Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 31–38, 2002

31

Role of Entrance-channel Dynamics in Heavy Element Synthesis
D. J. Hinde,∗ A. C. Berriman, R. D. Butt, M. Dasgupta, I. I. Gontchar,† C. R. Morton,
A. Mukherjee, and J. O. Newton
Department of Nuclear Physics, Research School of Physical Science and Engineering, Australian
National University, Canberra, ACT 0020, Australia
Received: November 13, 2001; In Final Form: April 17, 2002
In heavy element synthesis, the population surviving quasi-fission and fusion-fission is far out in the tail of the
distribution of reaction outcome probabilities, and should be sensitive to slight changes in the reaction conditions.
Because of the extremely low yields of very heavy elements, it is difficult to make detailed and systematic experimental studies. However, studies of less-fissile systems can give valuable information relevant to the formationof super-heavy elements. Measurements made at the ANU, Canberra, to study the influence of entrance-channel
properties on the subsequent reaction dynamics are presented. New and surprising data show that the entrancechannel mass-asymmetry plays a role in the compound nucleus formation probability, even when forming a nucleus
as light as 216 Ra. The influence of different physical configurations, related to different contact barrier energies, on
superheavy element formation is discussed.

1. Introduction
In planning experiments aimed at heavy element synthesis,
prediction of absolute cross sections without extrapolation fromnearby experimental cross sections is very challenging. This isdue to the extreme complexity of the process, and the very low
probability of evaporation residue (ER) formation. In the distribution of reaction outcome probabilities, the population surviving the competing quasi-fission and fusion-fission processes is
far out in the tail, and thus would be expected to be extremely
sensitive to slight changes in the reaction conditions. Because of
the very low yields, it is difficult and time-consuming to makedetailed and systematic experimental studies for the reactions
actually leading to very heavy, or super-heavy nuclei. However,such studies for reactions forming less fissile nuclei are morefeasible, and can give valuable information on the dynamical
processes occurring during the fusion of two nuclei, which will
also be relevant to reactions forming super-heavy elements.
The calculation of the cross section for formation of a superheavy element can conceptually be divided into three parts. In
reality these are not independent of each other, but are still sufficiently distinct to constitute a useful framework for discussion.
Firstly, the cross section for contact of the two colliding nuclei
must be determined. Contact may be defined as a configuration where complex nuclear reactions between the two nuclei
become highly probable. For light systems, this is at a radiusinside the peak in the potential barrier (capture barrier, or fusion
barrier), and automatically leads to a compact compound nucleus. For collisions of heavier nuclei, this must be multipliedby the probability (less than unity) of reaching a compact shapeinside the unconditional fission barrier. Those collisions which
do not achieve this compact shape contribute to the quasi-fission
or deep-inelastic yield. For those composite nuclei achieving acompact shape, the yield of the evaporation residues is determined by the probability of surviving fission decay from thiscompact configuration. The identity of the nuclei reaching thecompact shape will be dependent on particle evaporation during
the dynamical phase. Thus the evaporation residue (ER) formation cross section may be written:
σER (E ∗ , l) = σcontact (E ∗ , l, EC) · Pcompact(E ∗ , l, EC) · Psurv(E ∗ , l)(1)
∗Corresponding author. E-mail: David.Hinde@anu.edu.au.
FAX: +61-2-6125-0748.
†Permanent address: Omsk State Railway University, pr.Marksa 35,
Omsk, 644046 Russia.

where σcontact (E ∗ , l, EC) is the cross section for capture, for excitation energy E ∗ of the heavy nucleus with angular momentum
l h̄, and in general depends on specific entrance channel (EC)conditions. Pcompact (E ∗ , l, EC) is the probability of passing to
a compact shape, and Psurv (E ∗ , l) = [1 − Pfis (E ∗ , l)] is the survival probability against fission from the compact shape. It is
re-emphasised that in reality, the nucleus will cool by evaporation during the transition to the compact shape, so the latter two
factors are not independent. Pcompact (E ∗ , l, EC) is complementary to the probability of quasi-fission PQF (E ∗ , l, EC), namely
Pcompact + PQF = 1. To maximise the heavy nucleus survival crosssection, the product of all three factors must be maximised. As
will be discussed in detail, the physical processes associatedwith the entrance channel can make it impossible to simultaneously maximise all three factors individually, thus the choice ofreaction is in practice a trade-off of one factor against the other.
This can be seen in the similar yields of heavy elements in cold
fusion1 and hot fusion2, 3 reactions. Specific entrance channel
effects will be discussed in the next sections.
2. Contact of Two Nuclei
2.1. Entrance Channel Barrier Distribution. It is by now
well-established that in collisions of heavy nuclei, there is not asingle potential barrier, but a distribution of barrier energies,4
where D(E) is defined as the probability of encountering abarrier of energy E, and can be determined directly from experimental capture cross sections closely-spaced in energy.5, 6
The distribution can be understood classically in the case ofstatically-deformed nuclei, where different orientations of thedeformation axis with respect to the incident projectile result in
potential barriers at different radii, and thus energy.6 Stronglycoupled collective vibrations (quadrupole7 and octupole8 ), andmulti-nucleon transfer, can also give rise to broad barrier distributions. Typically, the width of the barrier distribution is between 5% and 10% of the mean barrier energy.9 Although thesedifferent barriers affect all reaction processes, here we are particularly interested in capture (or fusion, for lighter systems).
For systems light enough that quasi-fission is not present, all
the nuclei which pass inside the potential barrier(s) lead to an
equilibrated compound nucleus. It is possible to identify thesum of the fission and evaporation residue yields with passage
inside the capture barrier(s), and thus the term fusion barrier
distribution is appropriate in this regime. For heavier systems,
though the two nuclei may be captured inside the potential barrier, they are likely to re-separate after energy damping andmass-exchange (deep inelastic or quasi-fission processes). In

