seypeoy souy poysep aU, “swMogre Tyla sau] £q poyworpuy ase sjauuey Avoap ‘Te Jou Inq
‘quiog “seoteuoser YDeqyseg] PUB SsotRUOSEA adeYs OUT Paplarp are pUE soquIS punodwos oq axe _*N|
poyreur vorJod paxoq oq Ui s[aAay AB19ua oY, “WIOY OHMS UT AN; PUL SN Jo WeISEIp Jorg] ABIOUG
(a) E-@zg6r) sprEqUIEY pue ‘zohof ‘TeH ‘neaysarg ‘nvazeyy WoT] “A AGBL Wl pansy axe soyszouo
aT] PUL ,,,2,, PawUsIsop St PUG OY, *N J 9989S 4"Z_ 7 TP) YIM payeposse soouvaoses adeys payoxs
-a109 07 anp aye SoINIONIS IL, “9-F—a SOILS [LUOTILIGIA OY} UT AIS ."Ze F 94} OF .06 I” WoT}Das S809
YeHusrayIpP 943 Jo souepuadap ABsoug (q) [°(07L6T) IPIEYEY pur ‘zadof “pep “neaysory ‘nese
wor] 3X9} 995 “3FIYS syvad oy2 Jo woNwoo] ay} 34M AION “A XIPuaddy UT pozsy] axe sore ONL
+ ¢B,,PURq SB payeusisap oe pur o3eys "TT, J o4} YIM poyeposse sooueoser aduys poyPxo-2100 07 anp are
soanjonays ayy, ‘aAn3y ay} Jo aps IYBL ay} UI UMTS St aNd Ypva Joy a[ws BI, °S—] =a SoqeIS [BUOPLIGIA
af WLaqeIS "Ty J 29 10F ,06 3" Wor}Das sso [UNUAZOITp amp Jo thy WI ouapuedep ABsoUg (C) “Fh “OLY

Ue) AB19u9 uoutsa]9 WwapIou,

u on 6

f

VAY

asa VARARN

75


cited states which are closely spaced (~0.25 eV), each
of which may have an associated compound state. Thus
it may not be possible to resolve individual states,
especially since the states themselves may be relatively
broad.

The resonances discussed above would have two holes
in the normally filled shells of No, (KK) (o,2s)®(ov2s)®
(o92p)*(4u2p)* and would have three electrons in the
vacant orbitals, (#,2p) and (c,2p). Pavlovic et al.
(1972) calculate that, in the 22-eV region, the spacing
of such resonances is less than 0.25 eV.

We note that the resonances discussed in the previ-
ous section (core-excited shape resonances, a and a’,
connected with the A*Z,+ and B‘II, states, respec-
tively) have one hole in the normally filled shell and
two electrons in the vacant orbitals, whereas the reso-
nances near 2.3 eV (connected with the ground X !Z,+
state of Nz) have zero holes and one electron in the
vacant orbitals. Thus the shape resonances invoked by
Pavlovic e¢ al. follow logically from the two types
already discussed.

Figures 45 and 46 show the energy dependence and
the angular dependences observed by Pavlovic et al.
(1972) for the excitation of »=2. The energy depend-
ence of the cross section for exciting v=1 and »=3 is
very similar to that shown.

A measurement and an analysis of the angular dis-
tribution of electrons having excited the »=1 vibra-
tional state of Nz (and also CO) has been performed
by Truhlar et a/. (1972) with the aim of testing whether
a simple nonresonant mechanism can explain the vibra-
tional excitation near 20 eV. Such a model appears to
be applicable in the 20-eV energy range in the case of
H, (Trajmar et al., 1970). Trublar e¢ al. find that a
resonance model must be involved in the case of No
and CO in order to interpret the experimental results
on vibrational excitation near 20 eV. It should be
noted that the experimental results of Truhlar et al.
(1972) are in good agreement with those of Pavlovic
et al. (1972),

Iv. CARBON MONOXIDE

The electron configurations and the resulting levels
of compound states of diatomic molecules are deter-
mined essentially by the number of electrons, Therefore
Nz and CO, being isoelectronic molecules, should exhibit
very similar properties. In fact this is the case. How-
ever, the positions of the compound states and their
widths differ somewhat.

The CO molecule is not symmetric with respect to
inversion so that the g—« symmetry is not preserved.
Also, the permanent dipole of CO often cannot be
ignored. The following review of the carbon monoxide
molecule follows closely the discussion of Ne.

A. Resonance at Low Energy (1-3 eV) "II

The configuration of CO is identical to that already
listed for Nz, except that the subscripts g and « now

lose their meanings (see Table IX). As a consequence,
the 3dm orbital contains a p-wave component (Bardsley
and Mandl, 1968; O’Malley and Taylor 1968; Read,
1968). Thus the trapped electron tunnels through
a p-wave barrier which is not as high as a d-wave bar-
rier and, as a result, the width of the state is expected
to be larger (the lifetime is shorter) than in No. These
expectations agree with the experimental results.

1, Elastic Cross Section via *IL

The energy dependence of the differential elastic
cross section for CO is shown in Fig. 47. Compared to
Nz, the structure in the cross section is less pronounced,
although the peak in the neighborhood of 2 eV is
especially clear at 20 and 40 degrees. The individual
resonances become more obvious when the vibrational
cross sections are studied. Ehrhardt et al. (1968) esti-
mate’ the width at 0.4 eV.

2. Vibrational Excitation via "11

The energy dependence of the vibrational cross sec-
tion, as observed at an angle of 72 degrees, is shown in
Fig. 48, This curve, obtained by Schulz (1964) is in all
respects similar to the curve obtained at 20 degrees
(Ehrhardt et al., 1968), indicating that the shape of
the cross section does not depend on angle. The sum
of all vibrational cross sections has a relatively smooth
behavior, with a single peak at 1.7 eV and a magnitude

8
D o=3.5X 10-8 cm?
v1
In obtaining this value, Ehrhardt et al. (1968) took into
account the variation of the cross sections with angle.
The vibrational cross sections in absolute units is shown
in Fig. 49,

A notable difference exists between N: and CO if one
observes that the cross section for v=1 has a long tail
which extrapolates to the onset for v=1 (see Phelps,
1968) whereas N2 shows a tail which is smaller by an
order of magnitude. A direct dipole-type process is
probably responsible for the difference. Figure 50 shows
the details of the threshold region for excitation of »=1
in CO, as determined by different methods of measure-
ment.

The other notable difference between Nz and CO is
the larger width of the observed structure. As already
noted, this larger width is a result of the barrier being
predominantly of a p-wave character in CO, with d
wave mixed in. In Ne, the barrier is predominantly
d wave.

3. Angular Distributions

Figure 51 shows the angular distributions obtained by
Ehrhardt ef al, (1968) for electrons which are scattered
elastically and inelastically. Qualitatively, the curves
for the inelastically scattered electrons show a p-type
behavior of the curves, with a minimum at 90 degrees.

85


APPENDIX V

Position of resonances in neon (eV).

Metastable
Transmission experiments production
Sanche and Kuyatt Pichanick
Feature Schulz et al. and Simpson
designations* (1972) (1965) (1968) Designation
1-1’ 16.10-16.12° 16.04 (2p)®(3s)? *P oye
2-2’ 16.19-16, 22° 16.135 (2p)®(3s)? *Piye
3-3'(A) 16.85-16.91 16.92
wee ee 18.18
ase ase 18.29 ——_
4(B, C) 18.55 18.46 18.35-18.43 Optical excitation
5852 A
5-5'(D, E) 18.65-18.70 18.56 18.58-18.66 Kisker (1972b)
6(F, G) 18.95 18.86-18.97
7 19.47 19.50-19.54
8 19.57 19.60-
9 19.65
10(H) 19.71 19.69 -19.70
19.77-19.82
11-11’(I) 19.97-20.03 19.83 19.91-19.99
12-12’(J) 20.07-20.13 20.1 20.03-20.07
-20.19
20.60-20.64
20.70-20.74

* The “feature designations” refer to Fig. 25 (numbers) and Fig. 26 (letters), respectively.
» The first energy refers to a maximum, the second to a minimum.
° The widths of the *Psp, "P12 resonances have been deduced from experiment by Haselton (1973). He finds

T=8.9540.34 meV.

APPENDIX VI

Position of resonances in argon (eV).

Metastable
Transmission experiments production
Sanche and Kuyatt Pichanick and
Schulz et al. Simpson
(1972) (1965) (1968) Designation
11,10-11.13 11.064-11.094 3ph4s? 2 Ps
11.27-11.30 11.235-11.267 "Pin
11.71 11.72 3p%4s4p(?)
11.91 11.88-11.98 3p*4s4p(?)
12.89-12.92 12.80-12.93
12.95-13.06-13.11 13.08
13 ,.22-13.28 13.17-13.24
13.33 13.37
13.45-13.50 13.55

14.03-14.07-14.10



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Read, F. H., 1968, J. Phys. B 1, 893.

Reinhardt, J., G. Joyez, J. Mazeau, and R. I. Hall, 1972, J.
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140, A1466.

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110

the present text.

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(unpublished).

U.S. GOVERNMENT PRINTING OFFICE ; 1973—542-650/55


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iii


APPENDIX IL

Comparison of the values obtained by different authors for D.- states (eV).

Transmission Transmission
Inelastic Tnelastic
Vibrational Sanche Kuyatt Comer and. Vibrational Sanche Kuyatt Comer and
quantum and Schulz = et al. Read quantum and Schulz — etal. Read
number (D:-) (1972) (1966) (1971a) number (Ds-) (1972) (1966) (1971a)
Band “a” Band “‘c”
0 11.34 11.28 11.32 1 11.67 11.65
1 11.56 11.48 11.54 2 11.89 11.87
2 11.76 11.69 11.75 ; 8 ae
3 11.97 11.89 11.96 . .
4 12.17 12.09 12.15 Sanche and Schulz (1972)
5 12.36 12.28 12.32 Band “f” Band “g”
6 12.55 12.47 12.48 0 13.66 15.05
7 12.71 12.64 12.61 1 13.86 15.22
8 12.88 12.85 12.75 2 14-06 rae
. : . 3 14.25 15.55
9 13.05 4 14.43 15.71
10 13.22 5 14.57
APPENDIX II

Relative branching ratios for the decay of resonance series “‘a” in Hz in terms of absolute cross

sections (10-” cm?). The estimated error for the cross sections is in the order of 20%.

Exit channel v=0 v=1 v=2 v=3 vf=4 v=5
Brz,t
v=2 0.27 0.39 0.09 0.14 0.14
v=1 vee 0.41 0.29 0.39 0.18 0.10
v=0 0.67 1.4 0.76 0.21 see see
bx te
11.02 eV see 0.11 0.10 0.042 0.020 0.008
10.76 eV 0.031 0.087 0.063 0.039 0.015 oes
10.47 eV 0.042 0.063 0.048 0.024 0.007 see
10.17 eV 0.033 0.045 0.022 0.011 0.004 tee
6°2,+—Integrated values 2.0 2.5 2.5 1.4 1.0
X1E,+
v=5 eee 0.09 eee aoe
v=4 0. 0.2 0.02 .
v=3 0.14 0.23 ote
v=2
v=1
v=0 Pronounced interference structure

* Within an energy band of AE=60 meV. From Weingartshofer ef a/. (1970).

103


4E Ty
_ Ej (series 0)
+
ee a:
\ oF NE series 6)
L TT (series c)
g
uw ob
ab
2b
r,t j
0) 3

(a)

18,0]
14,0]
13,0)
12.9}
11,0}
loo}

9.0}

TO}

Elev) ——

60)

5.0)

40}

\

\
="

es
WO 12 14 168 18 20 22 24 26 28 30
Rta) ——>

(b)

Frc. 25. (a) Potential energy curves for Hy~ state (broken curves) which give the best fits to experimental data. Corresponding
curves for some Hz states (full curves) are also shown (Sharp, 1971). It should be noted that the energy scale is taken with respect to
the bottom of the ground-state potential curve. [From Comer and Read (1971a).] (b) Potential energy curves for Hy- derived from
calculations. The full curves represent the calculated compound states and the dashed curves are some of the parent Hz states. (A)

Hy *%,* consisting of C I.+7u2p'; (B) Hs *2,* consisting of C “Iu

‘udp’; (C) Hi *25* consisting of B1Z,*+ouls’; (D) Hi *B,* con-

sisting of *2.*-ouls’; (E) Hav *2u* consisting of X#2,*-ou; (F) Hz X !2,*; (G) One configuration result for Hs "2,* laglow. This curve
lies about 0.32 eV above the “exact” #,+ curve, but is used as a comparison with the H;~ calculation consisting of this configuration
plus an extra electron; (H) Two configuration result for Hz u(1op1mu-+loulm,). The minimum of this curve lies about 0.14 eV above
the experimental minimum. The He a ®2,* curve lies so close to this one that they are indistinguishable on this scale; (I) Same as H
for C4, and E*2,+; (J) Hs B12.+. [From Eliezer, Taylor, and Williams (1967).]

CO—CO.+¢ indicates that the theoretical predictions
for H-+H, —H2+e, as outlined above, are probably
correct.

B. Resonance in the 10-eV Region (Z,+)

The first excited state of Hz is the (1scy)(2po,)*=,+
state. In the notation for separated atoms this becomes
(o1s)(oy1s)*2,+. The dominant configurations of the
compound state associated with this excited state is
(1so,)(2po,)??Z,+ or, in the notation of separated
atoms, (og1s)(o,1s)?*Z,*. Agreement exists on this
assignment (Bardsley, Herzenberg, and Mandl, 1966a;
Eliezer, Taylor, and Williams, 1967; Bardsley and
Mandl, 1968).

When the real part of the potential energy curve for
the *2,+ is calculated as a function of internuclear sepa-

63

ration, it is found (Bardsley and Mandl, 1968; Eliezer
et al., 1967) that the potential energy curve crosses
the potential energy curve of the parent, i.e., the *Z,*+
state. As long as the potential energy curve for H:-
lies below the parent we are dealing with a core-excited
resonance of the Feshbach type. When the potential
energy curve lies above the parent we are dealing with
a core-excited shape resonance. In this case the assign-
ment varies as a function of internuclear separation.
Information regarding the 2Z,+ state of Hs- comes
from experiments on dissociative attachment. In other
channels, this state has not yet been observed. A com-
parison of two recent experiments on negative ion for-
mation with Hz in the range 7-17 eV is shown in Fig. 14.
An interesting isotope effect, not as dramatic as the
one for the *2,*+ state, has been discovered by Rapp


applied to these observations at that time. Although
there was a need to understand such structures in the
cross section and also the large vibrational cross sections
observed experimentally (e.g., Hz), the resonance model
remained confined for a long time to nuclear physics
alone, The application of the resonance model to mole-
cules in the early 1960’s led to a rapid progress in our
understanding of electron impact on molecules and
solved many long-standing puzzles in atomic physics.
Compound states in molecules which have been ob-
served to date have a lifetime in the range 10~°-10- sec
(r=h/T, where r is the lifetime and I is the width of
the state). They decay by the emission of an electron
into various final states which are accessible energet-
ically. The beauty of molecules is the variety of decay

os fr

4

O5-

0.4

& (v=O=1) (10"%em2)

0.3F

Orr

a a eee po

E (ev)

Fic. 3. Total vibrational cross section to v=1 in Hy. Experi-
mental results using double electrostatic analyzers: O Linder and
Schmidt (1971a); © Ehrhardt e¢ al. (1968); V7 Trajmar et al.
(1970); A Schulz (1964). Experimental results using swarms:
©} Engelhardt and Phelps (1963) ;--- Crompton ef al. (1970).
Eeperimenial results using the trapped-electron method: -»- Burrow
and Schulz (1969). Theory: —Henry and Chang (1972). [From
Henry and Chang (1972).]

channels that are possible for compound states: vibra-
tional and rotational excitation, electronic excitation,
elastic scattering, dissociative attachment, three-body
attachment, and others. Often, a major portion of the
cross section for these processes proceeds via a com-
pound state. This is especially true in the case of vibra-
tional excitation and in several instances of electronic
excitation near threshold, Dissociative attachment can
be completely understood in terms of the formation of
a compound state which subsequently autoionizes and
also separates into a neutral atom and a negative ion.
The lifetime of the compound state, together with the
separation time, determine the magnitude of the dis-
sociative attachment cross section.

The preferential decay of some compound states into
inelastic channels offers certain advantages for the

x
3

SCHULZ

2
°

a
°

2
iS}

ow
i

EHRHARDT et al.

Cross Section, cm?

»
°

5

a 1 | 1

00 10 20 30 40

Electron Energy, eV

Fic. 4. Vibrational cross section to »=2 in hydrogen. The slope
of the cross section near threshold is determined using the trapped
electron method and is indicated by the dashed lines, marked
TEM (Burrow and Schulz, 1969). Also shown are the double
electrostatic analyzer data of Ehrhardt et al. (1968) and Schulz
(1964a). [From Burrow and Schulz (1969) .]

study of compound states. When the bulk of the in-
elastic cross section consists of the decay of the com-
pound state, then the direct-scattering contribution is
nearly absent and one can observe the resonant con-
tribution alone, without interference with the non-
resonant contribution, When one considers the Breit-
Wigner formula, which governs the shape of single

so
soe? TM— T T
4oF
“e
c \ pananor etal.
S 30h 4
o
3
)
a
‘I 4
§ 20+ I
|
I
|
Lor / 7
/
TEM, /
en . .
10 20 30 40 50 60

Electron Energy, eV

Fic. 5. Vibrational cross section to o=3 in hydrogen. The
cross section near threshold is determined by Burrow and Schulz
(1969) using the trapped electron method, shown by the open
circles. The double electrostatic analyzer data of Ehrhardt et al.
(1968) are shown by the solid line. The dashed line is an inter-
polation. [From Burrow and Schulz (1969).]

49


T T T T T T T

Schul

penx (72 Spence & Schulz
s-#-- FITE ET AL.

>
®5

2, Spence & Schulz
& onset {—a— FITE ET AL.
<3 —o— O'MALLEY

£

B2

au

°
300 600 900 ©1200-1500

Temperature, °K

1800 2100-2400

Fic. 73. Temperature dependence of energies of onset and
energies at which peak of ‘Gssociative attachment occurs in O2.
Shown are the results of the same authors as Fig. 72. [From Spence
and Schulz (1969).]

cient shows pronounced structure at the positions of the
vibrational levels of the O:- system. The experimental
results of Spence and Schulz (1972) are shown in
Fig. 70, in comparison with the theory. The good agree-
ment between the energy levels of the O;- system ob-
tained from elastic scattering (shown on top of Fig. 70)
and the positions of the peaks is convincing evidence
that the process proceeds via the O:-(X II,) state.

B. Dissociative Attachment (4.4-10 eV): “Il, State

Dissociative attachment in O2 has been studied in
great detail and Fig. 71 shows that good agreement

T TT T T T
4 4
18
x10 9 TRAJMAR, CARTWRIGHT
2b AND WILLIAMS: 4
4 LINDER AND SCHMIDT
—10;- 4
a
§
Z er 4
Q
B of |
g .
4b . 4
ce]
CONTRIBUTION FROM
ab vecay oro; (ny) _|
. (NORMALIZED AT 7.0 ev)
“1 i ! \ nt 1 1

° 2 4 6 8 10
ELECTRON ENERGY, (eV)

Fic. 74. Cross section for excitation of the O2(a1A,) metastable
state. Shown by the points are the data of Linder and Schmidt
(1971) and of Trajmar, Cartwright, and Williams (1971). The
solid curve, due to Burrow, shows that portion of the cross section
to the 1A, state which proceeds via the Oz (*Iy) state. The cal-
culated curve represented by the solid line is normalized to the
experimental value of Trajmar et al, at 7 eV. [From Burrow

12 14

exists between the results of various experiments, The
cross section for O- production starts rising near 4.4 eV,
reaches a maximum of about 1.3X 10-8 cm? at 6.7 eV,
and then drops. No structure of any kind has been
detected in this cross’ section, nor is there a signal
below 4.4 eV at room temperature (the theoretical
onset for the reaction is about 3.6 eV), to a sensitivity
0.1% of the peak cross section. Spence and Schulz
(1969) and Chen (1969) have reviewed the subject
matter recently.

band “a”

DERIVATIVE OF TRANSMITTED CURRENT (ARBITRARY UNITS)

10 i]
ELECTRON ENERGY, (eV)
Fig. 75. Derivative of transmitted current vs electron energy
in O:. Structures 1-17 are interpreted as resonances whose grand-
parent is the ground state of O;*. A well-developed progression
of ten resonances, marked band “a”, appears near the end of the

spectrum. The grandparent of band “a” is the a ‘IL, state of O.*.
‘From Sanche and Schulz (1972).1]

Noteworthy are the studies of the dependence on gas
temperature of the onset and the absolute magnitude
of the dissociative attachment cross section. These
studies, performed by Henderson, Fite, and Brackmann
(1969) and by Spence and Schulz (1969) show that the
magnitude of the cross section increases as the gas
temperature is raised and that the onset is lowered at
higher temperatures. Figures 72 and 73 show the
results of these studies,

98


ry
L I
I
@ £19.95 eV Sr 1 42045
ryrtyitri * 7 I I
gtistesteiiiiy Cori ittgyty
o ol
ZL L I
5 | rt
Py £= 24,00 eV 10- I
< E I
= go [
F I
Qr I a I
S C I
Bur | | I I I &=22,00eV
B+ Il ] [a
Q guiit 1 boit 0 n n tiit
CUE tl i I
w- Ivy a rity
[ I I [ I I
is I [ I
a I F-23,000V a I £= 2400 eV
foot 11
1
Ca 1 1 1 iJ fone atu Lu J
a3 00 «0 «0° = 8 30 60 90 10°
ELECTRON ENERGY (eV)
Fic. 25, Angular distribution of electrons having excited the

285 state in helium. The incident electron energy E, is indicated.
‘The angular dependence at 19.95 eV corresponds to an s wave,
at 20.45 eV to a p wave and at 21.00 eV to a d wave. All curves
are experimental. [From Ehrhardt and Willman (1967).]

Fig. 26. However, it seems that a note of caution is
appropriate in analyzing the behavior of these excitation
curves within the first 0.5 eV of threshold. This regime
involves electrons which possess only 0-0.5 eV of
energy after the collisions and which must be accepted
by the electron analyzer. For the curves of Fig. 26 to be
meaningful, it is desirable that no energy discrimination.
be present in this energy range. This requirement
imposes a very severe demand on the electron optics
which must exhibit a complete absence of chromatic
aberration in the range 0-0.5 eV. This problem has not
yet been solved. Also, there should be a complete
absence of stray electric and magnetic fields, which
could cause severe discrimination problems. It is
probable that the curves of Fig. 26 are afflicted, within
0.5 eV of their thresholds, by an error of unknown
magnitude, i.e., a correction factor of unknown shape
should be applied to these curves.

One can obtain an indication of the seriousness of the
problem outlined in the previous paragraph by taking
the ratio of cross sections for the 2°S excitation at two
different energies, e.g., the ratio (20.45 eV) /o(19.95
eV). This is the ratio of cross sections near the center of
the ?P resonance to the peak near threshold. For the
curve of Fig. 26, this ratio is about unity (at 70°),
whereas it is about three (at 60°) in the older work of
Ehrhardt and Willmann (1967). One should prefer, at

the present time, the data shown in Fig. 26, due to
Ehrhardt, Langhans, and Linder (1968) in preference
to the older data of Ehrhardt and Willmann since the
former authors have made a study of the energy
discrimination in their apparatus and have come to the
conclusion that the error is less than 50% in the energy
range within 300 meV of the 28S threshold.

The experimentally measured width of the threshold
structure near the onset of the 285 state is about 150
meV and thus should have been noticed in measure-
ments of the total cross section for the 2°5 state.
Although the resolution of many of the experiments on
the total excitation of the 28S state had sufficient
resolution, such a structure was not observed (see,
e.g., Schulz and Fox, 1957) and the total 23S cross
section rises to a broad maximum near 20.3 eV. Pi-
chanick and Simpson (1968) made a careful examina-
tion of the threshold region with the purpose of
examining the threshold structure (see Fig. 23), but
failed to find any indication of its existence. If one
integrates the theoretical differential cross section over
all angles to obtain the total cross section, the threshold
structure becomes almost invisible [Burke et a/. (1967)
and Linder, private communication] and thus the
threshold structure near 19.95 eV cannot be observed
in the total cross section for exciting the 28S state.

e-He n=2

50° x20 '
2'P
ben
90° x2 haan 2p
20° xt

virtual
“
90° x4
70° x2
oy
90° x2
fi

20
L 1 1
2 23

2S

Differential Cross Section (arb. units)

1
19 20 7 22

Electron Energy (eV)

Fic. 26. Energy dependence of the differential cross sections
for the excitation of 2°S, 215, 2*P, and 2'P levels of helium near
threshold, at selected angles of scattering. The angle of observa-
tion is indicated, for each curve, on the left-hand side. The number
following the designation of angle indicates the enlargement of
the particular curve with respect to the 245 curve at 20°. Experi-
mental. [From Ehrhardt, Langhans, and Linder (1968).]

23


Hellum

SS |

oe VO

Electron Currents, (Arb. Units)

1
190 200 210
Electron Energy, eV

Fro, 20. The appearance of the (152s*) #5 resonance in helium
at different angles of observation. The vertical lines indicate a

10% change in the differential elastic cross section. [From Andrick
and Ehrhardt (1966).]

n
180

Adding a 1s electron, we obtain 2S, *P, 4P, and 2D
states. These are the only allowed states within the LS
coupling scheme, which is expected to be applicable
for the case of He~.

It was first pointed out by Fano and Cooper (1965)
that there are restrictions on the quantum numbers of
the compound states that can be reached by the
collision of an electron with a ground-state helium
atom (15). The parity and the total angular momentum
quantum number J of the input channel must be in-
variant in the collision. They must be conserved for the
system e-+He(!S) and for the system He~. The spin
quantum number S and the orbital angular momentum
quantum number are each individually conserved only
insofar as LS coupling is applicable. This should be the
case for helium.

We can eliminate all the quartet states in Table I
because these would require a spin-flip. Also, we can
eliminate, as pointed out by Kuyatt ef al. (1965) the
state *P* resulting from the 1s(2p)? configuration. The
parity of this state is necessarily even. In order to
produce this state from 4S state of helium (parity
even), the electron must have a parity (—1)!, where J
is the orbital angular momentum. In order to produce a
P state from an S state, we must have /=1, e.g., odd
parity. Thus we cannot conserve parity and must

DERIVATIVE OF TRANSMITTED CURRENT (ARBITRARY UNITS)

_ |» | y | 1 4

Fic. 21. Derivative of transmitted
current vs electron energy in helium,
below ionization. The gain of the
amplifier is increased by a factor of
25 for the lower portion of the curve
and by a factor of 100 for the inset in
the upper right, compared to the
region around 19.3 eV. The excursion
around 19.3 eV corresponds to a
change in transmitted current of about
10%. The smaller excursions (e.g.,
#12) thus correspond to a change in
transmitted current of about 0.01%,
which is the limit of this transmission

experiment. [From Sanche and Schulz
(1972).]

21 22 23

24 25

ELECTRON ENERGY, (eV)

19


APPENDIX I
Comparison of the values obtained by different authors for the Hs~ states (eV).

Transmission Inelastic Theory
Vibrational Sanche Kuyatt Comer Weingart- Eliezer
quantum number and Schulz et al. and Read shofer ef al. et al.
(Hs-) (1972) (1966) (1971a) (1970) (1967)=
Bands “a” and “d””
0 11.32 11.28 11.30 11.30 11.32
1 11.62 11.56 11.62 11.62 11.62
2 11.91 11.84 11.91 11.92 11.91
3 12.19 12.11 12.19 12.20 12.18
4 12.44 12.37 12.45 12.46 12.44
5 12.68 12:62 12.68 12.70 12.68
6 12.86 12.89 12.93
7 13.10
8 13.28
Band “b”
2 11.27
3 11.47
4 11.63
5 11.75
6 11.85
7 11.96
Bands “‘c” and “e”
0 11.43 11.46 11.19» 11.50 11.46
1 11.74 11.72 11.50% 11.79 11.75
2 12.03 11.99 11.80° 12.08 12.03
3 12.32 12.27 12.07% 12.38 12.31
4 12.58 12.53 12.58
5 12.83 12.77 12.84
6 13.06 12.97
Band “f”
Golden (1971)
) 13.66 13.62 13.63
1 13.94 13.91 13.93
2 14.20 14.19 14,20
3 14,45 14.46 14.47
4 14.69 14.72 14.70
5 14.93 14.97 14.92
6 15.18 15.21
7 15.43 15.44
8 15.65 15.66
9 15.85 15.87
10 16.07
11 16.26
Band “g”
15.09
15.32
15.57
15.77

* The theoretical values of Eliezer, Taylor, and Williams (1967) for band ‘“‘a” were incremented by 0.25 eV
for purposes of direct comparison with the experimental values of Sanche and Schulz (1972).
> From Joyez, Comer, and Read (1973).

102


KRYPTON

4p5(2P 3,2) 4p5(2P 1,2)
——— 4%

n
13,999 5s 5p 4d 5s 5p 4d is
Zz
~ a
z
13 °
n
lu
iz 4
>
= lab 12.04
. _|et.e7
> = Sll.s4
Oo S>11.40
ae Sil29
2 10.643'P, _lig.gz
wor M 10.562 3P
10.17
10 y 510.032 3p,
9.915 3P2 9.51
ot

Fic. 39. Energy level diagram for krypton. Numerical values are
listed in Appendix VII.

the form (2p%3s%), (3p%4s2), (4p°5s%), and (5p%s%),
respectively, each resonance being split by the amount
indicated in Table II into a *Ps and a 2P;2 component.

Just as in the case of helium, our knowledge of
resonances in Ne, Ar, Kr, and Xe comes from trans-
mission experiments (Kuyatt et al., 1965; Sanche and
Schulz, 1972), from experiments on total metastable
production (Olmsted ef al., 1965; Pichanick and Simp-
son, 1968) and from differential elastic scattering ex-

XENON

Sp5(2P3,5) 5p5(2P),2)
pane Leena eLLe

6s

6p 5d 6s 6p 5d

RESONANCES

ENERGY, eV

Fic. 40. Energy level diagram for xenon. Numerical values are
listed in Appendix VIII.

31

Li Li7

i* (s2) |
5.37 Li* (s*) 's

'p
3.82
2 2 3p
3.88. (!823d) 20 _ pe 3.80
3.84-7) 23.) 2 TD 3.75
(1823p) 2P 3.74
(1s*3s) 2s 3s__ 3.35
Ee 3.29
3.15
'
1.84 —~——— P_ wig
2. 2 .
(Is*2p) ©P \ Ip ~1.8
3
P 0.1
2
(1s@2s) 2s Is
-0.62

Fic. 41. Approximate energy level diagram for lithium and
the compound states calculated theoretically. Values for the
compound states are taken mainly from the work of Moores
and Norcross (1972) and Fung and Matese (1972). The energy
values, in eV, are only approximate. The electron affinity is taken
from Weiss (1968).

No Na
+ 6 '
5.14 Na*(2p®) |S
(2p®3d) 20
(2p®4s) 2s \
3.19 s 3.04
2p®3p) 2P '
oe
Do»
3p
(2p%3s) 2s 0.15
i)
S -0.54

Fic. 42. Approximate energy level diagram for sodium and
the compound states calculated theoretically. Values for the com-
pound states are taken mainly from the work of Moores and
Norcross (1972) and Fung and Matese (1972). The energy
values, in eV, are only approximate. The electron affinity is taken
from Weiss (1968), whose calculated value of 0.539 eV is in
excellent agreement with recent photodetachment experiments
of Hotop, Patterson, and Lineberger (0.5420.01 eV).


oN S OD ®

°o

DISSOCIATIVE ATTACHMENT
@

CROSS SECTION (102° cM?)

go 9°
bo

°
i)

10

9

"i

2

3 14 5 6 17 18 19

ELECTRON ENERGY (eV)

Fic. 15. Isotope effect in dissociative attachment in the neighborhood of 10 eV in Hs, HD, and Ds. [Taken from Rapp, Sharp, and
Briglia (1965).]

analysis, Crompton et al, have to. assume a reasonable
energy dependence for the rotational cross section and
that their approximation to the solution of the Boltz-
mann transport equation is applicable. To that extent,
a discrepancy exists in the threshold behavior, as de-
duced from beam and from swarm experiments.
Crompton’s results based on an analysis of transport
coefficients are also shown in Fig. 3.

The cross sections for excitation of the second and
third vibrational states of H, come from electron beam
experiments and are shown in Figs. 4 and 5, respec-
tively,

The experimental results presented lead to the con-
clusion (Bardsley et al., 1966b; Eliezer et al. 1966) that
the *Z,+ state of Hs is involved in the excitation
process. The width of this state is several eV, as can be
seen in Fig. 6, which shows the dependence of the
width on internuclear separation. Also, shown in Fig. 6
is the dependence on internuclear separation of the
real part of the potential energy curves.

Breig and Lin (1965) and Takayanagi (1965) calcu-
late the vibrational cross section to v= 1 without invok-
ing a compound state, but they include the dependence
of the polarization on the internuclear separation. Breig
and Lin obtain fairly good agreement with the experi-

55

mental observations. (See, e.g., Chen, 1969.) The argu-
ment is sometimes made that the resonance model is
not needed for an interpretation of vibrational excita-
tion. However, it is often easier to understand the
physical processes involved and the processes become
more explicit and readily understandable when one uses
the resonance model. There seems to be no compelling
reason to “hide” the compound state. The resonance
model becomes even more useful for an understanding
of the isotope effect in dissociative attachment, as will
be discussed below.

3. Rotational Excitation via the *%,,* State
and Angular Distributions

The general problem of rotational excitation of mole-
cules has been very recently reviewed by Golden, Lane,
Temkin, and Gerjuoy (1971) and by Takayanagi and
Itikawa (1970), The reader is referred to these reviews
for reference. Of interest for the present purposes is
pure rotational excitation and rotational excitation
which accompanies vibrational excitation, both proc-
esses proceeding via the *2,* compound state in H2.
Figure 7 shows that the energy dependence of the cross
section for simultaneous rotational and vibrational ex-


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is narrow. The structure above 1.8 eV had been previ-
ously observed in the vibrational cross section by
Schulz (1964) and interpreted as evidence for the "II,
compound state, which in Np is sufficiently long-lived
to show vibrational structure. Below 1.8 eV, Schulz did
not observe any structure or other evidence for a com-
pound state, whereas the total cross section of Golden,
shown in Fig. 26, exhibits such structure below 1.8 eV.

In order to resolve this discrepancy, Ehrhardt and
Willmann (1967) re-examined the elastic and inelastic
differential cross sections as well as the total cross sec-
tion, but were unable to reproduce the structures below
1.8 eV. In order to insure the proper working order of
their apparatus, Ehrhardt and Willmann studied the
low-energy structure in NO, which had previously been
measured by Boness and Hasted (1966), and confirmed
this structure both in the total cross section as well as
in the elastic cross section. Thus it is highly probable
that the structure below 1.8 eV, shown in Fig. 26, is
spurious.

The differential elastic cross section at different scat-
tering angles is shown in Fig. 27 and the angular distri-
bution is shown in Fig. 28.

The structure in the elastic cross section above 1.8
eV, as well as in the vibrational excitation indicates the
existence of a compound state whose lifetime is com-
parable to or longer than a vibrational period. The
compound state is formed by the addition of an elec-
tron in a a, orbital to the ground electronic state of No
(Gilmore, 1965; Krauss and Mies, 1970), and this

DERIVATIVE OF TRANSMITTED CURRENT (ARB. UNITS)

| Band
1 tl
Ww
Band "b” Band "c”
pot oy
v 12 13 4 15

ELECTRON ENERGY, (eV)

Fic. 42. Derivative of the transmitted current vs electron
energy in Nz (11-15 eV). The giant resonance marked 1-1’ is the
2y,* state and forms the starting member of band “b,” whose
parents are the # *3,* and a15,+ Rydberg states of No. The grand-
parent is the ground state of Net.Structures 3and 4are shape res-
onances. The other resonances, including bands “c” and “d”
which appear on the higher sensitivity run on the bottom of the
figure, have the A‘, state of Nz* as a grandparent. [From
Sanche and Schulz (1972).]

o's;

ve4 6 8 10121416

Bx,
V=6 8 10 1214

DERIVATIVE OF TRANSMITTED CURRENT (ARBITRARY UNITS)

band “a”

Joy J 4 J 4
9 10 N
ELECTRON ENERGY, (eV)

12

Fic, 43. Derivative of the transmitted current vs electron
energy in Ne (7-12 eV). Structure in the region 7-9 eV is due to
inelastic processes involving the B I, state of Nz. The locations
of the B'II, state, the B1#Z,~ state, and the 212, state of Ne
are indicated. Band “a” is a progression of core-excited shape
resonances associated with the B ‘II, state, and the large structure
(1-1’) is the first Feshbach resonance, *2,+. The bottom trace
Soe with a higher sensitivity. [From Sanche and Schulz

assignment is proven by angular distribution studies
(Ehrhardt et al., 1967, 1968) of inelastically scattered
electrons.

2, Vibrational Excitation via *I,

The vibrational excitation cross sections for the exci-
tation of the first eight levels of the ground electronic
state of Nz clearly show structure which is characteristic
of the compound state. Figures 29 and 30 show the
vibrational cross sections at 20° and 72°, respectively,
as obtained by two different groups. The shape and
general behavior of the cross sections are in good agree-
ment, Table III lists the positions of the maxima of
the features, as observed in the »=0 and v=1 decay
channels. Actually, the positions of the peaks occur at
different positions, depending on the channel of ob-
servation, ie., the peaks shift to higher energies for
higher vibrational states. This effect, first discussed by
Schulz (1964), is shown in Fig. 31. This feature, as
well as the regularity of the structure in the vibrational
cross section, stimulated theoretical interest in the

73


20

x10

3

TOTAL COUNT

0-5)

(a)

[1M

tt

ENERGY (eV)

1

41-0

40-5

24:2

24-4

OPTICAL LINE INTENSITY

He :

_

a Oe

23.5 24

ELECTRON ENERGY (eV)

TOTAL COUNT x10~
o

a

Vl
Ss

WH
6

7

4D

89

ENERGY (eV)

an

2
Ir

Fic. 29. (a) Optical excita-
tion functions of the 415 and
43S states of He (5047 A and
4713 4) after averaging for
180 h. The energy scale is deter-
mined by setting the second
prominent peak of the “15
excitation function at 23.937
eV and for the 4*S excitation
function at 23.939 eV. These
energy values were determined
in a. previous run, [From
Heddle, Keesing, and Kurepa
(1973)-] (b) Optical excita-
tion functions for the 3*D and
48D levels in helium (5876 A
and 4472 A). [From Heddle
(private communication) .] (c)
Optical excitation functions for
the #P (3889 4), 4°P (3188
A), and S*P (2945’A) levels of
helium. From Kisker
(1972b).J

n
24-0
25

2

4


pointing to each vibrational member of a given band.
The first 3 bands have four vibrational members and the
bands start at 5.04, 5.41, and 5.46 eV, respectively.
Band “d” starts at 6.45 eV and six vibronic states

belonging to that band have been observed; four of
these are shown in Fig. 61. The vibrational spacings of
each band and the Franck-Condon probabilities for
bands “a”, “b”, and “d” are compared with the cor-
responding values for the X *Z* ground state of NO+
in Appendix VII. Bands “a”, “b”, and “c” have about
the same spacing, which agrees well with the spacing of
the grandparent NOt core. Band “d” deviates slightly
from the grandparent spacing. Franck-Condon prob-
abilities for bands “‘a”’, “‘b”, and “d” agree qualitatively
with those of the NO+ ion core, even though bands
“a”, “b”, and “c” overlap. All Franck—Condon prob-
abilities listed are normalized to »=1 for comparison
purposes.

The comparisons suggest that all four bands in NO
are composed of two Rydberg electrons temporarily
bound to the same X 4Z+ core of NOt. The parent of
band “a” is probably the A ?=+ Rydberg state of NO
which lies at 5.48 eV. The A state, whose electron
affinity from the above argument is 0.45 eV, cor-
responds to an electron in a Rydberg orbital of the sym-
metry 3so bound to the X 42+ core of NOt. The addition
of another 3so electron to the core gives the 12+ sym-
metry for band “a”.

Bands “b” and “c” which lie 0.07 and 0.02 eV
below the A *Z* state of NO, respectively, could result
from the addition of a 3po or 3pr electron to the A state.
Alternatively, the parents of bands “b” and “c”
could be the C*II and D?Z*+ states of NO, which lie at
6.49 and 6.60 eV, respectively. As far as band “d” is
concerned the only likely parents are the C and D
states of NO.

Paquet, Marchand, and Marmet (1971) have

Not NO-

Fic. 63. The energy
level diagram of rele-
vant NO* grandparent
states (left side of dia-
gram) compared with
the energy level diagram
of the NO~ states ob-
served in the present
experiment (right side
of diagram). The two
energy scales have been
displaced by the binding
energy of the lowest
member of band “a”
with respect to

22
elt
2

STATES, (eV)

>
fe)

|
|

io
=

its
grandparent X ‘2+ state
of NO*. Each state of
NOt, shown on the left
of the diagram, gives
rise to a Rydberg series
of NO- states. [From
Sanche_ and Schulz
(1972).]

“gd

Is+ NY
xz “eg

POTENTIAL ENERGY OF NO

=

L

POTENTIAL ENERGY OF NO* STATES, (eV)

| ek 5 vse vn? vee ved

hyd

WIDE ANGLE - TOTAL
(SPENCE & SCHULZ)

x

DIFFERENTIAL - ELASTIC
(BONESS & SCHULZ)

o~ TRANSMISSION - TOTAL
(BONESS & HASTED)
SHIFTED O.4eV

CURRENT , ARB, UNITS

[__— TRANSMISSION - ELASTIC
(HASTED & AWAN)
SHIFTED 0.25 eV

poet

n n
04 06 O08 1.0
ELECTRON ENERGY, eV

Fic. 64. Comparison of four experiments on the structure in
the electron impact cross section in O.. The top curve shows the
wide-angle total cross section (Spence and Schulz, 1970), the
next curve shows the differential elastic cross section (Boness
and Schulz, 1970). The bottom two curves represent transmission
experiments. The curve by Boness and Hasted (1966) is shifted
by 0.4 eV and the curve by Hasted and Awan (1969) is shifted
by 0.25 eV, both to lower energies. The agreement in the spacing
of the structures is considered good. The indicated quantum num-
une to the O;-(X*I,) state. [From Boness and Schulz

recently postulated the presence of two long-lived
bound negative ion states at 7.8 and 8.2 eV, in order to
explain two peaks they observe in the cross section
for O~ formation from NO at these energies. The postu-
lated states should appear in the total scattering cross
section, The 5th vibrational member of band “d,” which
lies at 7.83 eV, could possibly account for the 7.8-eV
peak in the O~ data at Paquet e¢ al.

2, Region 12 eV-18 eV

The resonances shown in Fig. 62 for the energy range
12-18 eV seem to have as their grandparents excited
states of NO*. At least ten bound excited states of NO*
are known at the present time and four of these, namely
the 5°II, A Il, c*I, and B'Tl ion states, can be con-


W716 _

19 Moveable

| 13 \ Molecular Beam

Monochromator

Rotatable

Fic. 4. Schematic diagram of a typical electrostatic monochromator with electrostatic analyzer. Angular distribution can be ob-
tained by rotating the analyzer with respect to the monochromator. Elastic and inelastic differential cross sections can be obtained
with such an instrument. [From Pavlovic, Boness, Herzenberg, and Schulz (1972).]

are counted. Use of a well-collimated molecular beam
reduces Doppler broadening of the resonances. The
electron optics is designed to maintain constant trans-
mission characteristics throughout the spectrometer.
Many shields are usually necessary (S,-Ss) to restrict
stray electrons from reaching the multiplier. One
usually eliminates magnetic fields from the collision
region, either by using a magnetic shield or by using
Helmholtz coils.

Double electrostatic analyzers of the type shown in
Fig. 4 have given a wealth of information on resonances.
Usually, one obtains the energy dependence of the
elastic or the specific inelastic cross section at a fixed
angle of observation. Structure in such curves is
analyzed and the position and the width of resonances
can be deduced. Alternatively, one can obtain at a
given incident energy the angular distribution of elec-
trons. Such information is valuable for determining the
configuration of particular resonances. The inelastic
cross sections that have been studied are the vibrational
and the electronic cross sections. Rotational cross
sections have been studied only in the single case of He.

Measurement of Resonances in the Total Cross Section:
The Transmission Method

The transmission method can also be used for
studying resonances. In the appropriate geometry, the
transmitted current J, through a gas-filled chamber is
related to the incident current J) by the relation
I,=Io exp (—NQ.L), where N is the gas density, Q; is

the total cross section, and L is the length of the colli-
sion chamber. Small excursions in the cross section Q;
which often indicate the existence of resonances are
exhibited by structures in the transmitted current. In
fact, when NQ:L 21, then some amplification of the
structure takes place; i.e., the percentage change in the
transmitted current is larger than the percentage
excursion in the cross section. This fact can be utilized
for a very sensitive measurement of resonances. A
further refinement can be introduced by modulating the
energy in the collision chamber and by observing
essentially the derivative of the transmitted current.
An example of the arrangement for a transmission
experiment is shown in Fig. 5. Here, a trochoidal
monochromator is used for creating a monochromatic
beam in an axial magnetic field. The electrons then
enter the collision chamber region, maintained at a
pressure of about 10-* Torr, in which a cylindrical
electrode M is mounted. A small modulation voltage
(0,005-0.06 V) is applied to electrode M so that the
electron energy in ‘the collision chamber is modulated.
The modulated transmitted signal is detected on the
collector C. The retarding electrodes R are used to cut
off all those electrons which have made collisions in the
collision chamber, so that only the unscattered electrons
are transmitted to the collector C. Only under such
circumstances is the exponential relationship between
the transmitted and the incident current valid.
Copious examples are given in the text showing the
sensitivity of this method of measurement, both for


() O° ENERGY LOSS

(0) €°5'g AE=H.87 eV

20° ENERGY LOSS
Joe
a” 5g, AE=12.23 ev

& Iq AE=11.87 eV

12.0
(b) _
ae reer es
12.0 13.0 20 ENERGY LOSS
0 /\_
Ae
12.0 13.0

METASTABLES
@)
120 13.0 140
IMPACT ENERGY (eV)
L (c) Threshold V=0 E°S¢
xy x exp,
e] * 014+2co0s?6
3 .
é .
sr x
g .
8
£ .* *
3 x « vio ESS
ot 8 : | e 2908
H tae
2
3
3 corwadTM,
aivewadl,
ie i, 5
re a ee Re nal nar nee,
50 100 eo
scattering angle incident energy (eV)

Fro. 44. (A) Threshold region for excitation of the £#2,+ and a’’1,* states of Nz. Shown are the differential cross sections of
Heidemann et al. (1966a) at 0°, and Ehrhardt and Willmann (1967) at 20°. Also shown is the excitation function for metastables
(Lawton and Pichanick, 1973). [From Lawton and Pichanick (1973). (B) Energy dependence of the differential excitation cross
section for the J *,*(v=0) state of Ns, at different angles of observation. The sharp peak near 11.90 eV hasa half-width of 35-5 meV
at 90° and exhibits the angular behavior shown in Fig. 44(C). [From Mazeau, Hall, Joyez, Landau, and Reinhardt (1972b).] (C)
Angular distribution of electrons having excited the E *2,*(0=0) state in Nz at 11.90 eV. Also shown is an angular distribution of the
form (1-+2 cos*#), normalized to the experimental data at 90°. The good agreement between the angular distributions points to a
po partial wave, indicating that the threshold behavior is dominated by a shape resonance. [From Mazeau, Hall, Joyez, Landau,
and Reinhardt (1972b).]

74


(arb. un.)

differential cross sections

=

DERIVATIVE OF TRANSMITTED CURRENT (ARB. UNITS)

8

ZS

ENERGY, (eV)
3

10 "
collision energy (eV)

ANNI

12
ELECTRON ENERGY, (eV)

ooo"
scattering angle

coTM
cota?n
cota

Feshbach
Res.

—- ee.

L_4 cotx?s*

in

[Grandparent

Fic. 55. (A) Derivative of trans-
mitted current vs electron energy in
CO, Resonances 1-4 are associated
with the 635+ and B1z+ parent
states of CO. The locations of these
states and the j and ¢ states are
indicated. Band’ “a” whose grand-
parent is the AIT state of COt,
appears near the end of the spectrum.
‘The gain on the lower curve has been
increased by a factor of 8. The smaller
structures on that curve represent
variations in the transmitted current
of about 0.01% which is the detection
limit of the present experiment.
[From Sanche and Schulz (1972).]
(B) Schematic energy level diagram
of CO and the compound states. The
lines with the arrows show the pre-
ferred decay channels for the com-
pound states. On the left side of the
diagram are shown the low states of
CO, i.e., a5 (6.01 eV); a’*B* (6.86
eV); Ai (8.03 eV); b%E+ (10.39
eV); and B+E+ (10.78 eV). The pre-
ferential decay is based on the work of
Comer and Read and of Mazeau et al.
The decay into C+O> (dissociative
attachment) is shown on the right
side. (C) Differential excitation func-
tions for the b*E* v’=0 level in CO.
‘The curves on the left show the energy
dependence at 40°, 70°, and 90°. The
downward pointing arrows point to
shape resonances at 10.7 and 11.2 eV.
The upward pointing arrows indicate
Feshbach resonances (11.3 and 12.2
eV). The diagrams on the right side
show angular distributions at specified
electron energies. The points on the
diagram in the center (10.7 eV) rep-
resent the function (1+7 cos’),
normalized at 90°. [From Mazeau,
Gresteau, Joyez, Reinhardt, and Hall
(1972a).]


x
3
T

TOTAL PHASE SHIFT
ET
T

T

CROSS SECTION

|
‘° Eo Ee °

ENERGY >

Fic. 1. Partial wave phase shift near a resonance (top portion)
and resulting shape of the cross section near a resonance (bottoms
portion). The figure illustrates the interference between potential
and resonance scattering. [After Smith (1966).

ference. The phase shift 7 which always enters the ex-
pression for the elastic cross section [for s-wave scat-
tering we can write o(Z) =4nX* sin? 7], increases by
radians as the energy traverses each resonance. This
can be seen from the expression for the resonant con-
tribution to the phase shift, tres= — cot [(E—Ey) /41°}.
The smaller the width I’, the more rapidly occurs the
traversal of the phase shift by radians. In Fig. 1 we
plot the phase shift as a function of energy near a
resonance for four arbitrary cases. The phase shift for
potential scattering is different for each case, but in
each case it increases by radians as the energy
traverses the resonant energy Ey. The shape of the
resulting cross section, shown on the bottom of Fig. 1,
shows the expected interference structure. The position
of Ey is defined to be the energy at which the resonant
portion of the phase shift has increased by 47; ice.,
Mres=3(2n-+1)m. That is the position where the total
phase shift (consisting of the sum of the phase shifts
due to potential and resonant scattering) has increased
by x/2 radians above the phase shift due to potential
scattering which prevails just below the resonance.

When we are dealing with inelastic scattering, decay
can take place to a state other than the ground state,
and the resonant portion of the cross section becomes
aL inTour/[(E~Eo)?-+ (41)*]. Here Tin is the width
for decay into the ground state plus a free electron and
Tous is the partial width for decay into the excited state
plus a free electron. Then we have P=Tin+Tout-

It is often desirable to evaluate line profiles of
resonances using the formula due to Fano (1961) and

to Fano and Cooper (1965a) :
o(E) =o (q+6)?/(1+e) }+0..

Here, og and gp are the resonant and nonresonant
portions of the cross section, e= (E—Ey)/3T, and q is
the “line profile index.” Simpson ef al. (1966) describe
how one can evaluate the parameter g from experi-
mental measurements. In fact, many authors extract
this parameter from their experimentally observed line
profiles. Figure 2 shows the line profiles plotted for
various values of the parameter g.

If one wishes to analyze the line profile in terms of a
symmetric and an asymmetric component, one can
write (Shore, 1967)

o(E) =C(E) +40 BL(E— Bo)*+ (1/2)?
+D(E- Ey) ((E—Ey)*+ (1/2)?

The parameters B and D, specifying the symmetric and
asymmetric components of the line, are constants. They
are related to the Fano formula by the equation B/D=
(¢@—1)/(29). Comer and Read (1972) have developed
a simple method for obtaining resonance energies from
broadened profiles using the formulation of Shore.

Recent reviews of the theory have been assembled by
Smith (1966) and by Burke (1968).

B. Relationship of Theory to Experiment

The search for resonances in atoms by experimental
methods consists of a search for structures in various
cross sections. In circumstances when this structure is
relatively narrow (<300 meV) and far removed from
neighboring resonances, little ambiguity exists. In
cases when the structure is broad, further verification is
needed. Often, the angular distribution of scattered
electrons can elucidate the process involved. In mole-
cules, dissociative attachment and vibrational excita-
tion provide extra evidence. This multiplicity of decay
channels often makes the identification of resonances
easier in molecules than it is in atoms.

There are many theoretical approaches to the cal-
culation of resonances but a thorough review is beyond
the scope of this paper. Nicolaides (1972), in reviewing
the field recently, lists many of the pertinent theoretical
references. One may rather arbitrarily divide the
theories into the following classifications:

(a) Theories using the “scattering viewpoint.”

(b) Theories treating resonances as a “decaying
state.”

(c) Theories treating resonances as special types of
bound states using projection operators.

(d) Theories treating resonances as special types of
bound states without use of projection operators.

The theories which use the scattering viewpoint, as
exemplified by the close-coupling method, essentially
simulate a scattering experiment and they calculate
cross sections for various processes from the phase


APPENDIX XI

Core-excited resonances in O2 as observed in a transmission experiment (Sanche and Schulz, 1972).

1-1’ 2 3-3! 4 5-5’
8.03-8.06 8.12 8.24-8.28 8.34 8.47-8.54
6-6! 7 8-8" 9-9! 10-10’
8.71-8.78 8.90-8.98 9.08-9.11 9.16-9.23 936-944
11-11 12 13-13-13 14-14’ 15-15’
9,53-9.61 9.73 9.86-9.92-9.98 10.43-10.48 10.55-10.61
16-16’ 17-17'
10.74-10.82 10.91-11.00
Band “a?
11.81 11.93 12.05 12.17 12.29
v=1 v=2 v=3 =4 v=5
12.40 12.51 12.62 12.73 12.84
v=6 v=7 v=8 v=9 210
Band “b”
14.27 14.43 14.58 14.72
*The writing of this review was supported by the National Lett. 1, 169.

Bureau of Standards, Office of Standard Reference Data, as
part of the National Standard Reference Data Program.

Abram, R. A., and A. Herzenberg, 1969, Chem. Phys. Lett.
3, 187.

Badger, R. M., 1935, J. Chem. Phys. 3, 710.

Bardsley, J. N., A. Herzenberg,, and F. Mandi, 1966a, Proc.
Phys. Soc. Lond. 89, 305.

Bardsley, J. N., A. Herzenberg, and F. Mandl, 1966b, Proc.
Phys. Soc. Lond. 89, 321.

Bardsley, J. N., and F. H. Read, 1968, Chem. Phys. Lett.
2, 333.

Bardsley, J. N., and F. Mandl, 1968, Rep. Prog. Phys.
31, 472.

Bates, D. R., and H. S. W. Massey, 1954, Philos. Mag.
45, 111.

Berkowitz, J., W. A. Chupka, and D. Gutman, 1971, J. Chem.

Phys. 55, 2733.

Birtwistle, D. T., and A. Herzenberg, 1971, J. Phys. B 4, 53.
Black, K. F., and N. F. Lane, 1971, in Electronic and Atomic
Collisions, Abstracts of Papers of the VIIth International

Conference on the Physics of Electronic and Atomic
Collisions (North-Holland, Amsterdam), p. 332 (1971).
Blatt, J. M., and V. F. Weisskopf, 1952, Theoretical Nuclear

Physics (Wiley, New York), p. 360 (1952).
Boness, M. J. W., and J. B. Hasted, 1966, Phys. Lett.
24, 526. ,
Boness. M. J, W.. J. B. Hasted, and I. W. Larkin, 1968, Proc.
R. Soc, A305. 493.
Boness, M. J. W., and G. J. Schulz, 1970, Phys. Rev. A
2, 2182.
Borst, W. L., and E. C. Zipf, 1971, Phys. Rev. A 3, 979.
Breig, E. L., and C. C. Lin, 1965, J. Chem. Phys. 43, 3839
Brongersma, H. H., A. J. H. Boerboom, and J. Kistemaker,
1969, Physica (Utr.) 44, 449.
Brongersma, H. H., and L. J. Oosterhoff, 1967, Chem. Phys.

108

Browne, J. C., and A. Dalgarno, 1969, J. Phys. B 2, 885.

Buchelnikova, I. S., 1959, Sov. Phys.-JETP 8, 783.

Burke, P. G., and A. L. Sinfailam, 1970, J. Phys. B 3, 641.

Burke, P. G., 1968, Adv. At. Mol. Phys. 4, 173.

Burrow, P. D., 1973 (unpublished).

Burrow, P. D., and L. Sanche, 1972, Phys. Rev. Lett. 28, 333.

Burrow, P. D., and G. J. Schulz, 1969, Phys. Rev. 187, 97.

Celotta, R. J., R. A. Bennett, J. L. Hall, M. W. Siegel, and J.
Levine, 1972, Phys. Rev. A 6, 631.

Chang, E. S., and U. Fano, 1972, Phys. Rev. A 6, 173.

Chanin, L. M., A. V. Phelps, and M. A. Biondi, 1962, Phys.
Rev. 128, 219. .

Chantry, P. J., 1968, Phys. Rev. 172, 125.

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Chantry, P. J., and G. J. Schulz, 1967, Phys. Rev. 156, 134.

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16 a2)

TOTAL EXCITATION CROSS SECTIONS (10

COLLISION ENERGY (eV)

Fic. 49. Absolute cross sections for vibrational excitation of
the CO molecule, The arrows point to the threshold energies of
the individual vibrational states. [From Ehrhardt, Langhans,
Linder, and Taylor (1968).]

time enough to vibrate once before autoionization takes
place, Thus the Nz:~(*H,) state lies intermediate in
lifetime between long-lived compound states [e.g.,
Os-(X*I,)] and short-lived compound states [e.g.,
H;-(?2,*+)]. This “boomerang” model is shown sche-
matically in Fig. 34.

[aor

cba

6

‘SCHULZ |
| emmerorwe
HAKE
_b :
PHELPS

10
Electron Energy, eV

e's
B88!

1

Cross Section, cm?
2
a

°
es
1

2

Fic. 50. Threshold behavior of the cross section for exciting
the o=1 state in CO. Shown are the results of Hake and Phelps
(1967). The portion of the data by Hake and Phelps indicated
by the dashed line are only approximate. Also shown are the
results of Ehrhard ef al. (1968), Schulz (1964), and the trapped-
electron data (marked TEM) ‘giving the slope near threshold
(Burrow and Schulz, 1969). [From Burrow and Schulz (1969).]

78

e-CO elastic channel

Wev ft .145eVt, 20eVt. 350
10 . . .
mn °0 30 6 0° BGO 90D HBO 900 BO BS
2 e-CO inelastic channel v=1
2 . 1.55eVt .1.83eV + 2.35eV
< 9973060 G0” 0-30 G0 90° 0 30 60 90
e-CO inelastic channel v=2,34,6
ve2 ve3 veh vs6
of + 2.25eV1 + 2.25eV [| .1.80eV | , 2.05eV

0 aa,
0 30 6 90 0 30 60 90 0 3060 90 0 30 50%

scattering angle C degrees

Fic. 51. Angular dependences of elastic and inelastic scattering
of electrons by CO molecules at different collision energies. In
the elastic channel (upper row) the angular dependence changes
rapidly with energy since the scattering contains several partial
waves with varying phase shifts (energy close to threshold).
The constancy of the curve shapes for all inelastic channels at
energies within the resonance region demonstrates that a com-

yund state with a well-defined set of quantum numbers exists.

Front Ehrhardt, Langhans, Linder, and Taylor (1968).]

4 | Franck-Condon Region

eV
2 0(3P)+c(3P)

Observed
onsets for CTM
.
84— 0(3p)+C(4s)
-9.62— o (2p}+-c(3p)

POTENTIAL ENERGY, (eV)

fe COX E*)

siitl iii
06 10 14 18
INTERNUCLEAR SEPARATION (R)

Fic. 52. Hypothetical potential energy curves for CO- sys-
tems showing the possible decay of the 2+ resonance at 10 eV
into the O-@P)+C(@P) and O(¢P)+C- (45) dissociative attach-
ment channels. The onsets for the negative ions are taken from
the work of Stamatovic and Schulz (1970). [From Sanche and
Schulz (1972).]


APPENDIX IV
Energies of resonances in Nz (11-15 eV).

Feature Differential elastic | Trapped Total
number Transmission and inelastic electron metastable E*Z,+, a’ 12,+
Sanche and Heideman Lawton and
Fig. Schulz et al, Comer and Read Hall ef al. Pichanick Mazeau et al.
42 (1972) (1966a) (1971b) (1970) (1973) (1972b)
“bp? 11.47-11.51 11.48 11.48
11.74-11.78 11.75 11.75} band “b”
12.02
3 11.92 11.87 11.87 11.87 11.90
4-4! 12.18-12.27 12.205 12.25 12.12/12.25 12.14
5 12.64 12.59 12.54
6 12.87 Ehrhardt and Will- 12.78
mann (12,+) 12.80
on 13.00 13.0 13.03 12.98
13.23 13.24 13.21
13.50 13.52 13.44
13.70 13.66
“a” 13.88
14,12 14.2 13.73
14,36 13.86
14.57

All structures are Feshbach-type resonances except structures 3 and 4-4’, which are identified as shape reso-
nances. Additional shape resonances have been observed by Mazeau et al. (1972b) at 12.40 eV in the E*Z,* (v=1)
channel and at 12.70 eV in the E*2Z,*+ (v=0) channel.

APPENDIX V
Energies and spacings of shape resonances connected with the BI, state in Ne.
Transmission Bl, decay channel (Mazeau et al., 1972c)
(Sanche and Schulz, 1972) Energy,* eV
Energy,» eV Spacing, meV v=1 v=2 v=3 v=4 v=5
9.070
9.23 9.220 9.155
9.35 130 9.360 9.300

9.49 125 9.500 9.445 9.400 9.365

9.61 120 9.635 9.590 9.540 9.505
9.73 120 9.760 9.730 9.675 9.645 9.600
9.85 115 9.885 9.860 9.810 9.780 9.730
9.96 115 10.005 9.980 9.940 9.910 9.860
10.07 110 10.120 10.095 9.065 10.035 9.990
10.18 105 10.200 9.175 10.155 10,115
10.29 105 10.305 9.285 10.265 10.230
10.39 100 10.405 9.395 10.375 10.345
10.49 100 10.505 9.495 10.480 10.450
10.58 90 9.595 10.575 10.555
10.67 90 9.695 10.670 10.655
10.76 90 10.765 10.745
10.85 85 10.850 10.835
10.93 85 10.930 10.920
11.02 85 11.000
11.075
11.150

104


2. Vibrational Excitation (0-1.4 eV)

The vibrational cross section, as measured by Spence
and Schulz (1971) using the trapped-electron method,
exhibits (similar to the case of Oz) a series of spikes
superimposed on a slowly rising background (“direct”)
cross section. The results are shown in Fig. 58. Here, the
vibrational levels of the compound state (as determined
by the elastic scattering experiments of Fig. 56) are
shown by the vertical lines. The agreement between the
location of the “spikes” in the vibrational cross section
and the location of the compound states from elastic
scattering is very good and justifies the model used.

One important result obtained by Spence and Schulz
involves the observation that the »=4 state of NO is
accidentally coincident in energy (within +10 meV)
with the v’/=6 state of NO-. The trapped-electron
method has a high sensitivity for detection of such
coincidences. This comes about by plotting the positions
of the peaks in the trapped-electron current as a func-
tion of well depth. If an excitation function contains a
dominant spike (resulting from a resonance), then the
peak of the trapped-electron current occurs at the
energy of the spike and a plot of the position vs well
depth is a horizontal straight line. Otherwise, such a
plot is a straight line with slope of unity.

Spence and Schulz (1971b) observe that the
branching ratio, ive., the ratio of cross sections for
various final states of NO via a given state of NO-, is

°

°
&

2

Potential Energy (ev) ——

°

-0.|

nN n L L 1 1
WW Sa SN

Internuclear Separation (4) ——

Fic. 59. Potential-energy curves for NO(X#U,) and
NO-(X#3-). The width of the levels of NO- have been omitted.
In order to bring the NO curve into agreement with the results
of photodetachment experiments, one should shift the minimum
of the NO- curve to 1.258 A and the spacings of the vibrational
levels should be decreased. [From Spence and Schulz (1971b).]

seeee Paquet ot al. (1971)

Ono 00.00 Rapp & Briglia (1965)
0000 Chantry (1968)
z
Z
a
g
<
z
=
z
5
3
z
g Q °, 5
7 3%, %o
"00
~ TM °° bog
65 70 75 80 85 90 95 100 105

ELECTRON ENERGY (eV)

Fic. 60. Negative ion formation by dissociative attachment in
NO. Shown are the results of Paquet, Marchant, and Marmet
(1971), of Chantry (1968), and of Rapp and Briglia (1968).
Dissociative attachment in NO leads exclusively to electronically
excited N. [From Paquet, Marchand, and Marmet (1971).]

close to unity, in sharp contrast to the case of Os.
They deduce that the barrier height involved in the
case of NO is lower than that in O2 and that probably a
p wave dominates the electron escape. The resulting
lower barrier leads to a short lifetime of NO~ (~10-"
sec) compared to the lifetime of 0. (~10-® sec).
The assumption of a p-wave barrier is consistent with
the theoretical considerations of Bardsley and Read
(1968) who point out that the partial waves which are
being mixed are the px and dm waves (see Sec. VII).
Bardsley and Read also point out that in resonance
formation and decay at low energies, a p-wave com-
ponent is much more efficient than a d-wave component.
The centrifugal barrier through which the incoming or
outgoing electron must tunnel is much higher for d
waves than for p waves. Although d waves may be
more important than p waves in the interior of the
molecule, this is not necessarily true near the surface.

Spence and Schulz (1971b) deduce the values of w,
from the spacing of the peaks in the elastic and the
vibrational cross sections, and they calculate the
equilibrium internuclear separation for NO~ using
Badger’s rule (Badger, 1935). Table VII shows a
comparison of the values thus calculated with the values
from photodetachment experiments. The schematic
potential energy curve deduced by Spence and Schulz
is shown in Fig. 59. In order to bring the NO~ curve into
agreement with the results of photodetachment experi-
ments, one should decrease r. to 1.258 A and should
decrease the spacing of the NO“ levels somewhat so that
the coincidence of the level »'=6 of NO~ with »=4
of NO can be maintained and so that the v’=0 level
comes to —0,024 eV.

89


(1971a), all the rotational effects can be interpreted
by considering both the direct-excitation component
and the resonance component to the phase shifts. The
theory of Abram and Herzenberg (1969) which is based
on a pure resonance model accounts well for the angular
distributions observed by Linder and Schmidt (1971a)
for pure rotational excitation, o( j= 1-3).

The suggestion has been advanced by Frommhold
(1968) that electrons of thermal energy (10-100 meV)
exhibit resonant behavior in exciting rotational states
of Hz and D». Evidence for this hypothesis comes from
the pressure dependence of the drift velocity, which is
observed by Frommhold and by Crompton and Robert-
son (1971) in swarm experiments.

Recently, Raith and Land (1972) used a time-of-
flight electron spectrometer to perform a transmission
experiment in H, and De in order to confirm the exist-
ence of resonances at very low electron energies in H2
and D:. In Hp, they observe structures in the trans-
mitted current at about 24 meV and in the range 60-90
meV. In Dz the results are qualitatively different, with
structure appearing between 26 and 60 meV. The
width of the 24-meV structure in H; is approximately
3 meV, of which about 1.5 meV can be attributed to
Doppler broadening. Rotational excitation is expected
to be governed by the selection rule AJ=0, +2, where
lis the orbital quantum number of the scattered elec-
tron. Thus we expect inelastic processes to have thresh-
olds at 44 meV (for J=0—2) and at 75 meV (for
J=1-—3) in Hy) and at half these values in Dz. The
observed structure thus lies below the first inelastic
process in H, and above it in D.. If the structures ob-
served in the experiment of Raith and Land are reso-
nances, which is by no means certain, one must await

io}

a

N —_

ray 1140 ev

a

a VI

4 f 1170

£ a)

2 1.27 4%

Ee | 012.00

=z { {

Fic. 16. Fine struc- 11.57 ©

ture in dissociative at- © Po
tachment i in He. - [Taken 3 { °°
from Dowell and Sha 12.25)
(4968)..] xP 3 11.87 oF

5 °

cI fp.

a °°

= 12120

a °

&

e °

»

° °

z

S

1 tid 1 a)

ELECTRON ENERGY (ev)

— Band

=

z

: |

>

z

<

=

e

3 HV Anmenrnn

2

=<

= Band "f"

FA

2

2

5

3

re]

z

Z

= inl ”

. Tot

Littiis

° Band “a”

2

=

<

i i

z |

& YW
Pei | yo ] yo | yj yt
W 12 13 4 15 16

ELECTRON ENERGY, (eV)

Fic. 17. Derivative of transmitted current vs electron energy
in Hy. Four progressions of negative ion states are labelled “a,”
‘c,” “f,” and “g.” See Table II. Band “b” seems to be observable
only i in high vibrational states, and thus does not seem to appear
in transmission experiments. Band “d,” if it exists as a separate
entity, is energetically coincident with band “a.” For the lower
portion of the figure, which shows bands “f” and “g,” the gain
has been increased by a factor of seven. [From Sanche and
Schulz (1972).]

a theoretical interpretation for an understanding of this
phenomenon.

The preliminary theoretical work by Kouri (1968)
has not confirmed the reality of this process, and further
developments must be awaited. At this writing, the
existence of resonances in the energy range 10-100 meV
is puzzling, since no molecular orbitals are available
at such low energies, and since close-coupling calcula-
tions (Henry and Lane, 1969) do not give an indication
for rotational resonances.

4, Dissociative Attachment at 3.75 eV

The ?5,,* state of H:~ also plays a role in dissociative
attachment. It is characteristic of many compound
states that they decay into all channels that are ener-
getically accessible and allowed by selection rules, The
dissociative attachment channel opens up at an electron
energy (D—A), where D is the dissociation energy of
Hy (4.48 eV) and A is the electron affinity of H (0.75
eV). Thus one would expect a threshold for H~ forma-
tion from H, at 3.73 eV. Figure 11 shows the experi-
mental result of Schulz and Asundi (1967), who ob-

57


20

Fic. 11. The energy dependence of
the total cross section for dissociative
attachment in Hs, HD, and D; near
3.7 eV. The process shows a very large
isotope effect and proceeds via the
32, states of Hz. Part (a) shows the
experimental results of Schulz and
Asundi (1967) and part (b) shows
the unfolded cross sections as re-

ted by Chen and Peacher (1968a).
Fe should be noted that the experi-
mental curves of Schulz and Asundi,
shown on the left side of the diagram,
have peak cross sections differing by
orders of magnitude (1.6X10~ cm?
for Hz, 1X10 cm? for HD, and 8X
10-TM cm? for Dz). Whereas the H~/H:
cross section was obtained with an
electron energy distribution of 0.1 eV
the curves for HD and D, had to be
taken with an energy distribution of
0.45 eV in order to gain sensitivity. 5
This accounts for the difference in
the threshold behavior. The rising

tion of the D-/Ds cross section,
Indicated by dashes, is real having
been reproduced by Ziesel and Schulz
(unpublished). It could result par-
tially from the wings of the 25,* re-

1022

15

10

4
X OOK

1023

(a) (b)

22 He
10° x oDK

7.5 x 107 x oh?

HD
XODR

1
|
!

1.7 x 10% x 082

1 l i

sonance near 10 eV.

by Sanche and Schulz (1971, 1972), who find that many
experimentally observed negative ion bands can be
simply correlated with grandparent positive ion states.
They find that the compound states usually lie about
4 eV below the grandparent from which they are de-
rived, ie., the binding energy of the two Rydberg
electrons is 4 eV.

Resonances associated with valence excited states are
also known, but as pointed out above, they do not seem
to lead to sharp structures in cross sections. Their
effect has been studied in dissociative attachment and
in vibrational excitation; they may also play a role in
excitation of electronic states of molecules. It is pointed
out by Pavlovic e¢ al. (1972) that at higher energies
the density of doubly excited valence states becomes
large and that resonances associated with each valence
states may make a dominant contribution to excitation
functions at energies in the 20-eV range.

Il. HYDROGEN

The ground state of Hz consists of two electrons in
the 1so, (=ggls) orbital (Herzberg, 1950). The lowest
unfilled orbital, in the notation of the united molecule,
is 2pe., which is equivalent to o,1s. It is this orbital
which the incident electron occupies when forming a
resonance at low energy. In escaping from this orbital
the electron must tunnel through a p-wave barrier.
Bardsley et al. (1966b) and Eliezer et al. (1967) have
shown that the ground state of Hi is indeed a shape
resonance and that its designation is *2,+. The angular
distribution measurements of Ehrhardt ef al. (1968) on
electrons having excited the v=1 vibrational state of

l
3.6 38
Electron energy, eV

45 5.0 4.0 4.2 44 46

Hy show a p-wave character (minimum at 90°) and
thus confirm the designation given above,

A. Resonance at Low Energy: 0-4 eV (°2,*)
1. Elastic Cross Section

The lifetime of the *2,* state is very short and the
width very large; therefore there is little or no evidence
for the *2,+ state in the elastic cross section (Golden
and Nakano, 1966). Figure 1 shows the energy de-
pendence of the total cross section as measured in a
Ramsauer-type apparatus by Golden and Nakano and
the elastic cross section only, as measured by Linder
and Schmidt (19712). No clear-cut evidence of the
action of a resonance can be seen in these curves.
Rather, one has to study other decay channels to
establish the existence of this state. Vibrational excita-
tion, rotational excitation (including angular distribu-
tion), as well as dissociative attachment, are the pos-
sible decay channels that can be usefully studied by
electron impact in order to establish the existence of
such resonances. Also, angular distribution measure-
ments are very useful in establishing the existence of
resonances. These are discussed separately for each
molecule and a summary is given in Sec. VII. The ex-
perimental and theoretical considerations regarding
elastic and rotational cross sections in H; have been
recently reviewed by Golden ef al. (1971) and the
reader is referred to this reference.

2. Vibrational Excitation in Hz via *2,.+

It is only in the past 10 years that experiments on
vibrational excitation have led to the present-day under-

53


T T T
Eo*=9.56eV
0.10 F 4
_
°
S
£
&
fry
Gg ops F n 4
a °
g 0,01 ev
S 0.03 ev
2 0.04ev
@ = 90° 0.048 ev
AG=15° 0.110 eV
08 +- A¢gzi5 4
520.06 eV
1 L !
as 9.0 9.5 10.0

105

ELECTRON ENERGY (eV)

Fic. 14. Comparison between experimental and calculated cross sections in the region of the 1S and *P resonances in hydrogen.
The positions of the two resonances are fixed at 9.56 and 9.73 eV, respectively, and the width, I'o* of the 1 resonance is varied from
0.61 to 0.110 eV. The best fit to the experimental data, indicated by the circles, is obtained when I's =0.043+40.006 eV. [From McGowan

(1967).]

with a broader electron energy spread. Also, the sharp
peak near threshold is consistent with theory.

Two subsidiary peaks in the experimental curve
shown in Fig. 17 occur at 10.45-+0.03 eV and at 10.65
0.03 eV, ie., just above the »=2 state of hydrogen.
According to McGowan et al. (1969), the first of these
is statistically real and the second is not. McGowan
et al. argue that the 10.45-eV peak may be an inter-
ference effect of the first resonance, as calculated by
Marriott and Rotenberg (1968), or another shape
resonance. Geltman and Burke (1970) used the pseudo-
state expansion theory in an attempt to confirm the
experimental structure near 10.45 and 10.65 eV. Their
theory, however, shows no signs of the experimental
structures and shows a smooth behavior in this energy
range. It should be remarked that the pseudo-state
expansion theory has achieved measures of success,
notably in calculating the ratio of excitation cross
sections o(1s—2s)/o(is—2p) in remarkably good
agreement with the experiment of Ott, Kauppila, and
Fite (1970).

Below the n=3 state of hydrogen, a number of
resonances appear in both the experimental and theo-
retical curves of Fig. 17. For the lowest 4.5 resonance,
agreement exists between theory and experiment as to
position and width. The dominant feature of the theory

15

below the »=3 threshold is the 1D resonance near
11.8 eV, but the dominant feature of the experimental
curve appears about 0.1 eV higher. McGowan et al.
(1969) argue that the theory is insufficient to predict
the position of the 'D resonance accurately and that
more states need to be included in the theory to give the
proper position for the 'D resonance. Thus it may be
more desirable to correlate the “dominant” features of
experiment and theory.

The broad maximum in Fig. 17 just above the n=3
threshold appears to be a core-excited shape resonance
(McGowan et al., 1969).

C. A Resonance Involving H- —

Electron impact experiments on neutral atoms cannot
give information on the possibility of the existence of
resonances which involve doubly charged negative
ions, e.g., H- ~. In order to gain such evidence, one has
to perform experiments in which electrons collide with
negative ions. Such an experiment has recently been
reported by Walton, Peart, and Dolder (1970). They
studied the reaction e+H-—>+H+2e in a beam experi-
ment; their results are shown in Fig. 18. Noteworthy
is the sharp structure appearing near 14.5 eV, which
Walton et al. (1970) attribute to a state of H-~, with a
lifetime of about 10-" sec.


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44


Taste I. Semantics of resonances.

Energy vis a vis

First name Last name Parent parent Some characteristics Examples
Single-particle on Ground electronic above (0-4 eV) Vibrational excitation; Nz (2.3 eV)
Shape state dissociative attach- Hy (2-4 eV)
(1 particle, 0 holes) ment at low energy
Feshbach; Mostly Rydberg below (~0.5 eV) Bands correlated to Nz (11.48 eV)
Type I; excited state grandparent; sharp Hy (Bands “a”
Core-encited closed-channel structure; many 3”)
Particle-hole decay channels
(2 patticles, 1 hole) Shape Rydberg or above (0-2 eV) Dissociative attachment Nz (9-11 eV)
Type Hi; valence excited Hy (8-12 eV)
open-channel state
Doubly core-excited  Feshbach Doubly excited below Above ionization; He (57.16 eV)
(3 particles, 2 holes) Rydberg and 2-electron decay
valence states
Shape above Ns (22 eV)

The latter term indicates that the attachment of the
electron often occurs at a definite energy, leading to
sharp structures in the cross section. However, some-
times the lifetime of the compound state is so short
that the width of the state, as given by the uncertainty
principle, is large. The terms compound state, temporary
negative ion, or resonance are used interchangeably and

The first reference to the possibility that compound
states might exist can be traced to a paper by Franck
and Grotrian (1921). Experimental evidence for struc-
ture in the total cross section (e.g., N2) became avail-
able shortly thereafter, but a resonance model was not

ve0 vel ve2
authors have even used superfluous nomenclatures such . .
as “temporary negative ion resonance.”
—6 total (Golden, im
Bandel, Salerno) =
= 5
~~ BP —°—Gelastic 6
2 Linder & Schmidt 6
2 2
gs" ;
4 7
3 Onn, ¢
o
my
o
e 5
6
ol. 1 J WN
ty) 2 4 6 8 10 12 0 100 200 300 400

collision eneray [eV]

Fic. 1. Total cross section in Hz (Golden ef al., 1966) and
elastic portion alone (Linder and Schmidt, 1971a). The absolute
magnitude of Linder’s curve is normalized to Golden’s value at
the lowest energy. The difference between the two curves rep-
resents the sum of all inelastic cross sections. [From Linder and
Schmidt (1971a).]

energy loss C channel number]

Fic. 2. Energy loss spectrum of 4-eV electrons after collision
with Hz molecules. The peak marked »=0 represents elastic
scattering. The peaks marked-v=1, 2, 3, and 4 represent the
excitation of vibrational quanta of the neutral molecule via the
short-lived negative ion state ?2,*+. [From Ehrhardt, Langhans,
Linder, and Taylor (1968) .]


Taste VI. Geneology of Feshbach resonances in Nz.

Resonance N;-

Grandparent Nz*+

Binding
Designation Energy, eV Spacing Designation Energy, eV Spacing eV
“b” CEy*) 11.48 0.27 XZ,t 15.6 0.27 41
11.75
12.02
“57 12.64 0.23 AM, 16.7 0.23 41
“6” 12.87
“er? 13.00 0.23
“qa” 13.88 0.22

The best fit to the experiment was obtained when
Birtwistle and Herzenberg (1971) used the parameters
for Nz shown in Table IV. For comparison, Table IV
also shows the parameters for the N:~ state from ab
initio calculation of Krauss and Mies (1970). The
excellent agreement obtained from these completely
independent approaches is most gratifying.

The model of Birtwistle and Herzenberg (1971) leads
to the conclusion that the N:~ compound state has only

no?
r ZERO
0?
oF ZERO
60°
a ZERO
Oe
€
2 40°
s
&
oo _ ZERO
2
a
é
2
€
of
1 4 1 L
0 1 2 3 4

collision energy CeVI

Fic. 47. Energy dependence of the clastic differential cross
section for CO at different scattering angles. The first peak is
only weakly indicated as a shoulder at 1.5 eV. I/2 is an approxi-
mate measure of the half-width of the compound state. The
structures are better developed in the vibrational cross section

see Fig. 48). The intensity scales for all curves are the same.

From Ehrhardt, Langhans, Linder, and Taylor (1968)..]

77

Sanne Gneeeeee
6+ vs!

al

ab °

a

o 7
co
EL LAwM?
4 L
si
BY Lv
8% oy
0!

2

ne VS
‘t Sia?
oO

2

f A v8
i

Electron Energy, eV

Fic. 48. Energy dependence of differential vibrational excita-
tion in CO at an angle of observation of 72°. The structure result-
ing from the *I compound state is more pronounced than in
elastic scattering but broader than the equivalent structure in Ne
[From Schulz (1964).]


observing the SF,~ current using a mass spectrometer,
one can obtain information regarding the threshold
behavior of inelastic cross sections. Often, the threshold
region of inelastic cross sections shows resonance
structures.

Measurement of Cross Sections for Metastable States
using Surface Ejection

Measurements of the cross section for production of
metastable states can be accomplished with high
efficiency if the metastable state to be measured has an
internal energy higher than about 10 eV. In this case,
one can use for signal detection the ejection of electrons
resulting from metastables impinging on a metal
surface. Any kind of electron monochromator, -mag-
netic or electrostatic, can be used for producing the
monochromatic electron beam. Figure 8 shows a
sketch of such an apparatus. If a single metastable state
is involved, the current measured on the metastable
detector is is given by in= tN QLyea, where N is the gas
density, io is the current incident on the collision
chamber, L is the path length, y is the number of elec-
trons ejected per metastable incident, a is the solid
angle subtended by the metastable detector, and Q is the
cross section for the particular metastable state. Since
atoms may have more than one metastable state (e.g.,
28S and 2!S states for He), and since each metastable
state leads to a different y, the total curve is not easy to
interpret. However, structure in the total metastable
cross section is often very pronounced. Examples of
such curves are shown in the text.

Measurement of Optical Excitation Cross Sections

Since resonances can be detected in any decay channel
it is obvious that the excitation cross sections to any
of the radiating states of atoms should also exhibit
structure resulting from resonances. Any kind of
monochromator which gives a sufficiently narrow
electron energy distribution in conjunction with a
sufficiently high electron current is acceptable for such
experiments. This type of measurement is particularly
suitable for detecting resonances at higher energies, e.g.,
a few eV below the ionization potential.

Measurements of the optical excitation functions
using narrow electron energy distributions are just now
receiving attention and a complete analysis of the
observed structures is not yet available. Thus this
review cannot do justice to this interesting experimental
field, but one can anticipate interesting results in the
near future.

Measurement of Positive Ions

Resonances can lie above the ionization potential of
the atom. Such resonances can be studied by the
methods previously outlined. However, it is now known
that such resonances can decay by two-electron emis-
sion, yielding a positive ion. It was actually the use of

10

COLLISION
CHAMBER

ELECTRON 4
MONOCHROMATOR

—|

METASTABLE “|

DETECTOR

Fic. 8. Schematic diagram of an apparatus for study of
metastable excitation by surface ejection of electrons.

the trapped-electron method which established this
type of decay (see Sec. IIIC). If one examines the
positive ion cross section very carefully, one can observe
the resonances lying above the ionization threshold. As
described in Sec. ITIC, such measurement must use
sophisticated signal accumulation techniques, since the
structure in the positive ion cross section is super-
imposed on a large monotonically varying background
resulting from “direct” ionization. This background
signal can be subtracted by use of electronic methods.

When measuring structure in positive ion cross
sections, one must be careful to distinguish between
“resonances”, i.e., temporary negative ions and states
of the neutral atom which lie above the ionization
potential (“autoionizing states”). Both of these types
of states can cause structure in the positive ion cross
section.

Electron-Energy Distributions in Fast Neutral-Neutral
Collisions

It has been pointed out by Barker and Berry (1966)
that the electron energy distribution of the electrons
resulting from collisions of fast neutral atoms could be
used for detecting “resonances.” The reaction leading
to the detection of resonances is of the type

He (1s?) +-He(1s*) Hee (152s?) +Het(1s)
—He( 1s?) -+Het(1s)-+e.

The electrons in the above reaction result from the
decay of the 1s2s? resonance and cause interference with
electrons produced directly. Thus, structure in the
electron energy distribution can be observed.

Actually, pronounced peaks consistent with the above
reaction have been observed by Barker and Berry
(1966) and by Schowengerdt, Smart, and Rudd (1973),
in the energy range up to 150 keV.

However, no new information regarding the location
or width of resonances has been generated with this
method up to the present time, and thus no further use


o Wv#0—1; Aj20)/ o(v20~ 1 Aje2)

1
(20

SCATTERING ANGLE 6°

1
140

1
160

°

0 20 40 60 60 100 0

Fic. 9. Ratio o(v=0—1, Aj=0)/e(0=01, j=1-3) vs
scattering angle at an electron energy of 4.5 eV. Experiment: O
Ehrhardt and Linder (1968); (] Linder and Schmidt (1971);
Theory: A—Abram and Herzenberg (1969); B—Henry (1970);
C—Henry and Chang (1972). [From Henry and Chang (1972).

nances consisting of two “holes” and three “particles”;
such resonances have been recently postulated (Pav-
lovic et al., 1972) and are well known in atoms (e.g.,
the 2s°2p state in He~ near 57 eV). Higher hole-particle
states appear to be plausible.

Core-excited resonances can lie either below or above
their parent. When they lie below their parent, one may
say that they exhibit a positive electron affinity. Such
states are called Feshbach-type (after Feshbach, 1958,
1962) or Type I, or closed-channel resonances (decay
into the parent state is forbidden). When core-excited
resonances lie above their parent, they are called Type
II or core-excited shape resonances, These resonances
are similar to single-particle shape resonances, except
that they are associated with an electronically excited
state.

B. Parentage of Core-Excited Feshbach Resonances

The parents for core-excited resonances may be, in
principle, either valence or Rydberg excited states.
Singly excited states of molecules may be classified
into valence and Rydberg states. Both these types of
excited states of the neutral molecule are formed by
the promotion of a single electron from the ground
state configuration into an orbital which is not filled in
the ground state. When the promotion takes place into
a low-lying vacant orbital, the principal quantum num-
ber of the electron does not change, and we designate
the excited state as a valence state. When the principal
quantum number does change by unity or more, we
designate such an excited state as a Rydberg state.
Rydberg states lie at higher energies and the orbitals
being filled look like atomic orbitals. This gives rise to
a Rydberg series of electronic states whose limit corre-
sponds to an ionization limit of the molecules.

52

Calculations (Weiss and Krauss, 1970) on the bind-
ing of the additional electron show that preferentially
Rydberg excited states have a positive electron affinity
for a fixed internuclear separation in the Franck-
Condon region. We therefore expect to find Feshbach-
type resonances, which lie below their parent, mostly
associated with Rydberg excited states. In this case,
the temporary negative-ion complex consists of two
electrons in Rydberg orbitals trapped in the field of a
positive ion core, which is called the “grandparent”
state. The parent (or parents) consists of a single
Rydberg electron bound by the field of the same ionic
core.

Core-excited Feshbach resonances have lifetimes
(10-10 sec) which are long compared to the vi-
brational period of a molecule and therefore can give
rise to bands, each of which consists of a progression of
vibrational levels. Since the two Rydberg electrons
trapped by the ion core are located far outside the ion
core we expect the negative ion and its grandparent
positive ion core to have similar vibrational spacings
and Franck-Condon probabilities. One can therefore
compare the vibrational spacings and Franck—Condon
probabilities for a given band of negative ion vibronic
states with the corresponding values for the many pos-
sible positive ion states of a molecule in order to identify
the parentage and electron affinity of the band under
investigation. This type of correlation has been made

; ]
G6 (j=1+3) |

“\ swarm
experiment

2
J--

— Henry, Lane
t ———Hara
——-—Lane,Geltman

cross section {10-6 cm’

6 8 10

collision energy [eV] — ~

Fic. 10. Pure rotational excitation in Hy. Shown is the cross
section ¢(j=1->3). The circles are the experimental results of
Linder and Schmidt (1971a). The lines are the theories of Henry
and Lane (1969), of Hara (1969), and of Lane and Geltman
(1967). The swarm data shown in the inset are recalculated for
o(j=1-3) by Linder and Schmidt (1971a) from the original
experiment of Crompton ef al. (1969) which gives o(j=0—»2).
[From Linder an? Schmidt (1971a).]




PAYA

9 . 9 _
in NZ
Fic. 34. The “boom- Reflected ructear wave
erang” model of | the in
nuclear wave function Colmost
applied to the N;- ion. - i  onnitilated by
This schematic model is
discussed by Herzenberg
(1968). It is based on
the assumption that the
magnitude and de- __ Intermediate
pendence of I'(R) are state
such that only a single %
outgoing and a single
reflected wave matter.
(From Birtwistle and
Herzenberg (1971).]
Emitted
electron
wen- eee Final N, state
Incident .~
electron
ee Initial N, stote
Ro
io
Nuclear separation A’

the location on the energy scale is very satisfactory.
Small discrepancies in energy probably result from the
method of evaluating the position of the resonances.
Also, interference effects can shift the position of the
peaks, which are not necessarily the true positions of
the resonances. The results of Weingartshofer ef al.
(1970) and of Comer and Read (1970a), who observe
resonances in those channels in which very little inter-
ference takes place (e.g., high vibrational states), are
free from such errors.

Eliezer e¢ al. (1967) assign to this band the configu-
ration (o,1s)(m.2p)(mu2p’) ?2,+, consisting predomi-
nantly of (C*II,+e). When one arbitrarily adds 0.25
eV to Eliezer’s calculated values, excellent agreement

69

exists between theory and experiment. (see Appendix
I). In any case, the spacing calculated by Eliezer ef al,
for band “a” agrees with experiment and thus the
assignment appears convincing. Comer and Read ob-
tain values of 0.975 A and 11.40 eV for the equilibrium.
internuclear separation and the energy minimum, re-
spectively, whereas the values deduced by Eliezer et al.
are 1.03 A and 11.18 eV. Band “a” seems to be firmly
established.

2, Band “b”
Band “‘b” has been observed only by Comer and

Read (1971a) in high vibrational levels of the ground
state of H;. They obtained a natural width of 30 meV


Although the structures near the thresholds of the
28S and 2!S states have a similar appearance, the
interpretation advanced by Ehrhardt (1969) for the
two effects is very different.

Ehrhardt and Willmann (1967) find that the threshold
peak at 19.95 eV in the 2°S differential excitation cross
section is independent of angle. Thus they deduce that
the threshold peak appears in the s-wave. In a number of
publications, Ehrhardt ef al. (1967, 1968, 1969) point
out that the threshold effect is caused by the tail
(i.e., the wings) of the 2*S resonance, whose center is
located at 19.34 eV. This conclusion relies heavily on
the fact that the theoretical work of Burke and of
Taylor could not account for other #S' resonances in this
energy range. In his review, Taylor (1970) further dis-
cusses the qualitative aspects of threshold peaks in
inelastic cross sections caused by core-excited reso-
nances lying below the inelastic threshold.

It is pointed out by Herzenberg (private communi-
cation), that very sharp peaks in inelastic cross sec-
tions near threshold can not be explained quantitatively
in such a simple fashion. Rather, one has to realize
that the decay width for a Feshbach resonance (e.g.,
2S in helium) shows an abrupt increase in a narrow
energy range starting at the inelastic threshold. Thus,
in the case of helium, one can understand how a narrow
width (~8 meV) below the threshold of the 23S state
can be reconciled with a width considerably broader
(~1 eV) above the 235 state. This argument should

a
=e
z
—
6 +3.3;— 4
2
<
5 +01 4
g
2
&
3
o 31 4
2
E
= -63b- 4
Z |
Eos ly -
s \
° \ | —Transmission Exp.
2-127} U 4
< __Derived From
2 235+2'S Cross Section
&
a n | n l n

" 20 21 22

ELECTRON ENERGY, (eV)

Fic. 27. An expanded view of the derivative of the transmitted
current in the neighborhood of the lowest inelastic thresholds in
helium. The solid line shows the experiment of Sanche and
Schulz (1972) and the dashed line is obtained from the total
metastable cross section. The two curves are normalized to each
other in the region of the 2S excitation. The rise in the transmis-
sion curve just below the threshold for the 2°S and 2S states is
interpreted as a Wigner cusp in the elastic cross section. [From

e and Schulz (1972).

24

2 3S,115°
£ 21S 45°
z —

2
s
<
FA
6 23P,60°
re
&

>foe

feeweny 1 1
MS 220 225 230 235
ELECTRON ENERGY (eV)

Fic. 28. Differential inelastic cross sections in the energy range
22.4-23.5 eV for helium. The structures are due to the n=3
compound states. The final state and the angle of observation are
indiated for each curve. [From Andrick, Ehrhardt, and Eyb

1968).

be applicable generally to the threshold excitation of
those states which are parents of Feshbach resonances.

It would be satisfying if the threshold structure in the
21S state could be explained along similar lines. How-
ever, there seem to be good reasons to invoke a different
explanation. This explanation is based on the work of
Burke et al. (1967) and of Burke, Cooper, and Ormonde
(1969) who calculated, using close-coupling methods,
the cross section for the transition e+He(2°S)—>
He(2!S)-+e. They found a sharp peak at the threshold
of the 215 state, which they attributed to a *S resonance
close to the threshold of the 21S state. The existence of
such a resonance would, of course, also affect the cross
section e+He(1!5)—He(2!S)+e.

The elastic cross section for scattering of electrons
from the 21S state has a very large value (1430ma;")
near the 24S threshold, in the J=0 partial wave, again
indicating the existence of a *S resonance near the 21S
state. The threshold behavior of the elastic cross section
for scattering from the 2°S state is markedly different.
Thus Ehrhardt ef al. (1968) attribute the threshold
structure near the 2'S onset to a *S state existing near
the 2!S state and designate the *S resonance as a
“virtual” state. On this model, the electron is captured
just at the upper plateau of the potential well and
experiences a phase shift. Taylor (1970) describes this


should be noted that most of the structure visible in
the lower vibrational states of Fig. 18 consists of series
“a”, The values of the resonant energies obtained by
Comer and Read are tabulated for Hy- in Appendix I,
and for D;- in Appendix II. The results for Ds- are
very similar to those for H.-.

Studies similar to those of Comer and Read, using a
similar technique had been previously undertaken by
Weingartshofer et a). (1970). Their results (in absolute
units) at different angles of observation are shown in
Figs. 20 and 21, In addition to the X 12,+ decay channel,
Weingartshofer et a/. examined other decay channels:
the dissociation continuum, 6 *2,* (see Fig. 22); ¢ *IL,;
a*X,*; and several vibrational levels of the states
C4L,, B’1d,+, and D'I,. The branching ratios for the
decay into some of these channels are listed, in absolute
units, in Appendix III. Molecular radiation emanating
from the B'Z,* state of Hz and Dz also shows the
appropriate resonances, as has been shown by Mc-
Gowan and Williams (1969) and by Pichanick e¢ al,
(1971).

Figure 23 shows a schematic diagram of the five
energetically distinct compound states of Hs- and some
of the decay channels. Figure 24 shows the energies
at which various resonances have been observed in
different channels of decay. On the bottom of the

3.5

»
o

Electron Energy, eV
rn
uw

2.0

i
6

jj}
2 3 4 °5
Vibrational State

1
1

15

~

0

FiG. 31, Position of the peaks in the cross section vs quantum
number of the final state. If the *I, compound state were long-
lived compared to vibrational times, the solid lines would be
horizontal, i.e., the peaks would occur at the same energy regard-
less of the final vibrational state. The effect shown on this figure
indicates that the lifetime of the*1, compound state is comparable
to a vibrational period. [From Schulz (1964).]

67

2A
fi
4 Ae
% Thay
iy aw + %
Poy Ses
ial ave
PY Nave
: MAT e+

CROSS SECTION (ARB. UNITS)

a G
ee eee,

0
nett

22 6
ELECTRON ENERGY (eV)

3A

¥

Fic. 32. Comparison of experimental and theoretical vibra
tional cross sections for resonant e-Nz scattering. Crosses are the
experimental results of Schulz (1964). The curves show various
theoretical attempts to fit the experimental cross sections without
allowing for the variation of I' with internuclear separation. None
of these theoretical curves reproduce the regularity of the’ experi-
mental structure. The broken curve: Herzenberg and Mandl
(1962); chain curve: Chen (1964); dotted curve: Hasted and
Awan (1969). [From Birtwistle and Herzenberg (1971).]


}

‘Sr

H2X'Sg —*H7 b3zy at 10.47eV; 70°

y19¢)

differential cross section [1

Fre. 22. Energy dependence of the
absolute differential cross section for
excitation into a narrow band (~60 meV)
at 10.47 eV in He. The final state is the
dissociative continuum, 5*2,*. The zero
line is dashed. The length of the bar to
the left of the curve represents the
absolute scaling factor in units of 1.0X
10-” cm*/sr. The insert illustrates the
autoionization of the H:~ ion into the
energy band. [From Weingartshofer,
Ehrhardt, Hermann, and Linder (1970).

13
collision energy [eV]

The experimental cross section at the peak of the
3.75 eV process is plotted as a function of gas temper-
ature in Fig. 12. Spence and Schulz (1971a) find that
the cross section is independent of temperature in the
range 300~1300°K and conclude that rotational excita-
tion of Hz plays no role in the dissociative attachment
process at 3.75 eV in the above temperature range.
Also shown are the theoretical points calculated using
the theory of Chen and Peacher (1967) normalized to
the experimental data at 300°K. In this calculation it
is assumed that the electron capture cross section is
independent of the initial rotational state, which
should be a reasonable assumption in the present case.

It is, actually, not surprising to find that the dis-
sociative attachment cross section is independent of the
rotational states of the target. The vibrational time,
and thus the dissociation time, are shorter than rota-
tional times and one would therefore suppose that the
molecule is essentially nonrotating during the capture
and the breakup process. In fact, Bardsley, Mandl,
and Herzenberg (1966b) calculate with good success the
dissociative attachment in Hz by regarding the axis of
the diatomic molecule as fixed, thus ignoring rotational
motion, The experimental results of Fig. 12 seem to
confirm such a model.

6. Associative Detachment: H-+H-H;—>H,+e

There is a close relationship between dissociative at-
tachment reactions at low energy, which are discussed
in the preceding paragraphs, and low-energy associ-
ative detachment reactions of the type H-+-H-H;—
Hi-+e. Associative detachment is the inverse of dis-
sociative attachment and at low energies of the colliding
partners, the two processes proceed via the same com-
pound state, in this case Hz~. For a review of associative

60

detachment cross sections at thermal energy, see Fergu-
son (1970). In the case of H~++H, the reaction partners
approach each other along the potential energy curves
22+ and °Z,*. The former exhibits a short lifetime for
autodetachment; thus all or almost all collisions which
proceed along this potential energy curve lead to asso-
ciative detachment. The *2,+ curve is repulsive and
reactions proceeding along this curve at low energy
lead only to reflection or elastic scattering. One can
therefore expect that the low-energy associative detach-
ment cross section should be about one-half of that
given by the Langevin polarization cross section. This
prediction has been approximately checked for thermal
ions (Schmeltekopf e¢ al., 1967).

Since associative detachment proceeds via the same
intermediate state as dissociative attachment, there is
a strong connection between the two processes. How-
ever, in associative detachment there is the probability
that the resulting molecule is left in a highly excited
vibrational state, provided that the compound state
is short lived. Thus detailed balancing cannot be used
for predicting the bulk of the associative detachment
cross section from its inverse, since dissociative attach-
ment is generally studied only for molecules in their
lowest vibrational states.

For the case of H-+H—H2+e, theoretical treat-
ments are also available. Bates and Massey (1954)
and also Dalgarno (1961) have suggested that associ-
ative detachment cross sections could be Jarge and that
they could play an important role in upper atmosphere
reactions. Recently, more complete theoretical treat-
ments have become available. [Herzenberg (1967),
Chen and Peacher (1968) and Browne and Dalgarno
(1969), and also the review by Chen (1969)]. The
main conclusions from these considerations are: At low


0)

°
.

°
x

TOTAL 2p EXCITATION CROSS SECTION (ra

RESOLUTION 0.07eV
RESOLUTION 0.18eV

6 STATE APPROX.
———— 3 STATE + CORRELATION
—— —— 6 STATE NORMALIZED
FOLDED 0.07eV

°

m 4

0
10 W

12

ELECTRON ENERGY (eV)

Fic. 17. Total 2p excitation cross section in hydrogen. The high-resolution experimental data indicated by the closed points were
obtained with an energy spread of 70 meV and the low-resolution data, indicated by the open circles, were obtained with an energy
spread of 180 meV. The experimental data are from McGowan, Williams, and Curley (1969). The cross section is plotted on an ab-
solute scale, referenced to the values of Long, Cox, and Smith (1968). Also shown is the “six-state close-coupling” theory of Burke
et al. (1967) and the “three-state close-coupling plus electron correlation” theory of Taylor and Burke (1967), into which the experi-
mental resolution (70 meV) has been folded. [From McGowan, Williams, and Curley (1969).

explanation for these long-lived negative ions could be a
sextet of the type 3p*(*P)4s4p* for Cl-— and a config-
uration 2p*(45)3s3p" for O- ~. The energy of these levels
is not known.

I. HELIUM

As we review the field of resonances and go from
atomic hydrogen to helium, the most striking effect is
the decrease in theoretical effort and the increase in
experimental effort. Thus the guidance for classifying
the structures found by experimentalists is not too
extensive, and experiments usually precede theory. In
fact, much of the classification has been obtained
from experimentally measured angular distribution. The
experiments performed to date have analyzed struc-
tures in the 23S, 21S, 23P, and 2!P cross sections as well
as in the total elastic and total metastable cross section.

The discovery of resonances in atoms came from
measurements of the structure in the elastic cross
section, as shown in Fig. 19. This type of experiment,
especially when it is coupled with a measurement of
angular distributions (Fig. 20), gives a great deal of
information regarding the width, symmetry, and shape
of the resonance, especially for resonances lying below
the first electronically excited state of the atom.

For resonances lying above the first electronically
excited state, as in the case of core-excited shape

resonances associated with »=2 and _higher-lying
states, it is advantageous to study structures in the
electronically excited states, such as 2S, 24S, 2°P, 2'P,
etc. The decay into these final states is usually pre-
ferred.

For an overview of all the sharp resonances occurring
by electron impact, it is advantageous to use a trans-
mission experiment. These types of experiments,
pioneered by Kuyatt, Simpson, and Mielczarek (1965),
can be made very sensitive to sharp structures in the
cross section by modulating the electron energy and
thus performing a differentiation of the transmitted
electron current with respect to energy. Such experi-
ments have been performed for all rare gases by
Sanche and Schulz (1972). A sample of their data for
helium is shown in Fig. 21. The advantage of this type
of experiment is the overview of the location of reso-
nances on the energy scale. The disadvantage lies
in the limited information: One generally cannot
deduce the symmetry, the width, or the exact shape.
Nor is it possible to observe broad resonances (e.g.,
shape resonances) very clearly. Various elastic and
inelastic cross sections must be measured at different
angles of observation to fill out the picture.

As an aid to the subsequent discussion, Fig. 22 shows
an energy level diagram of the lowest states of neutral
He and the position of resonances, as observed by

7


Fic. 45, Transmission experiment
in Hg. The three low-lying resonances
are clearly visible as dips in the
transmitted current. [From Fano and
Cooper (1965).]

TRANSMITTED CURRENT

NOISE

n n

their ground states show a sharp peak near 2 eV
(Norcross and Moores, 1972). This effect is attributed
to the presence of the 1P resonance near the threshold of
the first excited state of the neutral atom.

VI. MERCURY

Kuyatt, Simpson, and Mielczarek (1965) observe
many resonances in their study of transmission of
electrons through mercury. All resonances appear as
dips in the transmitted current. An example of their
data is shown in Fig. 45 and the positions of these

5
ELECTRON ENERGY , eV

resonances are shown on the energy level diagram of
Fig. 46 in conjunction with the known electronically
excited states of Hg. The lowest three resonances
(marked 1, 2, 3) have been given the assignment
(6s6p*)*P12, “Paya, 4Psj2 (Fano and Cooper, 1965). The
ground state of Hg is (5d°6s?)1So.

Kuyatt ef al. point out that the resonances at higher
energies (near 8 eV) lie too high in energy to be at-
tributed to higher levels (*D, *S, ?P) of the 6s6p7
configuration. Rather, Kuyatt et al. suggest that the
parents of some of the resonances in the 8-eV region are

n T T T T T T T T T T
| | | +— ELASTIC. RESONANCES ——» | | | ]
2 45 67 69 “ 12 3
“Seb? (052 )6p7F;, 7
5d!6s(25) 6d 1d] 8d "De, "D123
° ° 'n Sd!Gp2
MERCURY 5d65717D50)6p | 7 | °F |" op |
( J
10g, (2: 3 iy Se | 1c
5d6s(25) 6p 5d!6s (25) 7s 55,] | 'So 8875} 1S +| UNIT Hg IL @5;y0)
ep A
‘ > ° r. 10.437 eV
% [* [» " t oll +,
1 1 " 1 1 L 1 1 i L 1 1
4) 5 6 1 8 0 " 2
ENERGY eV

Fic. 46. Energy level diagram for Hg and the associated resonances. The resonances are numbered and their energies are listed in
Appendix IX. [From Kuyatt, Simpson, and Mielczarek (1965).

34


10" em?

~ ‘Chen and Peachs
—— Spence & Schul:
ad

2.0

Cross Section At Peak
8

300 500 700 900 1100 1300 1500
Temperature, K

Fic. 12. Temperature dependence of the cross section for H~
formation from Hz at 3.75 eV. The experimental results (Spence
and Schulz, 1971) show that the negative ion formation is inde-
pendent of rotational excitation of the target, whereas the theory
of Chen and Peacher (1967) shows a strong dependence. [From
Spence and Schulz (1971).

standing of the process. The first observation of a large
vibrational cross section was due to Ramien (1931)
whose results at 3.5 and 7 eV were essentially correct
but were widely disbelieved because no simple inter-
pretation could be found (Massey and Burhop, 1952).
The use of a rather complex experimental method
(Hertz diffusion) and the limited nature of the ob-
servation (only two energies given) contributed to the
skepticism.

Subsequent experiments by Schulz (1964) and by
Engelhardt and Phelps (1963) confirmed the large cross
section for vibrational excitation, as did the experi-
ments of Ehrhardt et al. (1968). This large vibrational
cross section was successfully interpreted in terms of

o+co

POLARIZATION
“—~ CROSS SECTION

CROSS SECTION (10 Sem?)

© ENERGY, CENTER OF MASS (eV)

Fic, 13. The cross section for total electron detachment for
the reaction of O- with CO. The lower dashed line is the 1/o fit
while the upper line is the polarization cross section. The closed
circles are data points. The magnitude is calibrated by assuming
that the detachment rate at thermal energies is5.6X107" cm? sect
(Ferguson, 1968), but this value is known to an accuracy of only
+£30%. The polarization cross section was calculated using 19.5X
ie as the polarizability of CO. [From Mauer and Schulz

the resonance model by Bardsley, Herzenberg, and
Mandl (1966b) and the energy dependence of the meas-
ured vibrational cross section could be well reproduced.

The energy-loss spectrum for 4-eV electrons in H, is
shown in Fig. 2, which clearly shows peaks due to the
excitation of four vibrational states. The energy de-
pendence of the vibrational cross section for v=1 is
shown in Fig. 3 in comparison with the newest theory
due to Henry and Chang (1972). The theory of Faisal

3.541072

3.0

|. — Schulz

&

S

<— Rapp et al

Negative lon Cross Section (cm?)

!
14

1
16

a
18 20 22

10
Electron Energy (eV)

(2 24

Fi. 14. Formation of stable negative ions, H-, by dissociative
attachment in hydrogen via a repulsive curve. Shown are the
results of Rapp ef al. (1965) and Schulz (1959a). The broad peak
around 10 eV is interpreted as the reaction e+H:—H," (*2,+) >
H-+H. The peak near 14.2 eV is interpreted in terms of the
formation of excited H, e+H:>H-+H(2!S, 28P). The small
structure near 12 eV shown on Schulz’s curve has been studied
in detail by Dowell and Sharp (1968) and is shown in Fig. 16.

and Temkin (1972) is also in agreement with the
experiments.

Although Fig. 3 presents fairly good agreement be-
tween experiments, it is pointed out by Crompton e¢ al.
(1970) and also discussed by Golden ef al. (1971) that
the slope near threshold, as determined from electron
beam experiments by Burrow and Schulz (1969) or by
Ehrhardt et al. (1968) is too large to fit the measured
transport coefficients. In order to perform such an

54


3s tse
3s o eS OG 33
% ¢ st®ssee gs
fe ¢S 5205
i] > J
Ehrhardt et al Chamberlain £ £ S$ SHE = 8
24 —— ——— 2 2 2008 BE
5's ep Pis's P Pis'S*s's'S'8''8 “FO
Fic. 22. Survey of energy values for c
resonances in helium. On the left-hand L 3
side of the diagram we show the lowest =
energy levels in He. The names of the
authors are indicated above; just
below the names we indicate the decay 23;
channels in which the resonances are 3°s —
observed. The dots indicate the posi- 2
tion at which structures have been sP—
observed. Two theoretical columns 3’s—

are also included. Burke et al. (1969)
calculate the widths of the*P, 2D, and
2F resonances and these are indicated
by the vertical lines. The full
horizontal lines indicate those res-
onances which seem firmly estab-
lished. The many extra resonances
found by Golden ef al. (1970), as well
as the resonance at 19.45 eV (dashed
horizontal line), have been put in
doubt by the results of Sanche and

22)

Energy, eV

Schulz (1972) and must be seriously
juestioned at the present time.
from Sanche and sdhulz (1972). j

threshold effect

9

cross out the ?P* state in Table I. This leaves us with one
state from the 1s2s* configuration, *.S*, two states from
the 1s2s2p(2P°) configuration (one with spins in the
outer shell parallel, one antiparallel), and two states
from the 1s2p* configuration *S and 2D. The total
number is 5.

If the electrons in the outer shell are not equivalent,
then we have to write 1s2p2p’, where 2’ stands for
electrons in an np orbital (n=2— 0) and additional
states are possible, as postulated by Golden and Zecca
(1970). These additional states are also listed in
Table I, although they may not be real possibilities.

B. Resonances from 19.3 eV to the
Tonization Potential

In this section we discuss resonances above the
lowest 2*S at 19.34 eV, and list them in a sequence of
increasing energy. An attempt is made to establish the
reliability of each determination. At the outset it must
be stressed that differences in energy which are less than
the observed width of these resonances (i.e., about
0.05 eV) must be ignored. Resonances can exhibit a
different shape, depending on the angle of observation,

20

or the acceptance angle at a fixed angle, or depending on
the decay channel in which they are observed. Only a
complete analysis involving phase shifts could establish
a reliable guide to such differences.

1. 19.34 eV (152s, 2S)

The resonance occurring near 19.3 eV was the first
to be measured experimentally for an atomic system.
Although some discrepancies as to the exact energy and
width emerged initially, all the experimental values
have converged to the region 19.30-19.35 eV. Appendix
TI lists some of the recent values obtained by experi-
ment and by theory. Figure 19 reproduces the original
measurement of this resonance obtained by observation
of elastic scattering at an angle of 72 degrees, in a
double electrostatic analyzer. Simpson and Fano (1963)
confirmed the existence of this resonance and classified
it as the 1s(2s)??S state. Further experimental con-
firmation came from a Maier~Leibnitz type experiment
of Fleming and Higginson (1963). Andrick and Ehr-
hardt (1966) obtained the angular dependence in the
region of 19.3 eV and confirmed that the resonance
appears in the s-wave. Figure 20 shows that the


Mazeau et al. (1972a) and by Swanson et al. (1972).
They find that the ?2*, »=0 resonance at 10.04 shows a
preference for decay into high vibrational levels of
valence-excited electronic states: the v=3 state of
a'II, the v=4 state of A "ll, and the »=25 or 26 state
of a’ *Z+, Schematically, these observations are shown
on the energy level diagram, Fig. 55(B). One can under-
stand the experimentally determined decay scheme by
considering the equilibrium internuclear separation of
the various states (Mazeau ef al., 1972; Swanson et al.,
1972). The ?2*+ compound state, being a Rydberg
state, should have an equilibrium internuclear separa-
tion close to that of the positive ion X *2+ (r-=1.11 A)
or the two parents 6*E+ (r,=1.11 A) or BtE+ (r=
1.12 A); this places r, for the compound state near
1.11 A. The decay takes place to electronic states
with a larger equilibrium internuclear separation
(XB: r= 1.13 A; aM: 1.20 A; AM: 1.23 A; a! 8E+:
1.35 A). Thus, high vibrational quantum numbers will
be preferred in the decay, especially when the final
state has an r, very large, as is the case for the a! *Z+
state.

2. Shape Resonances and Inelastic Thresholds

Structures 3 and (4~4’) of Fig. 55(A) at 10.42 and
10.7 eV, respectively, are probably shape resonances,
by analogy with similar structures observed in nitrogen.
Angular distribution measurements in the 6 E+ decay
channel indicate that the 10.7-eV resonance has aI
symmetry. Figure 55(C) shows this measurement of the
angular distribution, and also the differential excitation
cross section to the 6*+ state at 10,39 eV.

The excitation cross section to the b *E+ state shown
in Fig. 55(C) exhibits a sharp rise near threshold and a
number of structures above threshold. At first sight,
this excitation function appears similar to the excitation
cross section to the £*Z,+ state in N2 [Fig. 44(B)].
However, there is a notable difference: Whereas the
angular distribution near the threshold of the E°2,+
state in No exhibited a p-wave dependence [see Fig.
44(C)]] characteristic of the decay of a p-type shape
resonance, in the case of the b#Z* state in CO, we see
from Fig. 55(C) that the angular distribution is iso-
tropic. Thus, an s wave is indicated.

We have already pointed out in Sec. ITIB2 that the
decay of the wings of the *2+ resonance, lying 350 meV
below the threshold of the 5 *Z* state, can cause a sharp
structure in the threshold behavior. This appears to
be the case. The large width of 22+ resonance in CO,
about 45 meV (vs only 0.6 meV for the *2,* resonance
in Ne at 11.48 eV) would provide a favorable circum-
stance for the observation of the decay of the *Z+
resonance into an inelastic channel.

3. Band “a”

At higher energies in CO, the transmission experi-
ment (Fig. 55) shows many overlapping resonances and

Wide Angle Total
(Spence & Schulz)

z

3

> Differential Elastic
g  (ehebordt and Wilmann
3

<

€

2

5

Uv

z Transmission Elastic

§ (Boness, Hasted and Larkin)
=

So

$

a

1
08
Electron Energy

0.0 04 12 16

(eV)

Fic. 56. Comparison of experiments on the structure in the
low-energy cross section of NO. The top curve represents a
recorder tracing of electrons scattered over a wide acceptance
angle (mostly elastic) (Spence and Schulz, 1971b). The middle
curve is the differential elastic cross section (Ehrhardt and
Willman, 1967). The bottom curve, which has been shifted by
about 0.4 eV to overlap the present results, represents the trans-
mission experiment of Boness, Hasted, and Larkin (1968). The
structure is interpreted as the resonant contribution to the elastic
cross section and the spacing of the structure is interpreted as the
spacing of the NO-*S- system. [From Spence and Schulz
(1971b).J

identification of particular bands is not possible.
However, one can identify six vibrational levels
belonging to a common progression (band “a”) near
the end of the spectrum shown in Fig. 55. This progres-
sion starts at 13.95-£0.05 eV with a spacing of 205,
190, 185, 175, and 165-45 meV, respectively. The prob-
able grandparent is the A *II state of COt.

D. Resonances above the Ionization Potential in CO

It was pointed out in Sec. IIID that there exist
resonances above the ionization potential of nitrogen,
in the range 20-24 eV. A similar process exists in carbon
monoxide. Chutjian ef al. (1972) and Truhlar et al.
(1972) have measured the cross section for excitation
of the »=1 vibrational state in CO [see Fig. 55(E)]
and find a broad peak around 20-eV energy. They find
that theories relying on potential scattering alone are

87


APPENDIX VII

Position of resonances in krypton (eV).

Differential
elastic and Metastable
Transmission exp. inelastic production
Sanche and Swanson. Pichanick
Schulz et al. and Simpson
(1972) (1973) (1968) Designation
9.50-9.53 9.52 4p°53? *Pop
10.16-10.19 10.14 10.05 Pip
10.66-10.69 10.67 10.63
11.29 11.29 11.10-11.20
11.40 11.42
11.54 11.42
11.67 11.67 11.70
11.97-12.04-12.10 11.97 11.94-12.04
12.04 12.28
12.10 13.08

Optical excitation experiments in krypton* (Kisker, 1972b).

4502 A 4464 4274 A 4376 A
12.90-12.95
12.93-13.00 12.97-13.04
13.19-13.25 13.13-13.18 13.11-13.18
13.23- 13.24-13.30
13.36-

* Given are values for max-min.

Swanson, Cooper, and Kuyatt (1973) compare the resonances in krypton with optical absorption data of Rb 1.
Such a comparison leads them to interpret the resonances in the energy range 10.5 eV—12 eV (i.e., all but the two

lowest states) as 4p%5s4d states. The 4° ion core can have J=} or 3.

APPENDIX VIII

Position of resonances in xenon (eV).

Metastable
Transmission experiments production
Sanche and. Kuyatt Pichanick
Schulz et al. and Simpson
(1972) (1965) (1968) Designation
7.80-7.90-7.92 7.74-7.77 5p56s? *Paye
8.48
9.11-9.26 9.02 9.0 *Pip
9.52
9.56 9.5
9.65
10.92 10.81-10.86 10.3
11.00

41


mination of the symmetry of compound states, Under
favorable circumstances the angular distribution of in-
elastically scattered electrons is determined uniquely
by comparing the symmetries of the resonant state,
the initial state, and the final state. The conditions
under which a unique angular distribution can be ob-
tained from symmetry considerations are listed by
Bardsley and Read (1968) and by O’Malley and
Taylor (1968):

(a) The scattering must be dominated by a single
resonant state, so that nonresonant scattering and the
contributions from other resonances are both negligible.
This situation is often found in the study of inelastic
collisions, but for elastic scattering there are always
considerable nonresonant contributions.

(b) The molecule does not rotate appreciably during
the lifetime of the resonant state.

(c) It must be assumed that when the resonant state
is expanded in spherical harmonics the contribution
from the lowest allowed value of / are dominant. For
resonances at low energies this is nearly always true.

(d) It must also be assumed that the Born—Oppen-
heimer separation of electronic and vibrational motion
is valid.

In the case of the N:-(*II,) resonance near 2.3 eV,
the extra electron must go into the m, orbital. It must
have even orbital angular momentum (/>2) and the
projection of the angular momentum on the molecular
axis must be unity. We may speak of a dr-wave, The
expected d-wave behavior of the cross section to vari-
ous vibrational states of Nz should show a subsidiary
peak near 90°. The experimental results of Ehrhardt
et al. (1968), shown in Fig. 36, exhibit such behavior,
and thus the angular distribution measurements con-
firm the designation of *II, for the first shape resonance
in Na.

5. Pure Rotational Excitation via "I,

Pure rotational transitions can also be excited by
compound states. It has already been pointed out that
experiments on the “elastic cross section”’ exhibit struc-
ture in the energy dependence which can be attributed
to the *II, resonance. However, beam experiments
do not have the resolution necessary for a study of
rotational excitation, or for distinguishing rotational
levels in vibrational transitions. Thus, in the case of Ne
and in fact all molecules except Ho, one has to rely on
theory. The results of the theory, for rotational excita-
tion J= 1-3, are shown in Fig. 37. Wide discrepancies
exist in the region of the "II, compound state. The
results of Chen (1966b) using projection operators
seem to be much below the close-coupling results of
Burke and Sinfailam (1970) and those of Oksyuk
(1966). It should be noted that in the resonance region
quantum jumps J=0—4 or J=1-—5, ie, AJ=4, are
possible in addition to the usual quantum jumps,
AJ=2. Chen (1966b) has calculated the cross sec-

tions for these transitions, with and without vibra-
tional excitation.

B. Core-Excited Resonances in the 11-15
eV Region

As pointed out previously, Feshbach-type resonances
are more likely to occur below Rydberg excited states
of molecules. In Ne, the lowest Rydberg state is the
£*Z,* state (Mulliken, 1957) at 11.87 eV and one
would expect that a sharp resonance would occur about
0.5 eV below this state. Such is actually the case.
Heidermann, Kuyatt, and Chamberlain (1966a) dis-
covered a very sharp resonance at 11.48 eV, using a
transmission experiment (Fig. 38). Comer and Read
(1971b) performed a different scattering experiment
in which the decay of the resonance could be observed
for v=0, 1, 2, and 3 of the ground electronic state.
Theiy results are shown in Figs. 39 and 40 and the
angular distributions for electrons having excited the
v=1 state are shown in Fig. 41. From these observa-
tions, Comer and Read deduce that the symmetry of
the 11.48-eV resonance is ?£,+ and that the most likely
parent is the Z*Z,* state. Actually, Fig. 40 shows that
a progression is involved here, of which the 11.48-eV
state is the first member. The other members of this
band, which we choose to call band “‘b” are listed in
Appendix IV in comparison with other experiments.
Table V lists the parameters of the *2,* state. It should
be noted that the 11.48-eV *2,+ resonance has also
been observed as a sharp peak in the optical excitation
function (A=3371 A) of the CII, state (Kisker, 1972).

The results of the recent transmission experiment of
Sanche and Schulz (1972) are shown in Figs. 42 and 43.
The features are numbered and the more obvious pro-
gressions are given letter names. The energy values are
tabulated in Appendix IV, in comparison with other
experiments.

The total production of metastable states has been
measured by Lawton and Pichanick (1972) and their
results are shown in Fig, 44(A). The differential in-
elastic cross sections to the E*Z,+ (v=0 and »=1),
a’’13,+ (y=0), and other electronically excited states,
have been studied by Mazeau ef al. (1972b). Samples
of their results on the energy dependence and the angu-
lar distribution of scattered electrons are shown in
Figs. 44(B)-(E). Figure 44(F) is a schematic energy
level diagram of the N2 and Nz systems and the decay
scheme for various resonances. We have indicated in
separate columns shape resonances and Feshbach reso-
nances.

Below we discuss the properties of individual bands,
as deduced from the various experiments. In Appen-
dixes IV and V we list the energies of the resonances.

1. Band “b”2E,+

Three members of band “‘b” are listed in Appendix
IV. The #2,+ resonance at 11.48 eV consists of two

82


h/T is the lifetime) of the compound state with respect
to autodetachment. This width is a function of the
internuclear separation R. The integration extends from
the formation point Rp to the stabilization distance R’
and »(R) is the relative velocity of separation of the
nuclei, We can replace the exponent by the appropriate
average width I and by the time 7, which is needed for
the products to reach the stabilization point. We then
write

Q-= Qo exp(—Tr/h).

It should be noted that the total width is the sum of
the partial widths for decaying into the various vibra-
tional states of the (H:+e) system. Separation into
three particles (H+H-+e) is energetically possible at
energies above 4.46 eV. In this model the isotope effect
arises from the variation of the survival probability
(exp—I'r/h) with mass. It is pointed out by Chen and
Peacher (19684) that the above expressions are only
approximate and that the capture cross section, result-
ing from the nuclear overlap integral, becomes as sensi-
tive to the mass as the survival probability itself.
Nevertheless, the simplicity of separating the dissoci-

H2
x! Ig (v=2)

+ 10°

differential cross sections {10-? sx?

120
collision energy [eV]

Fic. 20. Energy dependence of the absolute differential cross
sections for different scattering angles and into two different exit
channels, 0=2 and 4 of the electronic ground state. The zero lines
are dashed. The length of the bars to the left represent the scaling
factors in units of 1.0X 10" cm*/st. The resonances are members
of band “a.” [From Weingartshofer ef al. (1970).

59

H2
X'E5 (v=3)

+ 10°

differential cross sections [10° 9p?]

125

aC
collision energy [eV]

Fy, 21. Energy dependence of the absolute differential cross
sections to the »=3 vibrational level of the electronic ground state
of H; for four different scattering angles. The zero lines are dashed.
The length of the bars to the left of each curve represents the
absolute scaling factors in units of 1.0X10- cm!/sr. The res-
onances are members of band “a.” [From Weingartshofer,
Ehrhardt, Hermann, and Linder (1970).J

ative attachment cross section into two physically
meaningful simple terms has accounted for the exten-
sive use of the above expressions. Also, Chen and
Peacher’s considerations have not as yet been tested
against experiment.

5. Effect of Rotational Levels of the Hs Target
Molecule on H- Formation near 3.75 eV

Chen and Peacher (1967) predict theoretically a pro-
found effect of rotationally excited levels of Hz for the
reaction e+H;~>H,;-—>H-+H at 3.75 eV. In this reac-
tion the products depart with zero kinetic energy, and
Chen and Peacher predict a large increase in the survival
factor leading to an increased cross section for this
process as the population of higher rotational states is
increased. Chen and Peacher’s suggestion seems to stem
from the effect of the centrifugal repulsion on the time
the nuclei take to separate. To test this theory, and to
determine the effect of rotational levels, Spence and
Schulz (1971a) have studied the temperature depend-
ence of the dissociative attachment cross section in Hz
at 3.75 eV.


electrons of the Rydberg orbital symmetry 3s, tem-
porarily bound in the field of the grandparent X *Z,+
core of Nzt. This is evidenced by the fact that both
the spacing between the vibrational levels of band “‘b”
and the amplitudes of the structures are close in mag-
nitude to the corresponding values for excitation of the
ground state X *Z,* of Ns+. The spacing between the
structures of band “b” is 270 meV and the ratio of
magnitudes of the two peaks is 1030.5. These experi-
mental results agree well with the values for the X ?Z,+
state of Nst, which has a spacing of 271 meV between
the v=0 and v=1 states and which has a ratio of 9.96
for the Franck-Condon probabilities for exciting these
vibronic states.

Table VI shows these comparisons: The binding be-
tween the lowest member of band “‘b” and the grand-
parent X *Z,+ state of N2+ is 4.1 eV. This value repre-
sents the binding of the two 3sc, electrons to the posi-
tive ion core. It is noteworthy that the value of about
4.1 eV does not change as different grandparents are
considered, and in fact the value remains constant
even for other molecules (see Table X). But the value
is applicable only to the lowest band. The same grand-
parent can give rise to other bands, lying higher in
energy.

Only the zeroth level of the X *2,* grandparent state
is strongly excited in molecular transitions from the
ground state of Nz and we would expect that a similar
situation prevails for the resonances associated with
the X *2,* grandparent state. Thus we would not expect
to observe a long progression of vibronic states of the
*3,+ resonance.

2, Shape Resonances and Inelastic Thresholds

Structures 3 and (4-4’) of Fig. 42 (at 11.92 and
12.2 eV) have been identified as p-wave shape reso-
nances associated with the E *Z,+ Rydberg state of Nz
(Sanche and Schulz, 1972). The first of these lies near
the threshold for the E*Z,* state (11.87 eV), so that
one would expect a dramatic influence of the 11.92-eV
p-wave shape resonance on the threshold behavior of
the E*3,+ state. That the E*Z,+ state and also the
a’’1,+ state at 12.26 eV show a very sharp rise near
threshold has been observed by many investigators
(Heideman e¢ al., 1966a; Ehrhardt and Willmann,
1967; Swanson et al., 1971; Mazeau ef al., 1972b;
Lawton and Pichanick, 1973).

Figures 44(A) and 44(B) clearly show that the
cross section as well as the differential cross section to
the E*Z,* state rise very steeply near threshold. A
priori, a sharp rise near threshold can arise from three
causes:

(i) The existence of a shape resonance just above
the threshold. The angular distribution in this case
would exhibit a p-type (e.g., po) behavior.

(ii) The existence of a Feshbach-type resonance

83

below the threshold can influence the inelastic cross
section above threshold (Ehrhardt and Weingartshofer,
1969; Taylor, 1970). In the case of Ne, we would be
dealing with the “wings” of the ?Z,+ resonance which
lies 390 meV below the E state, Herzenberg and D. Ton-
That point out that the opening of a new channel of
decay (as is the case when the electron energy passes
through the energy of an excited state) leads to an
abrupt increase in the total width I. This effect
is especially pronounced when the electronic state is
the “parent” of the resonance, since the decay width
into the parent is generally large. Herzenberg and D.
Ton-That have worked out these considerations for
the case of the 2S resonance in helium decaying into
the 2*S state, showing that a sharp peak in the excita-
tion cross section of the 2°S state near threshold results.
It is expected that the model will be valid in other
cases as well. It leads to an s-wave behavior in the
angular distribution of inelastically scattered electrons.

(iii) The existence of a “virtual” state, similar to
one existing near the 2'S threshold in helium (see
preceding paper).

In order to distinguish between the three possibilities
outlined above, Mazeau ef al. (1972b) studied the
angular distribution of the electrons having excited
the E#Z,+ (v=0) state. Figure 44C shows that the
angular distribution near the threshold of the £ state
approximates the shape expected for a po-wave. This
experiment demonstrates that the threshold behavior
of the ZZ,+ state is dominated by the p-wave reso-
nance near 11.9 eV, and also confirms the assignment
given to this resonance by Sanche and Schulz (1972).

The resonance (4-4’) of Fig. 42, which lies between
12.1-12.2 eV, is also believed to be a shape resonance
(Mazeau ef al., 1972b; Sanche and Schulz, 1972),
probably of 71 symmetry. The angular distribution of
the scattered electrons having excited the E *Z,+ (v=0)
state near 12.1 eV exhibits, approximately, the shape
characteristic of a p-wave (Mazeau et al., 1972b).

The sharp onset of the excitation function is charac-
teristic of the E*Z,+ and the a” 1Z,+ states at 11.87
and 12.26 eV, respectively. Other inelastic cross sec-
tions, examined by Swanson ef al. (1971), (A *2,+,
BW, B'*3,-, a2", a, CM, EU, a! 12,+) do
not exhibit a sharp rise near threshold.

3. Structures 5 and 6

The energy of the lowest Feshbach resonance com-
posed of two Rydberg electrons trapped in the field of
the A II, core of Nyt can be estimated by adding to
the energy of the ?Z,* resonance (11.48 eV) the differ-
ence between the ionization potential for the X*2,+
and the A*II, states of Nz*+. Such an estimate gives
12.62 eV for the energy of that "II, resonant state
which would consist of two 3sc, electrons bound to the
AIL, core. Resonances 5 and 6 of Fig. 42 (at 12.64
and 12.87 eV) probably belong to that state. In fact,


Fic. 34. Derivative of transmitted
current vs electron energy in neon.
[From Sanche and Schulz (1972).]

DERIVATIVE OF TRANSMITTED CURRENT (ARBITRARY UNITS)

{oy | y |

Nevertheless, Kurepa and Heddle (1972) propose that
the large feature at 22.95+-0.02 eV which appears in
many of the excitation functions, be assigned to the
1s4s* state of He-. Similarly, the feature at 23.94+0.02
eV is assigned to the 5s? configuration. It is, of course,
understood that the above orbitals represent the domi-
nant wavefunctions and that admixtures of other states
are expected to contribute.

Figure 29(a) shows the results of Kurepa and Heddle

Taste I, Values of the splitting between the *Pys and *Pi2
levels in the positive ion and in the compound state for Ne, Ar,
Kr, and Xe.

Positive
Compound state ion

Sanche and Schulz Kuyatt, Simpson,
Gas (1972) Mielezarek (1965)
Ne 0.095 0.095 0.097
Ar 0.172 0.172 0.177
Kr 0.66 0.64 0.666
Xe “1.2 1.25 1,306

18 19 20
ELECTRON ENERGY, (eV)

(1972), as analyzed by Heddle ef al. (1973) who have
added all data from all their runs to aid in the distinction
of real features from small fluctuations. The peak near
23.94+0.02 eV is very clearly exhibited in Fig. 29(a).

Figure 29(b) shows the optical excitation functions
to two D states, and Fig. 29(c) the excitation functions
to three P states, obtained by observing the wavelength
indicated in the appropriate figure caption.

C. Resonances above the Ionization Potential:
(25°2p)?P and (2526?)?D

The lowest doubly excited states of helium are the
(2s*)1§ state at 57.82 eV, and the (2s2p)’P state at
58.34 eV (Rudd, 1964, 1965). Kuyatt, Simpson, and
Mielczarek (1965) discovered, using a transmission
experiment, that resonances of the Feshbach type are
associated with these states. Golden and Zecca (1970),
as well as Sanche and Schulz (1972), confirmed the
position of these resonances using the transmission
method (Fig. 30). Appendix IV lists the values for
these resonances, as found by different experiments.
Fano and Cooper (1965) classified these resonances as
(2s°2p)*P for the lowest (~57.16 eV) and (2s2*)?D
for the second (~58.25 eV). Various theoretical

28


review that every resonance is characterized by a well-
defined energy and width. Also, an attempt is made to
associate resonances with one or two molecular orbitals
of a negative ion state of the atom or molecule. Actually,
a superposition of a few molecular orbitals must always
be considered in order to describe a resonance properly.
When only a single term is given, it is understood that
this is the leading, i.e, dominant, term. Despite the
fact that these assumptions oversimplify the problem,
they seem to be applicable for most resonances discussed.
in this review. Exceptions are pointed out in the text.
Thus, it is sometimes necessary to invoke the energy
dependence of the resonance width and in other cases
the resonance center cannot be located precisely from
experimental information alone. Sometimes it does not
appear to be possible to associate a dominant molecular
orbital configuration with a particular resonance.

C. Isoelectronic and Isostate Comparisons

It is sometimes desirable to deduce the energy levels
of resonances, especially those of the Feshbach type,
from known energy levels of other atoms which exhibit
some similarities with the resonances. This approach is
of course only approximate but often the sequence of
resonant states and the physical picture can be deduced
from such comparisons.

A simple example is discussed by Herzenberg (1971):
The lithium atom in its ground state has the approxi-
mate electronic structure 15°2s, and is known to be able
to attach an electron with a binding energy of 0.6 eV to
form a stable Li- ion with the approximate structure
1s?2s?. The nucleus and the two 1s electrons in the ion
form a small tightly bound core of charge ++| e | which
provides an attractive potential to hold the two 2s
electrons, whose wave functions extend far outside the
core. A Het ion with its single 1s electron also con-
stitutes a small tight core of charge +| e | to which two
electrons can be bound in an approximate configuration
2s*, as in Li-. However, the resultant configuration
152s? of Heo lies now nearly 20 eV above the configura-
tion 1s?, and can therefore autoionize. It is the state
152s? which shows up as a Feshbach resonance, with a
binding energy of about 0.47 eV with respect to the
(1s2s)3S state of He. This binding energy is somewhat
smaller than the binding energy of 0.6 eV of the 1s°2s
state of lithium. Using such an approach, one can apply
this kind of numerology to other twinned atomic
systems.

Kuyatt, Simpson, and Mielczarek (1965) use a
somewhat different method of comparison: They con-
sider the known energy levels of doubly excited states
in helium (2s*, 252p, 2%, 3s3p, etc.). The two excited
electrons are moving in a Z=2 field, whereas the two
electrons in He~ (152s, 152s2p, etc.) are moving in the
Z=1 field of Het. Kuyatt ef al. take the energies
of the doubly excited states of helium relative to the
energy of Het + and divide this energy difference by
Z=4 in order to obtain the corresponding energies of

the Hee states relative to Het, There is a fair resem-
blance between the HeTM states thus obtained and the
measured values.

Still another comparative method is used by Swanson,
Cooper, and Kuyatt (1973). In order to interpret
resonances in krypton, they compare the spectrum of
resonances, i.e., Kr~, with the isoelectronic atom, RbI.
It appears that a fair comparison between these two
sets of energy levels can be made if an arbitrary scaling
constant is used.

D. Experimental Techniques

In this section we review briefly the particular ex-
perimental techniques which made possible the dis-
covery and the analysis of resonances. The develop-
ments described here span a period of about ten years,
but they are based on principles which have been known
for a much longer period. Actually we are dealing here
with a combination of methods which were brought to
bear on the problem of resonances in electron collisions
with atoms and molecules. Some of the techniques were
borrowed from other fields of physics: ultra-high
vacuum technology, low-current measurements, par-
ticle counting, and signal averaging. Also, progress
was partially facilitated by the commercial availability
of many of the necessary components. Parallel with
these developments was an improved understanding of
electron optics (see, e.g., Heddle, 1970; Read, 1970,
1971; Adams and Read, 1972) and the development of
new types of electron monochromators (see, e.g.,
Kuyatt and Simpson, 1967; Klemperer, 1965; Kuyatt,
1968). Good electron monochromators and electron
analyzers are a necessary prerequisite for the experi-
mental studies described in this and the following
review, since many of the phenomena of interest occur
in a very narrow range of energies and thus the use of
electron beams with a narrow energy resolution is a
sine qua non.

Since all of the techniques have been described in the
recent literature, in reviews (see, e.g., Bederson, 1968;
Kuyatt, 1968) and in books (Hasted, 1964; McDaniel,
1964; Massey and Burhop, 1969) only a very brief
outline of the techniques is given here. For details,
the reader is referred to the above reviews.

Many combinations of electric and magnetic fields,
using appropriate geometrical arrangements and suit-
able holes or slits, can give chromatic dispersion of
electrons and can thus be used for producing mono-
chromatic electron beams. Equally important is the
use of metals with desirable surface properties. One
wishes to have a surface with a uniform potential and
high conductivity. The surface should not be affected
by the gas which is being studied. Although many
surfaces have been tried by different groups (e.g., gold,
Advance, stainless steel, copper) it appears that
molybdenum is a most desirable surface.

A variety of geometries are useful for producing
monochromatic electrons: The parallel plate and the


APPENDIX X

Position of resonances in mercury (eV).

Kuyatt ef al. Fano and Cooper
(1965) Zapesochnyi and Shpenik (1966) (1965)
PS, 6D Sp
Feature No. » 5461 A 3650 A 4916 A
(Fig. 38) Transmission E, 7.73 eV 8.9 eV 9.2 eV Designation
1 4.07 see wee aoe (656%) *Pyyp
2 4.30 oe we (656f%)*Pae
3 4.89 vee see aoe wee (6s6p") *Po2
eee 5.0
vee 5.3
tee 5.6
4 7.81
5 7.94
6 8.14
7 8.22 8.5 8.2 see
8 8.83 one 8.8 see
9 8.99 0 9.0 9.1
10 9.75 9.7 9.6 9.8
11 10.29 10.0 10.2 10.2
12 10.4 eee tee
13 vee te see
11.2 11.1 11.1
see 11.9 11.7
we : ~12.2
tee 12.5 ~12.5 12.6

*The writing of this review was supported in part by the
National Bureau of Standards, Office of Standard Reference
Data, as part of the National Standard Reference Data
Program.

Adams, A., and F. H. Read, 1972, J. Phys. E 5, 156.

and H. Ehrhardt, 1966, Z. Phys. 192, 99.

H. Ehrhardt, and M. Eyb, 1968, Z. Phys.

Andrick, D., M. Eyb, and M: Hofmann, 1972, J. Phys. B

5, L15.
Baranger, E., and E. Gerjuoy, 1957, Phys. Rev. 106, 1182.

Barker, R. B. and H. W. Berry, 1966, Phys. Rev. 151, 14.

Bauer, E., and N. H. Browne, 1964, in Atomic Collision
Processes, edited by M. R. C. McDowell (North-Holland,
Amsterdam), p. 16 (1964).

Baumann, H., E. Heinicke, H. J. Kaiser, and K. Bethge, 1971,
Nucl. Instrum. Methods 95, 389

Baz, A. L, 1957, Zh. Eksp. Teor. Fiz. 33, 923. [Sov.
Phys.-JETP 6, 709. }

Bederson, B., 1968, Methods Exp. Phys. 7A, 67.

Bederson, B.. and L. J. Kieffer, 1971, Rev. Mod. Phys. 43, 601

Bhatia, A. K., A. Temkin, and J. F. Perkins, 1967, Phys. Rev.
153, 177.

Blatt, J. M., and V. F. Weisskopf, 1952, Theoretical Nuclear
Physics (Wiley, New York, 1952).

Bolduc, E., J.J. Quéméner, and P. Marmet, 1971, Can. J. Phys.
49, 3095.

“Bolduc, E., J. J. Quéméner, and P. Marmet, 1972, J. Chem.

43

Phys. 57, 1957.

Brode, R. 1929, Phys. Rev. 34, 673.

Burke, P. G., 1965, Advances in Physics, (Phil. Mag. Suppl.)
14, 521.

Burke, P. G., 1968, Adv. At. Mol. Phys. 4, 173.

Burke, P. G., J. W. Cooper, and S. Ormonde, 1966, Phys. Rev.
Lett. 17, 345.

Burke, P. G., 1969, Phys. Rev. 183, 245.

Burke, P. G., D. F. Gallaher, and S. Geltman, 1969, J. Phys. B
2, 1142. ,

Burke, P. G., S. Ormonde, and W. Whitaker, 1967, Proc. Phys.
Soc. Lond. 92, 319.

Burke, P. G., and H. M. Schey, 1962, Phys. Rev. 126, 147.

Burke, P. G., and A. J. Taylor, 1966, Proc. Phys. Soc. Lond.
88, 549.

Burke, P. G., 1969, J. Phys. B 2, 869.

Burrow, P. D., 1970, Phys. Rev. A 2, 1774.

Burrow, P. D., and G. J. Schulz, 1969, Phys. Rev. Lett.
22, 1271.

Chamberlain, G. E., 1967, Phys. Rev. 155, 46.

Chamberlain, G. E., and H. G. M. Heideman, 1965, Phys. Rev.
Lett. 15, 337.

Chamberlain, G. E., S. J..Smith, and D. W. O. Heddle, 1964,
Phys. Rev. Lett. 12, 647.

Comer, J., and F. H. Read, 1972, J. Phys. E 5, 211.

Cooper, J. W., and J. B. Martin, 1962, Phys. Rev. 126, 1482.

Crooks, G. B., R. D. DuBois, D. E. Golden, and M. E. Rudd,
1972, Phys. Rev. Lett. 29, 327.



Fic. 2, Natural line shapes for
different values of g. Reverse the
scale of the abscissa for negative g.
[From Fano (1961).]

shifts. When the phase shift rises rapidly by 7 radians,
the resonance is located. The width is determined from
the energy range over which the phase shift rises
through w radians. This method appears to be very
general and gives, in addition to the location and posi-
tions of resonances, cross sections for various processes.
However, in all but the simplest systems, the computa-
tional needs become enormous. Therefore, considerable
@ priori judgement must be exercised as to which states
to include to make a particular cross section meaningful.
A great deal of relevant insight has been gained by the
close-coupling calculations for various atoms and mole-
cules. The frame-transformation theory also belongs in
category (a). Here, an expansion is performed in the
molecular frame of reference and the region around the
molecule is divided into a “core region,” and an outer
region in which electron correlations are disregarded.
This method has had good successes in recent years.
Theories treating resonances as decaying states
(which they are) are based on the Kapur-Peierls
theory. Here, a stationary value for a complex energy is
obtained, which gives both the width and the energy of
the resonance. Problems are the need for good wave
functions and the need to define a definite radius of

interaction. Both shape and Feshbach resonances can be
treated in this manner.

Theories treating resonances by the use of projection
operator techniques solve directly for the expectation
value of the Hamiltonian, with the decay of the state
ignored. The decay can be later introduced to give an
estimate of the width of the state, but this is usually a
difficult step. Only Feshbach-type resonances can be
calculated in this manner.

Similar to the latter category are the techniques which
search for locally stationary points of the expectation
value of the Hamiltonian. A foremost example is the
“stabilization method.” Here, one takes a trial function
which contains all the knowledge one has about the
resonance. Both shape and Feshbach resonances can be
calculated in this manner, but the width is again a
difficult quantity to extricate.

When scattering amplitudes are calculated, struc-
tures in the cross section can be caused by poles, zeros,
and branch points in the scattering amplitude. Only
the poles should be associated with resonances. The
zeros in the scattering amplitude for a single partial
wave are associated with Ramsauer minima.

For simplicity of interpretation we assume in this


APPENDIX I

Resonances in H (below n= 2).

State Energy (eV) Width (eV) Method Author
1S 9.61 0.109 cc Burke and Schey (1962), Smith et al. (1962)
9.559 var O'Malley and Geltman (1965)
9.557 var Bhatia et al. (1967)
9.56 Gailitis (1965)
9.55 Holgien and Midtdal (1966)
9.56 0.048 Burke and Taylor (1966)
9.575 0.0543 cc Burke (1968)
9.560 0.0475 cece Burke (1968)
9.587 0.0501 ps. st. Burke, Gallaher, and Geltman (1969)
9.56:0.01 0.0430.006 Exp McGowan (1967)
9.558+0.01 Exp Sanche and Burrow (1972)
1s 10.178 var O’Malley and Geltman (1965)
10.177 var Bhatia et al. (1967)
10.178 0.00241 cc Burke (1968)
10.178 0.00219 ccc Burke (1968)
BAY 10.149 var O’Malley and Geltman (1965)
10.146 var Bhatia ef al. (1967)
10.151 1.89X 10% cc Burke (1968)
10.150 2.06 10 cece Burke (1968)
1p 10.178 var O’Malley and Geltman (1965)
10.179 2.26X 10% cc Burke (1968)
10.177 4.5010 cece Burke (1968)
3p 9.727 var O’Malley and Geltman (1965)
9.731 var Bhatia et al. (1967)
9.768 0.00797 cc Burke (1968)
9.740 0.00594 cece Burke (1968)
9.759 0.00571 ps. st. Burke, Gallaher, and Geltman (1969)
9.71+0.03 >0.009 Exp McGowan (1967)
9.7340.12 Exp _Kleinpoppen and Raible (1965)
9,700.15 Exp Schulz (1964)
9.73840.01 0.0056-0.0005 Exp Sanche and Burrow (1972)
1D 10.160 0.0078 cc Burke (1968)
10.125 0.0088 ccc Burke (1968)
10.128-£0.01 0.007340.002 Exp Sanche and Burrow (1972)
10.133-0.015 Exp Ormonde et al. (1969)
3p 10.194 0.0008 cc Ormonde et al. (1969)
10.190 0.0002 6-state Ormonde et al. (1969)
10.198 var O’Malley and Geltman (1965)
8S 10.202 var O’Malley and Geltman (1965)
1p 10.203 var O’Malley and Geltman (1965)

Abbreviations: cc: close-coupling calculations. ccc: close-coupling plus correlation. ps.st: pseudo-state calcula-
tions. var: variational calculations. Exp: experiment.

37


Taylor and Thomas (1972) calculated the position
and designation of the state responsible for the experi-
mental structure, using the stabilization method which
is described in detail by Taylor (1970) and by Hazi and
Taylor (1970). Taylor and Thomas (1972) find that a
short-lived resonant state, H-~, with a configuration
principally (2s)*2p2P° and an admixture of (2p),
exists at an energy of 14.8 eV and that its width can be
estimated to be about 1 eV. The calculated energy and
the lifetime are in good agreement with the experiment
of Walton et al. (1970). Taylor and Thomas further
point out that they find another resonance with a
largely (2p)? wave function at some higher, unspecified
energy.

The geometric structure of the H~~ ion has been
studied by Herzenberg and Ton-That (1973). They
suggest that the only geometry which can lead to a
quasistationary state must have all three electrons lo-
cated at about the same distance from the proton, near
the corners of an equilateral triangle. Then all three
electrons comprising the H~ ~ ion are attracted to the
proton. By minimizing the expectation value of the
Hamiltonian with respect to parameter controlling the

Jose
4 a3 stare
3
3
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“
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2 ‘
9 o
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F oadtnr \ 3 state
Bore x
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01
ta
0.0:
39 1010 (Ont tore

ELECTRON ENERGY (eV)

Fic. 15. (a) Close-coupling 'D cross sections over the resonance
region. (b) 1D cross sections folded with the resolution of the
experimental electron beam. The theoretical calculations cor-
respond to the left-most scale, and the experimental points to
the scale on the right. Because the measurements are relative,
the results are displayed as shown in order to emphasize the agree-
ment in shape between theory and experiment. [From Ormonde,
McEwen, and McGowan (1969).]

*P.ovo:
° EXPERIMENTAL

e oy
z
9
o
fp .088:
&
8
> .
S
=
S
rd
a
W .080:
a
oS
4
S

.0754

99 10.0 10.1 10.2

ELECTRON ENERGY (eV)

Fic. 16. Comparison of experimental and theoretical cross
sections in the energy range 10.0-10.2 eV, for 90° scattering in
atomic hydrogen. The theory (close-coupling) includes the 1D
and 'S resonances as well as the #*.S and *D background phase
shifts. The theoretical results are averaged over a 15° cone and
folded with the experimental beam width. The absolute scale for
the experimental points is obtained by normalizing the measured
differential cross section in the region below the lowest 15 res-
onance to the calculated cross section in that region. [From
Ormonde, McEwen, and McGowan (1969).1]

radial distance of the electrons from the proton and
the angles between the electrons, they find a quasi-
stationary state. Their value for the energy of this
state is 11.9 eV (compared to 14.5 eV for the experi-
mental value quoted above) and a lower limit for the
width is '>0,3 eV. The contribution of the s*p con-
figuration is 87%, that of the p* configuration is 10%.

Herzenberg and Ton-That also find an analogous
state in He-, at an energy of 45.9 eV, with all three
electrons equidistant from the nucleus. This state could
provide an interpretation for the broad resonance
around 50 eV (see Sec. IIIC) observed in helium by
Crooks et al. (1972).

Other doubly charged negatives have recently been
observed using mass spectrometry (Baumann ¢f al.,
1971). In this experiment, negative ions are formed in a
Penning source. Electric and magnetic deflection ex-
periments confirm that doubly charged negative ions
are present in the beam. The ions which have been
identified are O- -, Te~-, Bi--, F--, Cl-~, Br~~, and
I--. The lifetime of the above ions must be relatively
long in order for them to survive their trip through the
mass spectrometer (~10-*-10~ sec) . This is in contrast
to H-~, for which the lifetime is about 10 sec. Fano
(private communication) suggests that a plausible

16


can yet be made of this phenomenon. Nevertheless, the
reaction itself appears to be of interest to the under-
standing of electron exchange in neutral-neutral col-
lisions.

Electron-Energy Distribution in Fast Ion-Neutral
Collisions

Fast ion-neutral collisions also lead to electron
ejection which can be associated with resonances.
When a stable negative ion collides with a neutral
atom, the outer electron in the negative ion can be
promoted to a resonance state. A peak in the energy
distribution of ejected electrons occurs at the energy of
the resonance. The results of such an experiment,
involving O- ions, are discussed in Sec. VII.

It is conceivable that the impact of fast positive ions
on neutral atoms also could yield electrons associated
with resonances. This process would involve electron-
exchange, similar to that in neutral-neutral collisions.

Calibration of Energy Scales

Any discussion of new methods of measurement in
the field of electron impact on atoms and molecules
must point out the really significant progress which has
been made in the past ten years or so in our ability to
calibrate the electron energy scale accurately. Usually,
the “primary” standard is a known ionization potential
or an excitation potential. Important resonances are
calibrated against such a standard. The resonances, in
turn, can be used as “secondary” standards if they have
a natural width which is narrow compared to the elec-
tron energy spread. Such a calibration can be performed
to an accuracy of +0.03 or +0.05 eV, although in
some cases even lower values are quoted.

Ul. HYDROGEN

From the theoretical viewpoint atomic hydrogen is
obviously the simplest system for the calculation of
resonances, but measurements in atomic hydrogen are
difficult. The combination of establishing a mono-
chromatic electron beam and a source of atomic hydro-
gen in an experiment proved to be elusive for many
years. Thus, it is not surprising that the first indication
of resonances in the scattering of electrons by atomic
hydrogen came from theoretical work (Burke and
Schey, 1962) and the lowest state was identified as 1S,
lying about 0.6 eV below the n=2 state of hydrogen.
Since that discovery many determinations using a
variety of theoretical methods have been made of the
resonant energies.

The position of resonant energies can be evaluated
by variational methods as eigenvalues of the Hamil-
tonian with the open channel projected out. The
results thus obtained are approximations to the actual
physical resonances in that the shift resulting from the
coupling to the neighboring continuum is not included,
and the finite width of the state is not considered.

ll

It turns out, however, that the actual shifts are small
so that the variational calculations give a close indica-
tion of the position of the compound-state energy
levels. This can be ascertained from Appendix I, where
the results of the variational calculations are indicated
by the appropriate symbol.

The position of resonant energies can also be deter-
mined by calculating the elastic or inelastic cross section
for scattering of electrons with a very fine mesh of
incident energies. In such a calculation, the existence of
the resonance is exhibited by rapid transit of the phase
shift through 7 radians in the vicinity of the compound
state. From the variation of the phase shift, one can.
determine the position and width of the resonance and
thus obtain a more complete description of the resonant
behavior. The rapid transit of the phase shift through
x radians is reflected in the behavior of the cross section
by the appearance of sharp structure. To calculate the
cross section, one must include several states of the
target atom. For low-lying levels in hydrogen, it has
been shown that it is sufficient to include the three
lowest states of the atom in the close-coupling calcula-
tion (cc). As a next step, one can do close-coupling
calculations with correlations included (ccc). For some
calculations it has been found desirable to include six
states of the target atom in the calculations (6-state).

Appendix I lists the results of various calculations
for the energy and the width of resonances below the
n=2 threshold. An energy level diagram is shown in
Fig. 9. Here, only a single set of energy levels is shown,
extending up to the 2=3 threshold. Of the values listed
in Appendix I, it is expected that the most accurate
ones are those using an expansion of the wave function
in terms of the 1s, 2s, 2p states of the target, together
with up to 20 correlation terms. The results thus ob-
tained are marked (ccc) in Appendix I, following the
notation of Burke (1968). The values marked (cc) in
Appendix I are obtained by Burke using the 15; 25, 2P
states of the target atom in a close coupling expansion.
The agreement between the values obtained (cc and
ccc) gives confidence that the three-state close-coupling
results are reliable. In fact, the good agreement between.
Burke’s values and the values obtained by other
investigators is remarkable.

Alternately, one can use the pseudo-state method.
(ps. st.) developed by Burke, Gallaher, and Geltman
(1969) in which the first few states included are atomic
eigenstates while higher bound and continuum states
are represented by pseudo-states chosen to be orthogo-
nal. The results of these calculations are marked
(ps. st.) in Appendix I.

The theoretical values shown in Fig. 9 are those
obtained by Burke using the close coupling plus correla-
tion method (ccc). Above the lowest two levels, 1S and
3P, and below the n= 2 threshold of H, there are shown.
a number of states which converge to the n= 2 limit. It
has been pointed out by Gailitis and Damburg (1963)
that the degenerate dipole coupling between the 2S and


Resonances in Electron Impact on Atoms*

George J. Schulz

Department of Engineering and Applied Science, Mason Laboratory, Yale University, New Haven, Connecticut 06520

Electrons colliding with atoms can form, at well-defined energies, compound states consisting of the target
atom plus the incident electron. The compound states, which are also called “resonances” or “temporary
negative ions,” often dominate electron collision processes. In this review we discuss the experimental
methods which are useful for studying these resonances, and review the results obtained by various
investigators. We list the energies and the widths of resonances for H, He, Ne, Ar, Kr, Xe, Li, Na, Hg, and
. The configurations and other properties of resonances in atoms are discussed. Whenever applicable,
results are presented in the form of tables and energy level diagrams.

Key words: Atoms, H, He, Ne, Ar, Kr, Xe, Li, Na, Hg, 0; compound states; cross-sections;
electron impact; energy levels; resonances; temporary negative ions.

CONTENTS

I. Introduction
A. Theory
B. Relationship of Theory to Experiment
C. Isoelectronic and Isostate Comparisons.
D. Experimental Techniques

IL, Hydrogen,
A. Resonances in the Biastic Cross Section:
B. Resonances in the Inelastic Cross Sections.
C. A Resonance Involving H-~.

MY. Helium... ...eeseeeeee
A. Classification of Energy Levels in He.

B. Resonances from 19.3 eV to the Tont
tal

19. ,
19.45 eV (2)...
19.5-20.3 eV (2).
20.3-20.45 eV (22P)
Effects near the Thresholds
Excitation Cross Section
Structure in the Elastic Cross Section near the
295 and 215 Thresholds (Wigner Cusps) .
21.0 eV (2*D)..
22.42-24 eV (385, 3*P etc.) Optical Excitation
Functions.
C. Resonances Above’ the Tonization | Potential
(2s!2p)*P and (252p%)2D

IV. Neon, Argon, Krypton, and Xenon
‘A. Resonances below the Ionization Potential
B. Resonances above the Ionization Potential

V. Lithium and Sodium
VI. Mercury...
VII. Oxygen (0).

Px 2 PED

Appendixes

a)

. Resonances in H.....

II. Values for the 15(2s)?%5 Resonance in Helium

III. Position of Resonances below Ionization in Helium.

Ma. Larger Structures in the Optical Excitation Functions
of He

A

A Position of Resonances above the Ionization Potential
in He.............

IV.
V. Position of Resonances in Neon.
VI. Position of Resonances in Argon.
VII. Position of Resonances in Krypton
VIII. Position of Resonances in Xenon..
IX. Suggested Resonances in Ne and Ar.
X. Position of Resonances in Mercury. .

References... 0... ccc cece cece eee cee ne eee e ee ee ees

I, INTRODUCTION

This paper and the paper following deal with a
special topic in the field of electron impact on atoms and
molecules. The object of interest are “resonances,”
also called “compound states” or “temporary negative
ions.” These three terms are synonyms and will be
used interchangeably. “‘Resonances” occur at more orless
well-defined energies when electrons scatter from atoms
or molecules. The object can be considered as a “com-
pound state,” in that the incident electron attaches
itself to the target atom (or molecule) for times which
are longer than the normal transit time through the
atom or molecule. Since the projectile is always a
negatively charged electron, the “compound state”
has a negative charge. Hence the term “temporary
negative ion.”

The “resonances” can be viewed as nonstationary
(short-lived) states of an atom or molecule. In sharp
contrast to stationary states of atoms, “resonances”
decay by the emission of electrons, not by photons. Our
definition of “resonances” in the present context
excludes some types of nonstationary states which also
can be viewed as resonances. For example, doubly
excited states of atoms (e.g., the 2s? and 2s2p states in
helium) are nonstationary states which decay by
eléctron emission, yielding positive ions. Nevertheless,
such states are excited states of the neutral atom, and
therefore do not meet our definition, namely that the
states be temporary negative ions. This limitation of
the review is rather arbitrary.

Resonances were discovered almost simultaneously
by experiment and theory about 10 years ago, and great
progress has been made in our understanding of these
phenomena in the past decade. These two review papers
represent an effort to discuss the spectroscopy of
resonances in a more or less systematic fashion. The
review is divided into two parts: In the present paper,
we discuss resonances associated with atoms; in the
second paper we discuss resonances associated with
diatomic molecules. Resonances associated with more
complex molecules also exist, but too little is known
about them to justify inclusion in the present work.


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107


oa
Vve2

§

: /\ V=3

§ .

& Ve4

g a4;

-P8e8 eo 8, ok,

Fic. 30. Energy dependence of the vibrational excitation in
Nz. The angle of observation was 72 degrees. As in Fig. 29, eight
vibrational states are visible in the region of the *II, compound
state. The similarity of the curves with those shown in Fig. 29
indicates that the structures in the vibrational cross sections are
independent of angle of observation. [From Schulz (1964) .]

of the resonances in the B1Z,+ states results from a
d-wave component in the entrance channel, but have
discarded this interpretation because it leads to an un-
reasonably large d-wave amplitude in the entrance
channel.

The above considerations relay heavily on angular
distribution measurements which, in molecules, may

66

not be as well understood as one would wish. For exam-
ple, Black and Lane (1971) point out that in certain
decay channels transitions may show preference for a
change in rotational quantum number, e.g., j=0—j=1.
Such an effect would upset the simple interpretation
of angular distribution measurements and may render
unnecessary the assignment of a separate series for
bands “d” and “e.” More detailed analysis must be
awaited.

These uncertainties are taken into account in Table
II. Arrows point to series “a” and “d” and to series
“c” and “e,” indicating that future consideration may
show that “a”=“d” and “c”=“e.” In energy, these
two sets of series (‘‘a” and “d”; “c” and “e’”) are
almost coincident.

Samples of recent experimental results, as observed
in different decay channels, are shown in Figs. 17-22.
Figure 17 shows the results of a transmission experi-
ment by Sanche and Schulz (1972) in which the deriva-
tive of the transmitted current is measured directly.
This experiment, following closely in concept the ex-
periments of Kuyatt e¢ a/. (1964) and Schulz (1964),
exhibits higher sensitivity to sharp structures than
previous transmission experiments. In the experiment
of Sanche and Schulz (1972), optical focussing effects
are largely eliminated by the use of an axial magnetic
field and the detection sensitivity is enhanced by modu-
lating the electron energy in the collision chamber.
The advantage of the transmission experiment is the
overview that it provides for a large region of energy.
However, many details of resonances, such as the
decay channel and the angular distribution of scattered
electrons, cannot be easily extricated from transmission
experiments.

Figures 18 and 19 show the results of Comer and
Read (1971a) for which a double electrostatic analyzer
was used. By studying resonances in high vibrational
states of the electronic ground state, Comer and Read
are able to eliminate all interference effects between
resonant and nonresonant scattering; in fact they dis-
covered series “‘b” by observing resonant structure in
vibrational levels above »=8, as is shown in Fig. 19, It

Tasue III. Position of maxima in the elastic and inelastic
cross sections of Nz (Ehrhardt and Willmann, 1967).

Energy, eV
v 2=0 v=1
0) 1.89 1.93
1 2.15 2.24
2 2.40 2.55
3 2.65 2.82
4 2.89 3.07
5 3.13 3.31
6 3.36 3.53
7 3.58 3.76



HELIUM
>
=
a a
Sk
Fa
#
ZL
w
Sh
=
<h
Pd
ca
1 Lo inet |
19.0 20.0 21.0 22.0 23.0 24.0

IMPACT ENERGY (eV)

Fic. 23. Comparison of cross sections tor production of
metastables in helium. (experiments) a—resonance at 19.3 eV
observed in a transmission experiment; b—total metastable cross
section (Pichanick and Simpson, 1968); c—total metastable
cross section (Schulz and Fox, 1957); d—2'S differential cross
section at 72° (Schulz and Philbrick, 1964) ; e—2!S differential
cross section at 0° (Chamberlain, 1967) ; £285 differential cross
ant a 0° (Chamberlain, 1967). [From Pichanick and Simpson

resonance can be clearly observed at 90°, at which
angle the p wave disappears. An analysis of the phase
shift shows that the phase shift of the s wave for
potential scattering is 100 degrees, for the p wave 25
degrees, and for the d wave 4 degrees. These phase
shifts can be compared with a subsequent study of
Gibson and Dolder (1969) who obtained m=110°,
m= 17°, and m=3°. The agreement with the theory of
LaBahn and Callaway (1964) is satisfactory. The
variation of the resonance shape with angle is attributed
to the interference of the s-wave with the other partial
curves. Whereas the width of the resonance was
estimated by Andrick and Ehrhardt (1966) to be
15-20 meV, more detailed analysis by Gibson and
Dolder gives a value of 8 meV for the natural width at
half-height, in good agreement with previous estimates.
The value of 8 meV for the width of the resonance at
19.3 eV is probably the best experimental value
available at this time. Appendix II compares the
widths deduced from experiment and from theory. The
latest calculations of this width, due to Temkin et al.
(1972) and Sinfailam et al. (1972) give values of 14
and 15 meV, respectively.

2. 19.45 eV (?)

Asmall structure was observed by Gibson and Dolder
(1969) in the differential elastic cross section just above
the 225 resonance. This structure is most pronounced at
an angle of observation of 54.5° and disappears at 90°.
The angular distribution is indicative of a resonance in
the p wave and we would deduce that the designation of

21

the state is (1s2s2p) 2P°, The signal-to-noise ratio with
which the 19.45 resonance was observed at 54.5°
was only unity, and thus this observation alone cannot
be considered to be conclusive. However, this resonance
was observed at the identical energy in the transmission
experiment of Kuyatt, Simpson, and Mielczarek
(“peak” at 19.43-0.01 eV, “dip” at 19.47--0.01 eV),
but was visible only on the runs with the highest energy
resolution. Also, Golden and Zecca (1970) observed
structure in their transmission experiment (“peak”
at 19.47 eV, “dip” at 19.52 eV). Andrick and Ehrhardt
(1966), whose experiment is similar to the experiment
of Gibson and Dolder, did not observe the structure at
19.45 eV. Neither did Pavlovic (private communica-
tion) observe this resonance in an experiment which
was specifically performed to study this resonance.
Sanche and Schulz (1972) consider the 19.45 eV reso-
nance a spurious effect resulting from the replica-
tion of the (152s?) #5 resonance by electrons which have
lost energy on collision with slits.

In their theoretical study, Eliezer and Pan (1970)
found a ?P root at 19.6 eV, but it “stabilized rather
poorly.” The latter authors consider the evidence un-
convincing. Burke did not obtain such a state. Neither
did Temkin, Bhatia, and Bardsley (1972), who made a
purposeful attempt, using their quasi-projection theory,
to find states below 19.8 eV. Similarly, Sinfailam and
Nesbet (1972) searched for resonances below the 2°5
state with a fine mesh using a variational technique
which takes polarization and correlation effects into
account. They, too, find no evidence for resonances
apart from the #5 resonance. Thus we must conclude
that the existence of a resonance at 19.45 eV is uncertain
and in serious doubt.

3. 19.5-20.3 eV

Between 19.5 and 20.3 eV only Golden and Zecca
(1970) have observed resonances. These authors ob-
serve 4 structures, each exhibiting a peak and a dip.
The assignment given to these structures and the
energies (in eV) of the peak and the dip are: (1s2p)*Dyy:
19.58/19.62; (1s2p*)*D,,: 20.04/20.10; (1s2s2p)*P, 9:
20.17/20.21; (152p?)?S},: 20.3/20.35. No one else has
observed structure attributable to resonances in this
energy range (19.5-20.35 eV), although other trans-
mission experiments in fact had a higher sensitivity for
observing resonant structures. One would have to
invoke some special features of Golden and Zecca’s
apparatus which would make this particular apparatus
more sensitive to the particular resonances in the energy
range under discussion. The angular acceptance angle
for forward-scattered electrons could possibly be such a
feature, but up to now very little attention has been
given to such considerations.

Until the structure in this energy range is reproduced
by other experiments, one must retain a skeptical
attitude regarding the reality of the 4 structures in the



TROCHOIOAL
© MONOCHROMATOR

COLLISION
CHAMBER” OC

Fic. 5. Schematic diagram of a

transmission experiment (top) and
the details of the trochoidal mono-
chromator (bottom). | [From
Sanche and Schulz (1972) and
Stamatovic and Schulz (1970).]

AL
s)

Filament
Entrance

atoms and for molecules. The high sensitivity for
detecting resonances is thus established. However,
since one cannot obtain information on the angular
distribution of the electrons, one has great difficulty
in establishing the configuration of the resonances.
Also, it is difficult in this method to establish the final
state to which a resonance has decayed. Thus, if one
wishes to obtain more detailed information regarding
the configuration and the channels of decay, one has to
revert to the less sensitive but much more versatile
double electrostatic analyzers.

It should be noted that the transmission method for
detecting resonances need not use an axial magnetic
field. Instead of a retarding electrode (R), one then
can use a simple hole or slit for limiting the exit angle.
Either method, with or without a magnetic field, should
lead to an exponential dependence of the transmitted
current with NQL. Optical focussing effects, i.e., the
energy dependence of the transmitted current in the
absence of gas, are inherently different in these two
systems of measurement, but the optical focussing
effects are probably easier to overcome in the presence
of an axial magnetic field. And when one wishes to study
resonances in a wide energy range, it is essential that
optical focussing effects be small.

Total Cross Section Measurements using the Ramsauer
Method

The measurement of resonances using the Ramsauer
technique is a modern application of possibly the oldest
quantitative approach to the measurement of cross

be

sections, originated by Ramsauer and Kollath in the
1920’s and 1930’s. A review of the early work can be
found, e.g., in Massey and Burhop (1969). A modern
version of the apparatus is shown in Fig. 6. It is very
similar to that used by Ramsauer and Kollath, the
major modification being the provision here for differen-
tial pumping. Briefly, the electrons from an oxide-
coated cathode, or a thoriated iridium filament, are
momentum selected by the combination of the three
slits, Si, Se, Ss, and a uniform magnetic field is applied
perpendicular to the plane of the drawing. The electrons
are then allowed to interact with the gas to be studied in
the scattering cell, and the transmitted electron signal
is studied as a function of gas density in the scattering
region at a particular value of electron energy. If it is
assumed that a current of electrons I.o+J,.o= Jo enters
the scattering region, the current reaching the collector
is given by J,(Z)=I.o(E) exp[—o:(E)N«x], where
I. is that part of the current entering the scattering
region which would reach the collector in the absence
of scattering, :(£) is the total cross section, N is the
gas density, « is the path length of the electron beam
through the scattering chamber, and E is the electron
energy. The current reaching the scattering chamber
walls is given by I,=I,o+J.oL1—exp(—oNx) J, where
I. is that part of the current entering the scattering
chamber which would reach the scattering chamber
walls in the absence of scattering. Then we have
In [U-+I.) /Ie]= In [(Zeot-Ioo) /Too]+o.Nx. The total
cross section is directly determined by measuring the
slope of a plot of the left-hand side of this equation vs V,



virtual state as a “bound” state that just slipped out of
the potential well.

Taylor (private communication) describes the
formation of the two 2°S states as follows: The 28S
state mixes with the 28P state, thus forming a polariza-
tion potential which combines with the low screening
in excited states to form a well. The electron binds in
this well and we get a resonance below the 2°S state.
Similarly, the 2'S and 2!P states mix to give a resonance
below the 215 state. Both resonances have a *S' charac-
ter. As the two *S channels mix, the two states split
apart. The lower 7S state moves down to 19.3 eV and the
upper 2S moves up and slips out of the well, to become
virtual. This approach, if substantiated by calculations,
provides a very picturesque way to visualize the two
low-lying s-wave resonances in He. In fact, experiments
in other rare gases seem to indicate that such a picture
is applicable there too.

The designation of the virtual state in terms of
orbitals is by no means clear. Table I indicates that the
only 2S state which is not accounted for has the 1s2?
configuration. However it is not suggested that this is
the proper answer, since the 1524? may have a very
large width, and may lie at higher energies.

The resonance near the 24S threshold also strongly
influences the superelastic cross section e+He(2!S)—>
He(28S)+e. This cross section exhibits a strong peak
near zero energy. A very large average cross section for
this process (~3X10- cm?) for 300°K electrons had
been previously measured by Phelps (1955) and the
theory of Burke et al. (1969) shows agreement with this
large value, which was not completely understood until
the resonance process was invoked.

6. Structure in the Elastic Cross Section near the 2S and
218 Thresholds (Wigner Cusps)

The opening of an inelastic channel should be accom-
panied by the appearance of a cusp in the elastic cross

Tt

Fic. 30. Derivative of the
transmitted current in he-
lium in the region of doubly
excited states. The vertical
lines show the positions of
the 2s? and 252p excited
states of helium. [From
Sanche and Schulz (1972)..]

2) »

2
s

DERIVATIVE OF TRANSMITTED CURRENT (ARB. UNITS)

L. (2

57 59
ELECTRON ENERGY, (eV)

26

DOUBLY EXCITED RESONANCES,
STATES, He HeTM
2)!
sot 28") P55 95
> 2p2) 3p
° (20)? 59.64
ui
it
4
a
5
a
59
z (2s2p) 5P
3 —S— 58.34
a
6
5
fo} 2) 2
3 (282p%)?0 4 9
>
5 set
2) 1
in Gs" 's 57.82
2
tT
2 2
(2822p) 2P 5
57

Fic. 31. Energy level diagram for the lowest doubly excited states
of helium and the two associated compound states, He-.

section (Wigner, 1948; Baz 1958). Such a cusp has been
observed recently in a transmission experiment in
helium (Sanche and Schulz, 1972) as a sharp in-
crease in the transmitted current and its derivative
just below the threshold for the 2°. and 2'S states. The
results are shown in Fig. 27. In the differential elastic
cross section at 90°, the Wigner threshold cusp appears
as a downward step which causes the cross section to
decrease by about 1% (Cvejanovic, Comer, and Read,
1973).

7. 21.0 eV (2D)

The experimental determination of the location of the
2D resonance comes from the observation of a well-
pronounced peak in the 2°S and 2!S cross sections at
various angles of observation as shown in Fig. 26.
The decay into the elastic channel has not yet been
observed. The designation as *D comes from the angular
distribution and from theoretical considerations. The
experimental observations are as follows:

28S excitation: Schulz and Philbrick (1964) observed a
peak, at 21.0 eV with a width of about 0.4 eV, at an
angle of 72°. Ehrhardt and Willmann (1967) extended
the angle of observation to include the range 7—110°.
The angular distribution at 21.0 eV is found to be
characteristic of a d wave, as can be seen in Fig. 25.
Chamberlain (1967) studied forward-scattered elec-
trons having excited the 2*S state and finds structure at


&

_ tryst]
fo S =“
2
7
3 > 4
; 06] &
&
gos Zz a
doz F
e
5 o z 4
2 #
-oa 2
a , 4
oa ee
ost -1 1 1 L 1 L n L
1 es ren i tit 10° «1.2 14 1.6 1.8 2.0 2.2 2.4 2.6 «o
oat a
INTERNUCLEAR SEPARATION (A)—> INTERNUCLEAR SEPARATION (R)
@) )

Fic. 69. (a) Approximate potential energy curves for Oz and 0,7.

‘The Os" curve should have its minimum at 1.341 A (Celotta ef al.,

1972). The center of the v’ =4 state is located at 0.091+0.005 eV and it has a fine structure splitting (Igj2—Ilys) of 20-2 meV (Land
and Raith, 1973). The »=3 level of Ox(X #2,-) is coincident in energy with the v’ =8 level of Os-(X *U,) (Spence and Schulz, 1970).
[From Boness and Schulz (1970).]] (b) Ad initio calculations of adiabatic potential energy curves for O;~. [From Michels and Harris

(1971).J

the ratio of energies of the ejected electrons is also
close to unity since the compound state in Np is located
near 2.3 eV and the spacing of vibrational levels is
about 0.3 eV. Thus the barrier penetration in N2 does
not differ much for the decay channels leading to the
low vibrational states.

The widths of the »’=4—10 vibrational states of
O;-(X *II,) have been calculated by Koike and Wata-
nabe (1973) who find a value of 0.004 meV for the
v’=4 state. This value has a confidence limit of a factor
of about two (Watanabe, private communication) and
thus it is in good agreement with the estimate of
0,002 meV made by Herzenberg (1969) from the
absolute magnitude of the vibrational cross section in
O:. The calculated values of Koike and Watanabe are
listed in Appendix X.

3. Potential Energy Curve for Ox-(X "M,)

Using a Morse-function representation together with
parameters derived from electron spectroscopy, Boness
and Schulz (1970) derived the potential energy curve
for the O,-(X "I,) state. This curve, together with the
curve for the ground state of O2(X *3,-), is shown in
Fig. 69(a). The curve is drawn so that the »=3 level of
O2(X #2,-) coincides in energy with the v’=8 level of
O.-(X *II,). This coincidence has been established by
Spence and Schulz (1970) and by Linder and Schmidt
(1971). In order to bring the O.~ curve into agreement
with the results of Celotta ef al. (1972), it should be
shifted to smaller internuclear separations by 0.036 A,

95

so that the minimum of the potential energy curve
would be at 1.341 A.

Ab initio calculations for the low-lying potential
energy curves have been performed by Michels and
Harris (1971) and by Krauss, Neumann, Wahl, Das,
and Zemke (1973). The agreement between the two
sets of theoretical calculations appears to be good. The
set by Michels and Harris is shown in Fig. 69(b).

4. Equilibrium Internuclear Separation and Electron
Affinity: Photodetachment Spectroscopy

As in the case of NO, the electron affinity of O2 was a
matter of dispute for a long period of time. The various
values have been summarized, as of 1970 by Boness
and Schulz (1970). At that time it appeared that only
the value of Pack and Phelps (1966), obtained from
drift-tube studies of attachment and detachment
coefficients in thermal equilibrium, was free of serious
objections. The value of Pack and Phelps (0.43 eV)
has recently been confirmed in a conclusive experiment
involving photodetachment. The value of Celotta et al.
(1972) is 0.400.008 eV.

Other recent values for the electron affinity con-
verge on the above value. Among these are the experi-
ments of Nalley and Compton (1971), and those of
Berkowitz et ai. (1971) as interpreted by Chantry
(1971).

The photodetachment experiment of Celotta et al.
(1972) also gives a value of the equilibrium inter-
nuclear separation, 7,= 1.341+:0.010 A, making obsolete


rr ee T
[~ ---+~-- seonce & Schott] Experiment 7
| aol cera 1
ae 4
—£ sol- 4
2b 4
3
= go 4
sree Sh Tose
aad et
[es ee ee
Y 2 3. 4 5 6 7

Vibrational Quantum Number

Fic. 57. Width of resonances in the elastic cross section of NO.
Open symbols represent the experimental observations and the
dashed line is drawn through these points. Filled-in symbols
with the solid line drawn through them represent the “real” width
of the resonances, obtained by deconvolution. In the deconvolu-
tion both the electron-energy distribution and the resonances are
assumed to be Gaussian. The data shown are those of Spence and
Schulz (1971) and of Ehrhardt and Willmann (1967). the width
is defined as the full width at half-maximum. [From Spence and
Schulz (1971b).]

not adequate to explain this peak and conclude that a
resonance or a series of resonances must be involved
to explain the cross sections near 20 eV.

V. NITRIC OXIDE, NO
A. Compound State at Low Energy (0-1.5 eV) X *2—

Nitric oxide, like Oz, forms a stable parent negative
ion and thus NO has a positive electron affinity. The
lowest negative ion state is the X *Z~ state whose
zeroth vibrational level is stable with respect to
autodetachment; however, the higher vibrational states
autodetach since they lie energetically above the »=0
state of NO (X *II,). For an understanding of electron

Taste VII. Parameters of NO~(X =~).

Electron scattering:
(Spence and Photodetachment:
Schulz) (Siegel et al.)
Equilibrium separa- 1.286 As 1.258:0.010 Ab
tion, re
Electron affinity, 50 meV 24(+10, —5) meVv>
EA(NO)
we 1704-20 meV 18225 meV
Welke 1.00.25 meV oo

* Values obtained using Badger’s rule.
» Preferred values.

scattering, one wishes to know the electron affinity, the
vibrational spacings of NO-, the anharmonicity, and the
equilibrium internuclear separation. Information re-
garding these parameters comes from various types of
experiments, discussed below, which shed light on the
nature of the shape resonance in NO.

1, Elastic Scattering

The values of the vibrational spacings of the low-
lying shape resonance are deduced (for both O2 and
NO) primarily from electron scattering experiments:
The energy dependence of the elastic cross section
exhibits structure at the positions of the vibrational
levels. The vibrational cross section to various states of
NO also exhibits relatively sharp peaks at the positions
of the vibrational states of NO-.

1 1 n
06 08 10

Energy (eV)

1
04

n
02

°

Fic. 58. Approximate cross sections for vibrational excitation
of NO by electron impact. The vibrational spacing of the neutral
molecule is indicated below the curves, and the vibrational spaci
of NO above the curve. [From Spence and Schulz (1971b).

Figure 56 shows the structure in the elastic cross
section as observed by Spence and Schulz (1971b),
by Ehrhardt and Willman (1967), and by Boness,
Hasted, and Larkin (1968). The spacing of the peaks is
about 160 meV and the agreement between various
experiments appears good. Interestingly, the width
of the observed peaks increases as the quantum number
increases, from 70 meV for the first peak to 100 meV
for the fifth. This effect can be clearly seen from Fig. 57.
A similar broadening may also occur in Oz, but has not
been observed experimentally because the width of the
peaks in O» is much narrower than in NO, and thus the
experimentally observed width of the peaks in O» are
almost entirely caused by the instrumental resolution.
Any changes in the natural width are hidden, in the
case of Oz, by the instrumental resolution.

88


__ TROCHOIDAL
© MONOCHROMATOR

____ COLLISION
CHAMBER Cc

=

Fic. 5. Schematic diagram of a

transmission experiment (top) and
the details of the trochoidal mono-
chromator (bottom). — [From
Sanche and Schulz (1972) and
Stamatovic and Schulz (1970) .]

Filament /,
Entrance

atoms and for molecules. The high sensitivity for
detecting resonances is thus established. However,
since one cannot obtain information on the angular
distribution of the electrons, one has great difficulty
in establishing the configuration of the resonances.
Also, it is difficult in this method to establish the final
state to which a resonance has decayed. Thus, if one
wishes to obtain more detailed information regarding
the configuration and the channels of decay, one has to
revert to the less sensitive but much more versatile
double electrostatic analyzers.

It should be noted that the transmission method for
detecting resonances need not use an axial magnetic
field. Instead of a retarding electrode (R), one then
can use a simple hole or slit for limiting the exit angle.
Either method, with or without a magnetic field, should
lead to an exponential dependence of the transmitted
current with QL. Optical focussing effects, i.e., the
energy dependence of the transmitted current in the
absence of gas, are inherently different in these two
systems of measurement, but the optical focussing
effects are probably easier to overcome in the presence
of an axial magnetic field. And when one wishes to study
resonances in a wide energy range, it is essential that
optical focussing effects be small.

Total Cross Section Measurements using the Ramsauer
Method

The measurement of resonances using the Ramsauer
technique is a modern application of possibly the oldest
quantitative approach to the measurement of cross

sections, originated by Ramsauer and Kollath in the
1920’s and 1930's. A review of the early work can be
found, e.g., in Massey and Burhop (1969). A modern
version of the apparatus is shown in Fig. 6. It is very
similar to that used by Ramsauer and Kollath, the
major modification being the provision here for differen-
tial pumping. Briefly, the electrons from an oxide-
coated cathode, or a thoriated iridium filament, are
momentum selected by the combination of the three
slits, Si, Se, Ss, and a uniform magnetic field is applied
perpendicular to the plane of the drawing. The electrons
are then allowed to interact with the gas to be studied in
the scattering cell, and the transmitted electron signal
is studied as a function of gas density in the scattering
region at a particular value of electron energy. If it is
assumed that a current of electrons J,o+J.0=Jo enters
the scattering region, the current reaching the collector
is given by I.(E)=Io(E) exp[—o.(E)Na], where
I is that part of the current entering the scattering
region which would reach the collector in the absence
of scattering, o:(£) is the total cross section, NV is the
gas density, « is the path length of the electron beam
through the scattering chamber, and E is the electron
energy. The current reaching the scattering chamber
walls is given by I,=Iw+I-o1—exp(—o.Nx) ], where
Io is that part of the current entering the scattering
chamber which would reach the scattering chamber
walls in the absence of scattering. Then we have
In (U-+-I2) /TeJ= In [(Leot+-Lo0) /Teo]+o.Nx. The total
cross section is directly determined by measuring the
slope of a plot of the left-hand side of this equation vs V,


ENERGY INTEGRATED CROSS SECTION (10cm?)

P|

|
deep ft be pe

2 4 6 4 0 12 « 16 18
QUANTUM NUMBER OF COMPOUND STATE, v’

Fc 67. Plot of energy-integrated cross section for vibrational
excitation to »=1, 2, 3, 4 vs quantum number of compound state,
as measured by Linder and Schmidt (1971b). The cross sections
consist of a series of narrow spikes at the positions of the vibra-
tional levels, v’, of the compound state.

served angular distribution is isotropic. The lifetime of
the X "II, compound state, Oz-, is long (i.e., ~10- sec
for the lowest vibrational member, »’=4), as will be
discussed below. For such a long-lived object, one has
to include rotation in the theory and the result of such
a theory yields a near-isotropic angular distribution, as
shown in Fig. 66. It is pointed out in Sec. VII that the
partial wave in which the resonance occurs is dx,

The absolute magnitude of the energy-integrated
vibrational cross sections for the v= 1, 2, 3, 4 state of Oz
are shown in Fig. 67 and are listed in Appendix X.
Spence and Schulz also measured the energy-integrated
cross sections, but their set of measurements is less
complete than that of Linder and Schmidt.

Disturbingly, Spence and Schulz’ values are by a
factor of 10 lower than the values of Linder and
Schmidt for those states which are measured in both
experiments. No clear-cut criticism can be found in
either experiment. However, the values of Linder and

94

Schmidt must be preferred at this time since they
agree better in order of magnitude with the analysis of
swarm experiments (Hake and Phelps, 1967) although
a detailed comparison is not yet possible because the
analysis of swarm experiments has not been performed
with the proper set of relative cross sections.

An interesting feature of the data can be brought out
by plotting the branching ratio of the cross sections
for v= 2 to v=3 and v=1 to v= 2 vs quantum number of
the compound state as is done in Fig. 68, Both curves
show an enormous rise as the quantum number 2’ is
lowered, indicating that a given compound state
(especially for low quantum numbers, 0’) prefers to
decay to the lowest possible state of the neutral mole-
cule. The lowest possible state of the neutral molecule
is reached by the emission of an electron with the
highest possible energy, in the reaction O.->02(v)+e.
A high-energy electron penetrates the potential barrier
with a higher probability than a low-energy electron.
Thus the emission of a high-energy electron is favored.
For d-wave scattering which is involved in the present
reaction, the barrier penetration is proportional to ZS
(Blatt and Weisskopf, 1952), where Z is the energy of
the electrons.

When the ratio of electron energies of the ejected
electrons leading to various decay channels is large
(as is the case at low quantum numbers 2’) a large
branching ratio results. It should be noted that the
branching ratio for low-lying vibrational states in Na
and CO is close to unity. This results from the fact that

30 TTT TTT TT -T
x
o
g
5 20 4
o o (v=2)
° o (v=3)
8
4
5 \
1
2 10 4
oS
iva
o (vel)
o (v=2) \
NS ‘x.
[a a
394.5 6 7 8 9 10 I 2 13 14 15 16

Quantum Number of Compound State, v'

Fic. 68. Ratio of vibrational cross sections vs quantum
number, v’, of compound state. From data of Linder and Schmidt
(1971b).


The single peak at 6.7 eV suggests that a single com-
pound state, *IL,, is responsible for dissociative attach-
ment around 6.7 eV, although many more compound
states exist in this energy range. This view is reinforced
by the parametrization study of O’Malley (1967),
who used the shape and the magnitude of the experi-
mental cross section at room temperature and the tem-
perature dependence to arrive at the shape of a single
potential energy curve and the value for the width of the
state. It is pointed out by O’Malley, and confirmed
experimentally by Henderson ef ai. (1969) that the
temperature effects in O-/O» production can be ex-
plained solely on the basis of the vibrational excitation
of the target molecule, and that rotational excitation
does not play a significant role.

Vibrationally excited molecules have a large Franck—
Condon region and if the electron is captured while the
Oz molecule is at a large internuclear separation, the
survival probability for negative ion formation is
enhanced. As a result, the dissociative attachment cross
section increases for higher vibrational states.

The angular distribution of the O- ions resulting
from electron impact on O; in the energy range 5.75-
8.40 eV has been studied by Van Brunt and Kieffer
(1970). They find that the experimentally observed
angular distributions can be explained most simply in
terms of a transition to a single *II, repulsive state of
O:-. They arrive at this conclusion by comparing the
experimentally observed angular distributions with the
theory of O’Malley and Taylor (1968) and the sym-
metry arguments of Dunn (1962), The interpretation in
terms of a single compound state is consistent with the
evidence coming from the temperature dependence of
dissociative attachment and also with the measure-
ments of the O~ kinetic energy (Schulz, 1962b; Chantry
and Schulz, 1967). Van Brunt and Kieffer (1970) do
not exclude the possibility that another closely spaced
resonance also contributes, but they find this alternative
less attractive.

Burrow (1973) has recently measured the dis-
sociative attachment cross section from the a'A,
state of Os, i.e., the reaction e+O2(a'A,)—02- (?1,.)—>
O-(@P)+0(8P) and finds that this cross section is
larger by a factor of about 3.54:1 compared to the
ground-state dissociative attachment cross section.
This measurement, coupled with an analysis based on
O’Malley’s theory, enables Burrow to calculate that
portion of the excitation cross section to the a'A,
state which proceeds via the *II, state, i.e., the reaction
e+O2(X #2 ,-)—Os- (*IL, 02 (a 'A,)+e. The contribu-
tion from the decay of the compound state is found
to be a large portion of the total excitation cross
section at its maximum. The energy range over which
this mechanism is important, together with experi-
mental measurements of the a!A, excitation function,
are shown in Fig. 74.

The most likely means of excitation to the ‘A,
state from threshold to 5 eV and above 15 eV is pro-

vided by nonresonant exchange scattering. The cross
section for this process has been calculated by Julienne
and Krauss (1972) using the Ochkur-Rudge approxi-
mation to the exchange amplitude. The calculated cross
section is somewhat smaller than the experimentally
measured values.

Wong, Boness, and Schulz (1973) have recently
observed vibrational excitation to the v= 1, 2, 3, and 4
levels of the electronic ground state of Oz, in the energy
range 4-15 eV, with a peak near 9 eV. For an interpre-
tation of this process, Wong ef al. invoke some of the
O:- compound states which exist in this energy range,
eg. 2.7, 42,7, and “Il, states and possibly others.

C. Core-Excited Resonances

The only information regarding core-excited reso-
nances in Oz comes from the transmission experiments
of Sanche and Schulz (1972). Figure 75 shows the
derivative of the transmitted current vs electron
energy in the range 8-13 eV. The structures are labelled
and are listed in Appendix XI. Because of the extreme
complexity of the spectrum, especially in the energy
range 8.5-12 eV, Sanche and Schulz were not able to
identify the structures in detail.

The structures (1-1’) and (3-3’), spaced 220 meV
apart probably have as a grandparent the Oz+(X *II,)
state, which has a spacing of 232 meV. These two
resonances thus consist of two electrons in (3sc,)
Rydberg otbitals, attached to the X(*I,) core. The
“binding” of the two electrons, i.e., the energy difference
between the lowest resonance (8.04 eV) and the
O;*(X?I1,) state, is 4.02 eV, a number similar to that
found in other molecules (see Table X).

Structures 2 and 4 lie 40-45 meV above structures
(1-1’) and (3-3’), respectively. They could reflect
spin-orbit splitting of the *II, state of O.- into a "Iy2
configuration for resonances (1-1’) and (3-3’) and a
*IIi/2 configuration for resonances 2 and 4, The observed
doublet spacing is larger than the value of 24 meV
for the splitting of the ground state of Oxt.

1. Band “a”

At higher energies a well-developed progression of
ten resonances appears in the spectrum starting at
11.8140.05 eV. Sanche and Schulz (1972) compare the
vibrational spacings and Franck-Condon probabilities
of band “a” with those of the a‘II, grandparent
state of Ozt. They find that there is remarkable agree-
ment, whereas no such correspondence can be found
when the experimental data are compared with other
states of Ost, ie., the X*M,, A *M,, b42,-, and B22,-
of Ost.

This suggests that band ‘“‘a” results from vibrational
structure of a ‘II, Rydberg negative ion, formed by the
addition of two Rydberg electrons of the 3sc, orbital
symmetry to a Ozt core in the a ‘II, valence excited
state. The likely parents of the Oz- state could be

99


5 TT
4 |
c 3 Bond "f"——- |
“o 2 |
! |
0
RD) 1 bi Mimi dal
Ww rhebacl td |
a vl Meant ahd \
'
vol Talal tol '
' Fic. 24. Position of com-
> ' pound statng, a8 5 observed in
' various decay channels. On
i we) Tob t bad ' the bottom, the position of
s oe} | | | | ! various bands is shown, as
35 +—— Bond "a" observed in Hansmission
' eriments, The le
vem to tot tt ' region shows the extent of
© 1017 | | i the discrepancy between
2 ! experiments. Higher on the
H figure, we show the posi-
' tions’ of the compound
3 | H states as observed in
' various excited states and in
12 if] | the emission of radiation
' (marked RAD). The as-
ul {| Bond “b" Ilo: signment to various bands
is noted.
0 II Plito:
.. bribe
Wo 1 | btu
* 1 ‘a — Bond "a"
8 Id ;
5 bioue
|
vol ET Pot tit '
8
€
ee Oe ee
2
a I 2 13 14 15 16

Resonance Energy, eV

in Fig. 13. This rise is due mainly to the following
effect: At very low ion energies, ions can reach the
region of large associative detachment, which occurs at
relatively small internuclear separations, only via an
attractive curve. Ions entering the process along re-
pulsive curves cannot get close enough for associative
detachment to take place. However, at higher kinetic
energies, even ions entering the reaction along repulsive
curves can get close enough to the neutral species to

62

detach. Thus, the cross section exhibits a subsidiary
rise at 1.5 eV in the case of O-+CO and at 0,25 eV in
the case of O-+Hp.

Mauer and Schulz (1972) also performed an energy
analysis of the detached electrons and found that the
reaction leads predominantly to very low-energy elec-
trons, near zero eV. Thus very high vibrational states
of CO; are excited.

The experimental evidence from the reaction O--+


ee

Fic. 33. Comparison of the theoretical
cross section for vibrational excitation using

a variable I. The dashed curve (Birtwistle
and Herzenberg, 1971) is theoretical, using a
variable I, and the full curve is experimental
(Ebrhardt and Willmann, 1967). The theo-
retical cross section is calculated using the

parameters of Table IV. [From Birtwistle
and Herzenberg (1971) .]

40 2p
Electron energy (eV)

2p 30

figure, the position of resonances is indicated as they
appear in transmission experiments. The energy posi-
tions of the transmission experiments of Kuyatt et al.
(1966) and of Sanche and Schulz (1972) are shown.
The shaded region indicates the spread of values, which
rarely exceeds 50 meV. Thus the agreement is con-
sidered excellent.

Higher on Fig. 24, we show decay into high vibra-
tional states of the ground electronic state, into the
6*2,* continuum, and the B1Z,+ state as well as the
C'IL, states in the low vibrational levels.

Decay into the B 'Z,,+ state followed by the emission
of a photon is also indicated. Whereas McGowan and
Williams (1969) observe a “strong” and a weak series,
Pichanick e¢ al. (1971) observe only the “strong” series.
The shaded area indicates the degree of uncertainty
between the two above-mentioned experiments. The
short lines indicate the positions of the “weak series”
in the radiation. The “strong” lines agree best with
series “‘c” (or “‘e”) and the weak ones with series “a”
(or “d’’). Why this is so, ie., why one band seems to
dominate in radiative decay when it is not observed in
inelastic channels, is not understood.

Below we discuss some of the more prominent fea-
tures of the different bands. Appendixes I and II list
the energies in tabular form for H, and Dz.

A set of potential energy curves has been derived
from purely experimental information by Comer and
Read (1971a) and is shown in Fig. 25(a). A quasi-

variational calculation of Eliezer et al. (1967) gives
very good agreement with some of the experimental
observations and points to the proper designation of
the states. Eliezer e¢ al. find that the lowest two com-
pound states have *2,+ symmetry and that they consist
of the C*IL, and Cll, states, respectively, with an
electron attached which has (1,2p’) symmetry. See
Fig. 25(b).
1. Band “a”

Band “a” seems to decay into all possible decay
channels. The agreement between various groups as to

Taste IV. Characteristics of N;~ (*1,) resonance at 2.3 eV.

Birtwistle and Krauss and Mies

Herzenberg (1971) (1970)
Ro —Ry (cm)* 0.095(+0.003) x 10-* 0.12xK10°
wo (eV)> 0.244+0.003 0.24
mee 0.0051+0.0017 0.0046
T'(Ro) (eV) 0.5740.02 0.8

© Ro-, Ro are the equilibrium internuclear separations for Ns
and Nz, respectively.

» hw is the vibrational spacing of Ni.

° #e is the anharmonic constant.

4 T(Rp) is the width at Ro.

68


Le

DERIVATIVE OF TRANSMITTED CURRENT (ARB. UNITS)

PrivitiGirstiiivitiiin

95 10.0 To

ELECTRON ENERGY, (eV)

Fic. 10. Derivative of the transmitted current vs electron
energy in atomic hydrogen. The experimental results are shown
by the solid line. The points are the best fit that can be obtained
from the theoretical shape of the cross section, but leaving the
energies and the widths of the resonances as parameters. The
computer program which is used for obtaining these points in-
cludes Doppler broadening and approximates the electron energy
distribution by a Gaussian function with a half-width of 70 meV.
The energies and widths which give the best fit to the experi-
ment are listed in Appendix I. The arrows point to the energies
of the major resonances obtained using close coupling plus cor-
relation. [From Sanche and Burrow (1972).]

70.5

over the past few years: A trochoidal monochromator is
used and the electron energy in the collision chamber
modulated in a manner similar to that introduced by
Sanche and Schulz (1972). A plot of the derivative of
the transmitted current (which is the primary measure-
ment in this type of experiment) vs electron energy is
shown by the solid line in Fig. 10. The energies of several
compound states (taken from the theoretical calcula-
tions cited in Fig. 9) are also shown in Fig. 10. The
points in Fig. 10 are calculated from theory in the
following manner: Sanche and Burrow (1972) take the
theoretical values of the nonresonant phase shifts which
are believed to be “exact” and use the energies and
widths of the resonances in single-level Breit-Wigner
formulas as parameters. They fold these results with a
Gaussian electron energy distribution of appropriate
width (70 meV), and include Doppler broadening.
Then they calculate the derivative of the transmitted
current. The values for energies and widths of the
resonances which give the best agreement with experi-
ment are listed in Appendix I and the derivative of the
transmitted current vs electron energy which is ob-
tained when these optimum values are used is shown by
the points in Fig. 10. This experiment therefore shows
that the theory using close-coupling plus correlation
(ccc) is in agreement with experiment.

Kleinpoppen and Raible (1965) performed a crossed-
beam experiment and found a decrease in the cross
section (which corresponds to an increase in transmitted

13

current) at an electron energy of 9.730.12 eV, as
shown in Fig. 11. In addition, less pronounced structure
around 10.1 eV was observed by Kleinpoppen and
Raible, but was not discussed in their paper, probably
because the authors did not consider it a sufficiently
reliable observation. However, it is clear from Fig. 10
that such structure around 10,1 eV is expected to be
visible.

The third experiment bearing on the subject of ex-
perimental observation of resonances below the n=2
threshold of hydrogen was performed by McGowan,
Clarke, and Curley (1965) and their results are shown
in Fig. 12. At first sight, this experiment shows little
resemblance to the results of Kleinpoppen and Raible.
However, McGowan (1966, 1967) points out that there
is a strong variation of the differential cross section
with angle: The interference between the potential and
the resonant scattering causes the structure of the
differential elastic cross section to depend strongly on
the angle of observation. In order to demonstrate this
effect, McGowan (1966) calculated the differential
elastic scattering cross section in the region of the
resonances, at selected angles of observation. Figure 13
shows the results of these calculations in comparison
with some experiments. The experimental results of
Kleinpoppen and Raible (taken at 94°) resemble the
shape of the theoretical curve for 9= 100°. The experi-
mental data of McGowan, Clarke, and Curley resemble
the theoretical curve at 90°, as shown on the bottom
left-hand portion of Fig. 13. A more detailed comparison
is shown in Fig. 14. Here, the width of the 1S resonance
is left as a parameter. The best fit to experiment is ob-
tained when the width of the 1S resonance is taken to be
0.043-0.006 eV, in good agreement with the value of
0.0475 eV given by Burke.

The sharp hump observed just below the m= 2 level
of hydrogen in Fig. 12 can be ascribed to the effect of
the 'D state (Ormonde, McEwen, and McGowan,
1969). Figure 15 shows a detailed comparison between
theory and experiment in the region 9.9-10.2 eV,

23 10 Het My, fy! i
Be |
zs

05
ev

1 93 95 97 99 101

Electron Energy
Fic. 11. Elastic cross section for electrons on atomic hydrogen.
The angie of observation was 94°, and the width of the energy

distribution about 0.1 eV. [From Kleinpoppen and Raible
(1965).]


Taste IX. Parameters of O:-(X*,).*

Boness and Linder and
Celotta et al. Schulz Schmidt Gray et al.

(1972) (1970) (1971b) (1971)
Equilibrium separation, r, A 1.341+40.010 wee oe ae
Electron affinity, eV 0. 440+0.008. eee oe oe
B, (cm) 1,170.02 vee one wee
fie (meV) ee 135 135 140
Nevete (meV) ooo 1.5 1.0 3.0

* Additional features: The fine-structure splitting is 22-+2 meV (Land and Raith, 1972).

the previous determination of Boness and Schulz
(1970), obtained by use of Badger’s rule from the
vibrational spacings of O.-.

Table IX lists the parameters for O.-(X ?11,) deduced
from photodetachment spectroscopy and from electron
impact spectroscopy. It is seen that the values deduced
from these two types of experiments complement each
other. The value deduced by Boness and Schulz (1970)
from the vibrational . Spacing of O2- using Badger’s
tule (i.e, re=1.377 A) is not listed since the value
deduced from photodetachment spectroscopy is con-
sidered more reliable.

From the foregoing discussion it should be fairly
obvious that photodetachment spectroscopy is a
powerful tool for determining electron affinities and the
structure of negative ions. In both of the cases in which
a stable negative ion exists, namely O. and NO, no
evidence exists for excited negative ions lying below the
neutral species, i.e., only one electronic state exhibits a
positive electron affinity. Photodetachment experiments
do not, however, rule out the possibility of the existence
of excited states of O:- which have a large equilibrium
internuclear separation. The calculations of Michels and
Harris (1971) show that only the X*II, state of O.-
lies below the ground state of O2. Thus one must con-
clude that the only stable state of O;- which lies
energetically below the ground state of Oz is the X "II,
state.

Figure 69(b) shows the potential energy curves for
O;- as calculated by Michels and Harris (1971). In
addition to the X *II, state, Michels and Harris find 12
other attractive states arising from the limit O+-O-. All
these states are qualitatively similar, exhibiting shallow
potential wells at large internuclear separations (1.8-
2.0 A). The existence of a large number of autodetaching
states, Os", is. consistent with the experiments, on
associative detachment (Ferguson, 1968). The thermal
rate constant for the associative detachment reaction,
0-+0-0;--0;-+e, is large [Ferguson (1968) gives a
value of 3X 10~” cm? sec at 300°K], and it is reason-
able to suppose that some of the O:- states shown in
Fig. 69(b) serve as intermediates.

96

Recently, Lineberger and Patterson (1972), using
two-photon photodetachment spectroscopy, discovered
an excited state of a negative ion which lies below the
ground state of the neutral molecule. The molecule is
Cz, The ground state of the negative ion, Cx-(?2,+)
lies ~3.5 eV below the neutral ground state, C2 12,*.
About 2 eV above Cy-(*2,*) there is an excited state of
the negative ion, C;-(?2,+). It may be of interest to
study such systems using electron spectroscopy to ob-
tain complementary data.

5. Three-Body Attachment in Oz

Three-body attachment, i.e., the reaction e+20.—>
O:-+02, is now known to proceed via the XI,
compound state of O,. The reaction can therefore be
written as a two-step process: e+O:—0;~*, followed by

a ee

} (THEORY)

[Viioy=4 5 7 8 9 ON |
yeep rt r th 4
bat Pp i |
ied | TLL spence & Schulz = |

1 | (experiment) |

[ | | se CHAPMAN & HERZENBERG

bi

a a
oe 4
Sat * 1 | | 4
ep AR |
, ; oN 4
eb 4
é
|r Lu
0 O22 04 06 O08 IO 12

Electron Energy (eV)

Fic. 70. The three-body attachment coefficient of production
of Os in Os in comparison with the theory. The theory is norma-
lized to the experimental data at the second peak. The vibrational
levels of the O;-(X *II,) state are indicated by the lines on top.
The structure in the three-body attachment coincides with the
positions of the vibrational states of O:~. This figure shows that
three-body attachment on Os proceeds via the low-lying com-
pound state of O3. [From Spence and Schulz 1972).]


various investigators, both experimentally and theo-
retically. The solid horizontal lines indicate those
resonances which seem well established at the present
time.

A. Classification of Energy Levels in He

It has already been pointed out that the levels of the
compound states in helium and other gases arise from
the addition of an electron to a particular excited state

xlo- 4)

im

Cross section (em?)

al v 1
12

L 4 1

1 1
14 16
Interaction energy (eV)
Fic. 18. Cross sections for detachment from H- by electron
impact. The symbols Ill, @, and A, respectively, refer to measure-
ments with inclined beams in which the ion beam laboratory
energies were 7, 8, and 10 keV. The open circles denote earlier
measurements by Peart ef al. (1970). Estimates of energy resolu-
tion and 90% confidence limits of random error are shown for
each point. [From Walton, Peart, and Dolder (1970).]

of the atom. The resulting state lies, for the case of
Feshbach resonances (also called “closed channel”
and core-excited resonances), below the energy level
of the parent. Thus one can think of these states as
negative ions with a definite electron affinity, in the
range of about 1/2 eV. It is also possible for the com-
pound state to lie at the energy of the parent state
(“virtual states”) or above the parent state, by up to
3 eV. Thus one can list all the relevant configurations
which can be derived from an excited state of helium,
plus an additional electron. From the lowest states of
helium, 152s and 152, we can write the states listed in

18

HY

uagessalvaues

EEE

Distended Elastic Current, arbitrary units

H te
HE 4 a
“T 1
185 9 19.5 20 20.5

Electron Energy, eV

Fic. 19. The original observation of the (152s) 2.5 resonance
in helium. The Angle of observation is 72° and the elastic cross
section is measured. The decrease in the cross section near 19.3 eV
is approximately 14%. [From Schulz (1963)..]

Table I. The superscripts designate states of odd and
even parity. The 2s2p configuration can lead to *P and
*P states: The addition of a 1s electron to this term
results in two distinct *P states of different energy for
the 1s2s2p configuration. One of these states has spins
of the outer electrons parallel (2P;;), the other anti-
parallel (2P;,). The “parents” of these two states are
the (2s2p)*P and (2s2p)'P states, respectively.

The (2p)? configuration, being composed of two
equivalent electrons, results in 1S, *P, and 1D states.

Taste I. Possible states of He.

Additional states for
nonequivalent

Outer electrons electrons
equivalent (unlikely)
12s? 2544 2514
132s2p 2P rp, 2Ph 4, KO :
1s2p* 2S 4, Dy 4, Re, K *Se14, 2Pe, Dey



Resonances in Electron Impact on Diatomic Molecules*

George J. Schulz

Department of Engineering and Applied Science, Mason Laboratory, Yale University, New Haven, Connecticut 06520

In this review we present the energies, configuration, and other properties of resonances (also called
“compound states” and “temporary negative ions”) in diatomic molecules. Much of the information is
presented in the form of tables and energy level diagrams. Vibrational, rotational, and electronic excitation
are discussed whenever these processes have given information on resonances; often these excitation
processes proceed via resonances. The paper is divided according to molecular species (H, N;, CO, NO,
©), but the main conclusions are discussed by the nature of the processes involved.

Key words: Compound states; cross-sections; diatomic molecules, H:, Nz, CO, NO, 0:2; electron impact;
electronic excitation; energy levels; resonances; rotational excitation; temporary negative ions;

vibrational excitation.

CONTENTS
I. Introduction
A. Classifica 1p
B, Parentage of Core-Excited Feshbad!

IL, Hydrogen.
A. Resonance at Low Energy:
1, Elastic Cross Section.
2, Vibrational Excitation in Hy via *Z4*.
3. Rotational Excitation via the *2.* State and
‘Angular Distributions.
4. Dissociative Attachment at 3.75 eV.
5. Effect of Rotational Levels of the He Target
Molecule of H~ Formation near 3.75 eV. .
6. Associative detachment: H-+-H- HH +e.
B, Resonance in the 10-eV Region (5,*).. :
Cc Core-excited Resonances in the 11-15 eV: Region. .
Band “a”. .
Band “‘b”.
Band “c”.
Band “d”.
Band “e”.
Band ‘f”.
. Band “g”.
IIL. Nitrogen.
A. Reson: Low Energy (1.7-4 eV) *I,
1. Elastic Cross Section via "1
2, Vibrational Excitation via *
3. Threshold Behavior of the Cros
4. Angular Distributions.
5. Pure Rotational Excitation via
B. Core-Excited Resonances in the 11-1 15 6
1, Band “b”z,*.
2; Shape Resonances and Inelastic Thresholds
3. Structures 5 and 6.
4. Bands “c” and ‘d’
C. Bands “a” and “a’”:
nances,
D. Resonances above the Ionization Potential in Na. .
IV. Carbon Monoxide. :
A. Resonance at Low Energy (1-3 eV) "11
1. Elastic Cross Section via *I. . .
2. Vibrational Excitation via *1.
3. Angular Distributions. .
B. Dissociative Attachment (9.65-12 eV) .
. Core-Excited Resonances in the 10-15 eV Region
1, 2Z* Resonances (10.04 eV, 10.28 eV) .
2. Shape Resonances and Inelastic Thresholds
3. Band “a”
D, Resonances above the Ionization Potential in CO
V. Nitric Oxide, NO .
A. Compound Stat
1. Elastic Scattering
2. Vibrational Excitation (0-1. .
3. Equilibrium Internuclear Separation and Elec-
tron Affinity: Photodetachment Spectroscopy
B. Dissociative Attachment (7-10 eV) .
C. Core-Excited Resonances in NO.
1, Bands “a” to “d”. .
2. The 12 eV-18 eV Region:

NO gup er

92
92
1, Elastic Scattering 92
. Vibrational Exci
(0-1,0 eV) 93
3. Potential Energy Curve for O- ( 95
4, Equilibrium internuclear Separation and
Electron Affinity: Photodetachment Spec- 95
troscopy.
5. Three-Body Attachment in O2. 96
B.’ Dissociative Attachment (4.4-10 eV) :"IL, State.. 98
C. Core Excited Resonances 99
1. Band “a”... 99
2. Band “b” 100
VII. Conclusions. . 100
‘A. Shape Resonances. 100
B. Core-Excited Shape Resonances. 100
C. Binding of Rydberg Resonances. 101
D. Thresholds of Inelastic Cross Sections. 101
Acknowledgments 101
‘Appendixes
I. Core-Excited Hz" States. . 102
Il. Core-Excited D:- States. . 103
. Branching Ratios for Series “a” in Hy 203
Core-Excited Resonances in Nz (11-1 104
. Shape Resonances Associated with B '1, an
States in Nz (8-11 eV) . 104
. Resonances in CO (10-15 e 105
: Vibrational Spacings and Franc
abilities for Four Bands in NO~ 106
106
. pec of Vibrational States of O:- X(H,) . 106
ibrational Cross Sections and Resonance ‘Baergies in in
Os at Low Energies 107
. Core-Excited Resonances in Os. 108
References..........02.0ec0eee ee los

This paper is a continuation of the one immediately
preceding, which deals with resonances occurring when
electrons are incident on atoms. In the present paper
we present a review of the energy levels, the designa-
tions, and the general properties of compound states in
diatomic molecules. An attempt is made to present much
of the information in the form of tables and energy level
diagrams.

I, INTRODUCTION

Compound states are formed by the interaction of an
incident electron with a target molecule in which the
incident electron is temporarily captured in the neigh-
borhood of the molecule. The complex thus formed can
also be called a temporary negative ion or a resonance.

47


Taste VIII. Molecular orbital configuration of the ground states and of shape resonances in diatomic molecules. The
extra electron, which is responsible for the shape resonance, occupies the lowest vacant orbital shown in the fourth column.*

Lowest Dominant
Ground vacant Compound _ partial
Molecule Molecular orbitals of ground state state orbital state wave

Hy (Aso)? ay + 2pow at po
N: (1s09)2(2pou)?(2s0)?(3pou)*(3s09)*(Zpmru)* at 3dmq 1, dr
O. (3da,)? 3 3dr, oT, dr
co (1sa)*(2s0)*(2po)*(2pm)4(3s0)?(3po)* wt 3pr 11 dr+pr
NO os (3p) I, 3pr a7 dn+pr

* The notation used is the “united atom” notation of Herzberg (1950). See also Bardsley and Mandl (1968). The notation used in

the column entitled “dominant partial wave”’is dr, px; and po. The

first, Latin letter, refers to the angular momentum of the electron

partial wave at infinity, i.e.,/=2, and 1, respectively. The Greek letter refers to the component of this angular momentum along the
internuclear axis of the molecule as the electron comes close to the molecule.

sidered as possible candidates for compound state
formation from the ground state since their inter-
nuclear distances lie close to the internuclear distance
of the NO ground state. These states are listed in
Appendix VIII where their energies are given. Also
shown in Appendix VIII are the position of the reso-
nances in the energy range 12-18 eV. In the last column
of Appendix VIII we calculate the “binding” energy by
taking the difference between the energies of the
assumed grandparent and the lowest value of the
resonance, The constancy of the binding energy indi-
cates that the proper grandparents have been assigned
and that the potential well which binds the two 3s
electrons does not change, The binding energy of band
“a” (previously discussed) with respect to the X !2+
ground state is 4.23 eV, in very good agreement with
the other values for the binding energy shown in
Appendix VIII.

The various structures listed in Appendix VIII have
been interpreted by Sanche and Schulz (1972) as core-
excited Feshbach resonances or as core-excited shape
resonances, and their parents have been suggested. For
example, the 12.57-eV feature listed in Appendix VIII
is interpreted as the v= 1 state belonging to the progres-
sion starting at 12.36 eV, since the spacing and the
Franck-Condon factors agree with those of the 5*II
grandparent state,

An energy level diagram of the zeroth vibronic level
of each NO~ state is shown on the right side of Fig. 63,
On the left side of this figure the energy levels of the
NOt grandparent states are shown. The two scales
have been displaced by the difference in energies be-
tween the lowest member of band “a” with respect to
its grandparent, the X !Z+ core of NOt (4.23 eV), in
order to show the relationship between the NOt
state and its grandchildren NO~ states. This comparison
demonstrates that the binding energy of two 3s
Rydberg electrons does not depend on the configuration
of the positive ion core. It also illustrates that in NO

92

only Rydberg excited states give rise to core-excited
resonances in the total scattering cross section.

VI. OXYGEN

A. Compound State at Low Energy: X *II, (0-1 eV)

The lowest compound state of Os is the X *I, state.
The vibrational states v’=0 to v'=3 of O.-(X *II,) lie
below the v=0 state of O2(X *Z,-) and cannot auto-
detach. These vibrational states of O:- are therefore
stable. For higher quantum numbers, autodetachment
can take place and these higher vibrational states form
the lowest compound state of Oz. As in the case of NO,
a variety of experiments must be brought to bear on the
problem in order to gain a full picture which has
recently emerged. The important experiments are
elastic scattering, inelastic scattering (i.e., vibrational
excitation), photodetachment, various measurements
of the electron affinity, and three-body attachment.

The molecular orbital notation for the lowest states
of O2 and Os" is given in Table VIII, Sec. VII.

1, Elastic Scattering

The structure, consisting of peaks, in the elastic
differential and total cross sections of electrons on Oz
gives us the information on the position of the vibra-
tional levels of the Os- system. Figure 64 shows a
compilation of several experiments, suitably presented.
The spacings are also listed in Appendix IX. The assign-
ment of the proper vibrational quantum number does
not come from the elastic experiment alone. Rather,
the electron affinity of O, must be known in order to
achieve such an assignment and a backward extrapola-
tion, using the measured spacings and the anhar-
monicity, must be performed. Until recently the value
for the electron affinity was being questioned (see Sec.
VI A3) but we can now be confident that the values of
Pack and Phelps (1966) (0.432:0.02 eV) and of
Celotta et al. (1972) (0.440--0.008 eV) are correct.


sidering a state of He~ in which the three electrons
comprising He~ are equidistant from the nucleus. Such
a quasistationary state was calculated by Herzenberg
and Ton-That (1973) to exist around 45.9 eV. It is of
a similar nature as the state of H~~ discussed in Sec.
TIC, with the wave function having no radial nodes.
The 2s°2p state at 57.16 eV, which has the same ?P
symmetry, has a radial node in each of the 2s factors.

0095eV

16,04. al Teasev
4

ee

Neon

ge 0%

ELECTRON CURRENT (ARB. UNITS)

59 155 'e0 165 179
ELECTRON ENERGY (eV)

Fic. 36. Elastic cross section vs electron energy at designated
angles of observation in neon. The vertical bars designate a 10%
change in cross sections. The angular dependence of the resonances
is Seanctenisic of the » wave. [From Andrick and Ehrhardt

1966)...

Iv. NEON, ARGON, KRYPTON, AND XENON

The rare gases Ne, Ar, Kr, and Xe exhibit marked
similarities in terms of their resonances so that it is
appropriate to consider them under a single heading.

A. Resonances Below the Ionization Potential

The first resonances in all the rare gases discussed in
this section consist of two s electrons attached to the
positive ion core (Simpson and Fano, 1963). Since the
positive ion core is a doublet (J=} and J=$), the
resonances are also split. In fact, the splitting of the

resonances is in very good agreement with the splitting
30

NEON

2p5(2P3,0) 2p5(?P1,2)
——S
21.864 3s 3p 4s 38 3p 48 S
7 4
2
21h fe)
a
L wd
«
20,07
20- > 19.97
So19.71
ZF “Nese
19.57
> isk _| \i9-47
i) 18.95,
i 4 =
af Nisss
2
wise
16.671 3P,
ite 1
[16.848 'P, _lig gs
LM *\ M 16.715 5P9
16.619 3p, 16.20
16 Si6.11

Fie. 37. Energy level diagram for neon, showing states of
neon and the associated resonances. The values for the resonances
are taken from Sanche and Schulz (1972) and a comparison with
other values is shown in Appendix V. Metastable states are
denoted by the letter M.

of the ion core, as shown in Table II, where comparison
is made between the two available experiments on
resonances and the known splitting of the ion core. The
agreement between the splitting of the resonances and
the positive ion core assures that the designations
advanced by Simpson and Fano (1963) are correct.
Thus, the lowest resonances in Ne, Ar, Kr, and Xe have

ARGON
3p5(2P 3,5) 3p5(2P),9) o
—_— -— a
15.759 4s 4p 3d 48 4p 34
<
z
15}- 8
Ww
r Ca
> 4h |
o
- i 13.4
rad I—13.3
az 1 FSs%6
¥ TS 12'80
eS | :
Ww
12 '
fieze'P) lig,
LM = 11.723 3pQ 1-71
11.623 3p, 11.28
if 3 ae
11.548 Py

Fic. 38, Energy level diagram for argon. Numerical values are
listed in Appendix VI.


i.)
°

x
uw

Fic. 12. Differential scattering cross
section in hydrogen, The angle of ob-
servation is 90° with respect to the
bombarding electrons. The position of
the three lowest resonances, 15, *P, and
1D, are shown. [From McGowan, Clarke,
and Curley (1965) and McGowan
(1970).

“
°

a
uw
T

SCATTERED ELECTRONS (10% COUNTS/MIN)

a
°

9.50 10.00

CALIBRATED ELECTRON ENERGY SCALE (eV)

s
¢
= | trans-
< MITTED
= CURRENT 6=94°
oa 1 1 1 L
&
y f
3 H
H
s ft
z mat +
2 > v7
la a
BL y l—S
2 roa |
ry
8 ts 3p
° @=70° 6=100°
g L 1 L 1
re
g
E
s 's *p
a 1
@=90° 8=160'
L 1 1 L
95 10.0 95 10.0

ELECTRON ENERGY (eV)

Fic. 13. The experimental results of Schulz (S), Kleinpoppen
and Raible (KR), and McGowan, Clarke, and Curley (MCC)
compared with the differential scattering calculations of McGowan
(1966, 1967) for different scattering angles 8. The dashed line
corresponds to the calculated cross section for an angular window

15°. The position of the 1S resonance is taken to be 9.56 eV
and its width 0.04 eV. The *P resonance is taken to be at 9.73 eV
with a width of 0.01 eV. The solid line represents the same cal-
culation with the experimental value of the electron energy
distribution (0.06 eV) folded in. [From McGowan (1966).]

when the 'D state alone is considered. The agreement in
Fig. 15 must be, presumably, considered fortuitous
because a valid comparison between theory and experi-
ment must also include the S, P, and 8D contributions.
For a comparison at 90°, such as is the case for
McGowan’s experiment, the P-wave contribution to
the cross section should be zero. Figure 16 shows the
valid comparison between theory and experiment. The
1D compound state of H- seems to be the dominant
contribution near 10.1 eV.

It is clear from the work of McGowan that experi-
ments on the angular distribution of electrons in the
neighborhood of the 'S and *P resonances in hydrogen
are strongly dependent on the angle of observation and
on the acceptance angle of the apparatus. Further work
with much better angular resolution will be necessary
before a really satisfactory check of the very elaborate
theory can be made.

B. Resonances in the Inelastic Cross Sections

Resonances lying above the n=2 state of hydrogen
seem to be most pronounced in the inelastic cross
section. Figure 17 shows the cross section in the 2p
excitation from threshold to about 3 eV above threshold.
Structure in the cross section is evident and the location
of this structure is transposed onto the energy level
diagram, Fig. 9. Also shown in Fig. 17 are the theo-
retical curves. The sharp onset of the 2p excitation
cross section results from the proximity of the 1P shape
resonance, which is almost coincident with the »=2
level. This sharp peak near threshold seems to be con-
sistent with the earlier experimental results of Chamber-
lain, Smith, and Heddle (1964) which were obtained

“4


attachment:

o-=Qvep— ([" OR)

Ro fho(R)

Here, Qo is the cross section for formation of the com-
pound state and the exponential term represents the
probability that the system in fact survives to a
stabilization point R’. The term I is the width (and

DIFFERENTIAL CROSS SECTION (ARB. UNITS)

Ss
COLLISION ENERGY (eV)

to ‘BS

Fic. 18. Energy dependence of the absolute differential cross
sections for excitation of vibrational states in Hz above 11 eV. The
scattering angle is 85°. For each curve the cross section scale should
be multiplied by the factor indicated. The zero lines are shown
broken. The structure observed in the vibrational states »=1 to
2=8 is associated with series “‘a.” For 1=9 to o=11, series “a”
is visible in the energy range “i. 48-13.33 eV, and’ series “b”
appears at the low-energy end, i.¢., in the energy range 11.49-
1174 eV. [From Comer and Read (1971a)-]

served the onset for H~ production at the predicted
value. Also shown in Fig. 11 are the unfolded cross
sections for the three isotopes of Hz (Chen and Peacher,
1968). The isotope effect was first interpreted by
Demkov (1964) as a consequence of the smaller survival
probability factor for heavier atoms. Thus, D2 requires
a longer time to separate and remains in the region of
autodetachment for a longer time than does Hy. The
formation of D-/Dz is therefore smaller than H-/H:.
Bardsley, Herzenberg, and Mandl (1966b) give a simple
expression for the cross section leading to dissociative

58

Differential cross sections

T
B
"s
+ #
j=)
ee
v= 13
4 1 vas io
1-0 15 12-0

Collision energy (eV)

Fyc. 19. Energy dependence of the absolute differential cross
section for excitation of high vibrational states in Hz above 11 eV.
‘The scattering angle is 85°. The zero lines are shown broken. Only
series “b” is shown. [From Comer and Read (1971a).]


FORM NBS-IT4A (1-71)

T. PUBLICATION OR REPORT NO.
NSRDS-NBS-50 a

U.S. DEPT. OF COMM.
BIBLIOGRAPHIC DATA
SHEET

3. Recipient’s Accession No.

4, TITLE AND SUBTITLE

Resonances in Electron Impact on Atoms and Diatomic
Molecules

5. Publication Date

October 1973

6. Performing Organization Code

7. AUTHOR(S)
George J. Schulz

8. Performing Organization”

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS
DEPARTMENT OF COMMERCE,
WASHINGTON, D.C. 20234

TO. Project/Task/ Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Joint Institute for Laboratory Astrophysics,
National Bureau of Standards, Boulder, Colorado 80302

13. Type of Report & Period
Coveréd

Final

14, Sponsoring Agency Code

15. SUPPLEMENTARY NOTES,

Reprinted from Reviews of Modern Physics, Vol. 45, 378-486, July 1973.

16. ABSTRACT (A 200-word or less factual summary of most significant information, If document includes a significant

bibliography or literature survey, mention it here.)

Two reviews are presented on the energies, configuration and other properties of

resonances in electron impact on atoms and diatomic molecules.

In¢luded are

discussions of the experimental methods which are useful for studying resonances

and of the results obtained by various investigations.
is presented in the form of tables and energy level diagrams.

Much of the information

17. KEY WORDS (Alphabetical order, separated by semicolons)

Atoms; compound states; cross-sections;

diatomic molecules; electron impact; energy levels; resonances; temporary negative

dons.

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(7X) UNLIMITED.

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In both parts of this review we present a concise
discussion of the energy levels, the classification of
resonances, and their decay. Comparison with theory is
presented whenever such comparison is meaningful,
but a full exposition of theory is not attempted. Energy
level diagrams for resonances are constructed to aid
the overview and the tables of values can be found in the
appendixes. The discussion is organized by species.

A. Theory

In atoms, resonances are mostly associated with ex-
cited states (“core-excited resonances”). Resonances as-
sociated with the ground states of atoms have been
established only for the alkalis. One can distinguish
between two distinct types of resonances, namely those
that lie energetically below the state from which they
derive (i.e, below the “parent”) and those that lie
above. Thus we introduce what may be called the
geneology of resonances, a concept actually introduced
for a better understanding of resonances in molecules
and discussed in more detail in the second paper of this
review. A positive ion with a particular configuration of
electrons is considered the grandparent. Adding a single
electron to this positive ion configuration gives a
Rydberg state of the neutral atom or molecule: this is
the parent. Adding an extra electron to the parent, we
have a particular “resonance.”

Resonances which lie below their parent are inter-
changeably called “closed-channel resonances,” ‘“Fesh-
bach resonances,” or “Type I resonances” (Taylor
et al., 1966, Taylor, 1970). They arise when the inter-
action potential between the incident particle and the
excited state of the target is strong enough to support a
bound state. They usually lie approximately 0-0.5 eV
below the parent. When the excitation takes place near
the center of the resonance, decay into the parent is
energetically forbidden, but decay into some other
states (nonparents) is allowed. Because decay into non-
parents involves a change in configuration of the
atoms, Feshbach-type resonances are usually long-lived
and their widths are narrow. When such resonances are
excited in the high-energy wing, decay into the parent
may become energetically possible (Taylor, 1970),
and such decay is favored. The end-result of such a
decay is often a sharp peak near threshold in the excita-
tion function of the parent state. Such effects are known
in both atoms and in molecules.

A special case of a Feshbach-type resonance occurs
when the energy level lies near the very top of the
potential well. Such a state is called “virtual” and an
example is discussed in connection with the 21S state
of helium in Sec. ITIBS.

Resonances which lie above their parents are called

‘shape resonances” or “open-channel resonances,” or
‘Type II” (Taylor ef al., 1966). In this case, the
potential forms a penetrable barrier which traps the
incident particle near the target. The barrier is formed
by the angular momentum of the electron. Thus, we

expect p-, d-, f-wave resonances but generally not
s-wave resonances, since the latter have /=0 and thus
produce no barrier.

Shape resonances show a preference for decay into
their parents and very often dominate the excitation
cross section of their parent. Thus shape resonances
usually have a shorter lifetime (ie., larger width)
compared to Feshbach resonances. An exception occurs
when a shape resonance exists barely above an inelastic
threshold (Macek and Burke, 1967). In this case the
barrier can be viewed as being very thick (Taylor,
1970) and the resonance becomes long-lived, i.e., the
width is narrow; such a case exists in atomic hydrogen.

The presence of resonances is ascertained experi-
mentally by measuring structure in the energy de-
pendence of elastic or inelastic cross sections. Because
the structure is often very sharp, monochromatic
beams of electrons are needed for such studies and the
techniques generally employed are briefly reviewed
below. These techniques are also useful for the study of
resonances in molecules.

A particular resonance can decay, by the emission
of an electron, into many final states. We thus may
speak of “channels of decay” for a given resonance.
Therefore the existence of a resonance may be detected
by measuring the structure in the energy dependence of
the cross section of any state which lies energetically
below or near the resonance. In fact, sometimes it is
possible to detect the existence of a resonance even in a
state which lies energetically above the center of
resonance. This effect is caused by the “wings” or
“tails” of the resonance (Taylor, 1970). Not all decay
channels are equally useful for detecting a particular
resonance. Often, the branching ratio favors a particular
decay and then it is easier to detect structure in the
final state which is favored, provided that the non-
resonant portion of the cross section is of the same order
in the two states. Such phenomena are particularly
important in molecules.

The energy dependence of the elastic cross section in
the neighborhood of an isolated resonance in the s wave
with a single decay channel can be expressed by the
Breit-Wigner formula (Blatt and Weisskopf, 1952),
o(E)~ak | A+{T/[(E—Eo)+(4i)T]} 2. Here, A
represents direct “potential” scattering which varies
only slowly with energy; I’ is the “width” of the state,
i.e., the range of energies over which the resonance has a
large effect on scattering; Ep determines the location of
the resonance; E is the energy; and 4 is the reduced
wavelength of the electron. The cross section off
resonance becomes 7A? | A |?. When direct scattering is
small, the cross section near a resonance becomes
aX{T?/(E—Ep)?+ (40)?]. The maximum cross section
then occurs at the resonance energy Ey and the half-
width is I. In general, however, interference occurs
between direct scattering and resonance scattering so
that the shape of the cross section becomes more com-
plicated, leading to destructive and constructive inter-


Band
I

"a"
T

DERIVATIVE OF TRANSMITTED CURRENT (ARBITRARY UNITS)

1 1
5.8 6.2 6.6 74

ELECTRON ENERGY (eV)

70

Fic. 61. Derivative of transmitted current vs electron energy
sn the 5-7.5 eV region in NO. Four bands belonging to a Rydberg
series of NO- states are shown; each band consists of a vibrational
progression. The spacing of each vibrational progression agrees
with the vibrational spacing of the X12* ground state of NO*,
which is the grandparent. [From Sanche and Schulz (1972).}

3. Equilibrium Internuclear Separation and Electron
Affinity: Photodetachment Spectroscopy

Values of the electron affinity of NO (and also of Oz)
have been in a state of violent fluctuation until very
recently, But as a result of the recent photodetach-
ment experiments of Siegel e¢ al. (1972), a reliable
value is now available:

EA(NO)=24(+10, —5) meV.

In the experiments of Siegel e¢ a/., an argon-ion laser
photodetaches electrons which are energy-analyzed. A
Franck-Condon factor analysis of the observed cross
sections determines the molecular constants for NO-:
we= 14704200 cmTM; r.=1.258+0.010 A; and B.=
1,427--0.02 cm", and also the electron affinity quoted
above (24 meV). The very recent value of McFarland
et al, (1972) is 28-14 meV, in good agreement with
Siegel. Older values of the electron affinity of NO are
listed by Siegel e¢ al. (1972) but they all seem less
reliable: The other values are 9004100 meV (Farragher
et al., 1964), 650 meV (Stockdale et al., 1969), 904100
meV (Berkowitz et al., 1971), 0 (Lacman and Hersch-
bach, 1970), and 50 meV (Spence and Schulz, 1971b).

B. Dissociative Attachment (7-10 eV)

Dissociative attachment in NO, leading to the forma-
tion of O-, indicates the existence of a repulsive poten-
tial energy curve in the region 7-10 eV, as shown by the

90

negative ion production of Fig. 60. The structure ob-
served by Paquet ef al. (1971) may well be due to the
traversal of the repulsive curve responsible for O-
production through the potential energy curves
responsible for the core-excited resonances. Noteworthy
is the conclusion of Chantry (1968), who determined
froni kinetic energy measurements of the O- ion, that
the dissociative attachment process leads exclusively
to the formation of electronically excited N, ice.,
e+NO0-+N(?D).

C. Core-Excited Resonances in NO

Fewer experiments on core-excited resonances are
available in NO than in the molecules previously dis-
cussed. Differential measurements have not yet become
available. Nevertheless it was the NO molecule which
revealed the interpretation of core-excited resonances in
terms of Rydberg compound states (Sanche and
Schulz, 1971), Figures 61 and 62 show a plot of the
derivative of the transmitted current vs electron energy
in the energy range 5-18 eV. The features on Fig. 61
are given letter designations and are discussed below.

1. Bands “a” to “a”

The location of four bands of resonances,

igo
c’

a, Mh,
, and “d”, is indicated in Fig. 61 by vertical lines

TTT
a
E
2
=)
o
a
<
5 |
5 x
a
4
5 Fic. 62. Electron transmission
cS) spectra for NO in the 12-13 eV, 14-15
el, ty 4 eV, and 17-18 eV regions. Each seg-
= ment shows resonances associated
E] 12 125 13 with the b4I1, AL, and BUI excited
= states of NO* which are the respective
2 grandparents. The binding of the first
2 compound state in each segment rela-
Ps xl tive to the corresponding grand-
- parent state is nearly constant. [From
ro Sanche and Schulz (1972).]
w
S 4 15
=
<
2
4
a
x4
1 1 1
VWs 18
ELECTRON

ENERGY, (eV)


Fis en OO 1
6fo. 10 is
wo
3 t
55 j
>
a
Fs b
ate
a
€
az | Hg 54612
>
z
a
Zz
re
Zz 2
Ut Pete
\\ — ELECTRON ENERGY
oO Fame eercaneee anette

L Li
7 10 15 18 eV

Fic. 47. Excitation function of the 5461-A line of Hg. (a)
Low-resolution results of Jongerius; (b) result obtained by Smit
and Fijnaut (1965) using the retarding-potential difference
method with a resolution of 0.1 eV. [From Smit and Fijnaut

states of the configuration 5d%6s*6p. The resonances
would then have configurations such as 54°6s6p”.

The structures observed in transmission experiments
can be compared with structures observed in optical
excitation functions; care must be exercised in excluding
structures resulting from sharp thresholds of higher
energy levels which may contribute structure in low
levels due to cascading.

Figure 47 shows the structure obtained by Smit and
Fijnaut (1965) using a relatively narrow electron
energy distribution (~0.1 eV) and observing the
5461-A line in Hg. These results are in very good agree-
ment with the work of Zapesochnyi and Shpenik (1966)
who also used monoenergetic electrons for their ob-
servations and in addition to Hg (A=2537 A, 5461 A,
3650 A, 4916 &) examined a wide variety of optical
excitation functions in He, Zn, Cd, Na, and K. Zapeso-

35

chnyi and Shpenik list the positions of the structure
they observe. Appendix X compares their observed
structures with the structures listed by Kuyatt et al.
(1965). On the whole, there seems to be good agree-
ment. It should be noted that Zapesochnyi and Shpenik
interpret the observed structures in terms of cascading.
However, it appears that the interpretation in terms of
resonances could be equally valid.

VU. OXYGEN (0)

The determination of the location of compound states
in atomic species which occur naturally as molecules is
very difficult, as pointed out in connection with the
discussion of atomic hydrogen. Normally, one attempts
to form a beam of the atomic species and crosses this
beam with monochromatic electrons. A novel method
for measuring compound states has been recently
presented by Edwards, Risley, and Geballe (1971)
and applied to atomic oxygen. In this method, a beam of
stable O- ions with about 2 keV of kinetic energy is
incident on a rare gas target (He) and the electrons
resulting from this interaction are energy-analyzed and
recorded. Structure in the energy spectrum of the elec-
trons is observed and is associated with the existence of
resonances. Figure 48 shows an example. The peaks in
Fig. 48 seem to arise from the reaction

O-+He+0-*+ He 0+ He+e,

where O-* denotes the compound state.

2keV O-on He
Qs9°

7. 10.112

Fic. 48. Electron energy spectrum obtained after colliding a
2-keV beam of O- with He. The electron energies given above
the peaks are corrected for the velocity of O- and are the proper
energies for compound states. ‘Thepeaks areinterpreted as resulting
from the formation of compound states up atomic oxygen. [From
Edwards, Risley, and Geballe (1971) .]


25 1

2.0

Fic. 71. The cross section for O-
formation by dissociative attachment
in Oz. The value of Craggs et al. (1957)
(-+s-) is undoubtedly too high. The
values of Buchelnikova (1959) (---), of
Schulz (1962b) (-+-), of Rapp et al.
(1965) (---), and of Christophorou et al.
(1965) (—) all agree very well. [From
Chen (1969).]

in
a

°o

Cross section 10-"8 cm2

bd
a

O2-*+0:02-+O2. Here, O2-* denotes a particular
vibrational level of the O.-(X *II,) state. The general
features of this model have been deduced by Chanin,
Phelps, and Biondi (1962) who clearly established the
three-body nature of the process from their swarm data.
The modern approach to the theoretical considerations

Electron energy, eV

is due to Herzenberg (1969), The swarm experiments of
Chanin et al. show a smooth variation with energy of
the three-body attachment coefficient as would be
expected for swarm experiments.

If one performs.an experiment with essentially mono-
energetic electrons, the three-body attachment ‘coeffi-

Fic. 72. The dependence on tempera-
ture of the peak dissociative attachment
cross section in Oz. Shown are the results
of Spence and Schulz (1969) , of O’Malley

Cross Section, cm*

(1967), and of Henderson, Fite, and lor 7
Brackmann (1969). [From Spence and — Spence & Schulz
Schulz (1969).] 08 070, at 6.7eV
06 —O- O'MALLEY (Theory)
4 HENDERSON ET AL.
04 4
02+ |
olit poder triad Li
300 500 1000 1500 2000 2500

97

Temperature, °K


APPENDIX IL

Values for the 1s(2s)?#S resonance in helium.

Energy Width Method Author
Experiment

19,300.05 one 72° elastic Schulz (1963)

19.310.03 see Transmission Kuyatt et al. (1965)

19. 285--0.025 on Total (elastic) Golden and Bandel (1965)

19.340.1 see 90° elastic McGowan (1965)

19.3040.01 0.008 Transmission Golden and Zecca (1970, 1971)

19,340.02 wee Transmission Sanche and Schulz (1972)

19.350.02 see 90° elastic Mazeau et al. (1972)
0.008 Differential Gibson and Dolder (1969)
0.015-0.020 Differential Andrick and Ehrhardt (1966)

19.355-40.008 wee Differential Cvejanovic et al. (1973)

Theory

19.5(-+0.1, —0.2) 0.008 Variational Kwok and Mandel (1965)
0.03

19.33 0.039 Close-coupling Burke et al. (1966)

19.67 one Variational Young (1968)

19.3 ore Stabilization Eliezer (1970)

19.34 tee Bound-state Weiss and Krauss (1970)

19.69 see Perkins (1971)

19.363 0.014 Quasi-projection, Temkin et al. (1972)

19.4 0.015 Variational Sinfailam and Nesbet (1972)

APPENDIX IIL

Position of resonances below ionization in helium (eV).

Metastable
Transmission experiments production Differential
Feature Sanche and Pichanick and
number Schulz Kuyatt et al. Simpson Ehrhardt and
(Fig. 13) (1972) (1965) (1968) co-workers Designation.
1-1’ 19.30-19.37 19.31-19.37 BS
19,43-19.47
2-2' 19.80-19.90 19.818 Wigner cusp+2°S
20.34 20.45 2p
3-3" 20.58-20.62 20.59 Wigner cusp+2'S
20.99 21.00 2D
4 21.19
21.50-21.55

5-5'-5"" 22.34-22.42-22.50 22.34-22.39 22.44 22.42 BS

6-6-6" 22.60-22.65-22.73 22.54-22.60 22.55/22.67 22.55/22.60 BP

7-7-1" 22.88-22.92-22.97 22.81-22.85  22.75/22.86 22.75/22.85

8 23.05 23.05

9-9" 2335-23 .43 23.30-23.44 23.39 n=4
10-10’ 23 .48-23 55, 23.49
11-11/-11” 2382-23 .88-23.93 23.75-23.82 n=5
12 24.03

38