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

3.1. Quasi-fission Measurements. Generally, different potential barriers correspond to different conditions or configurations of the two nuclei at the capture barrier radius. The question
then arises, does the configuration at the capture barrier radiusinfluence the outcome of the reaction? If an equilibrated compound nucleus is always formed, according to Bohr’s independence hypothesis, the answer should be no. If this is not the case,as in quasi-fission, some influence could in general be expected.
From the discussion of eq 1, it may seem that there are two complementary methods of experimentally investigating this question, which should give the same information. The first is to lookfor changes in the fission properties indicating the presence ofquasi-fission, whilst the second is to investigate inhibition of theevaporation residue yields. The situation is not quite so simple,
however, since the general dependence of the fission process onangular momentum could result in quasi-fission competing withfusion at high angular momenta, resulting only in suppressionof fusion-fission, but not affecting the evaporation residue yields
which arise from the lower angular momenta. This question will
be addressed in sect. 4.3 and 4.4.
A number of experimental studies have been made whichhave been interpreted as showing that, for a given reaction, thequasi-fission probability depends on the conditions at the capture barrier. The first such data interpreted in this way wasfor the reaction 16 O + 238 U, where the fission anisotropy was observed to rise dramatically as the beam energy fell through thecapture barrier region, which can be seen by comparing Figure 1(a) and (c). In that work, it was proposed that fusion at
the lowest beam energies, which results exclusively from the
projectile approaching the tips of the prolate deformed target
nuclei, leads preferentially to quasi-fission. Qualitatively, thispicture could explain the trend of the data. There was also asmall asymmetry in the fission mass-distribution, which became
more pronounced at the same beam energy as the change in theanisotropy, as shown in Figure 1(b).
The hypothesis that PQF (E ∗ , l, EC) depends on the orientation

To investigate this important question, a comparison of two
reactions already known11, 12 to have substantial quasi-fission
probabilities was made. The two reactions compared were32
S + 208 Pb (where 208 Pb is spherical) and 32 S + 232 Th (where232
Th is prolate deformed). Recent measurements at the Australian National University (ANU) mapped out the detailed behaviour of the fission properties across the capture barrier energy region. Figure 2 shows the capture barrier distributions, thecentroids of the fission mass distributions measured at a back-800
d2(Eσ)/dE 2 (mb/MeV)

3. Dependence of Quasi-fission Competition on Contact
Configurationof the heavy deformed nucleus as the projectile reaches the capture barrier could be specific to heavy nuclei with a large static
deformation. Alternatively, it could be a reflection of universal behaviour in heavy nucleus-nucleus collisions, in which low
capture barriers (which are generally associated with large barrier radii) could always result in enhanced quasi-fission, withconcomitant suppression of fusion.

(a)

16O + 238U
600
400
200
0
-200

(b)
0.50
M

such cases, the entrance-channel model describes the capture
cross sections, and so we refer to the capture barrier distribution. It is important to appreciate that entrance channel models
should not be compared with evaporation residue yields in suchcases, since the capture cross section is only one of the factors in
eq 1 which defines the ER cross sections. Similarly, a dynamical
model describing the probability of passing to the compact configuration, but neglecting the dynamics in the entrance channel
may also result in misleading conclusions.
The presence of the wide capture barrier distributions which
necessarily occur during the collision of two heavy nuclei (dueto the high charge product), should constitute a significant element in interpretations or predictions of cross sections for reactions forming super-heavy nuclei. In general, reactions at energies below the uncoupled potential barrier occur not throughtunneling through that barrier, but by passage over a lower barrier, which is encountered with a probability defined by the barrier distribution. In the language of Myers and Swiatecki,10
those collisions which actually lead to very heavy nuclei arealmost certainly “unshielded”, the capture barrier having been
below the bombarding energy. The fact that there is almost no
potential pocket for the uncoupled barrier will surely influence
the extent and probability of finding barriers at energies lower
than the uncoupled barrier, but lower barriers will exist. To maximise ER cross sections, not only should the weights (probabilities) of these lower barriers be maximal, but the elongation of
the composite nucleus at contact, after passing the potential barrier, should be as small as possible. The latter point is illustrated
below from experimental measurements.

Hinde

0.49
0.48
(c)

2.4
W(180o)/W(90o)

32

2.2
2.0
1.8
1.6
1.4

TSM

1.2
1.0
70

75

80

85 90
E c.m. (MeV)

95

100

Figure 1. (a) The capture barrier distribution for 16 O + 238 U together
with a model calculation. (b) The measured centroids of the fission
mass-splits (symmetric fission is indicated by the dot-dashed line). (c)The energy dependence of the fission anisotropy. In panels (b) and (c),the predictions of the TSM with the inclusion of couplings in capture
are given by the dot-dashed lines, whilst the assumption for pure quasifission is given by the dotted lines. The predictions of the orientation
dependent quasi-fission model based on these values are indicated by
the full lines.

Role of Entrance-channel Dynamics in Heavy Element Synthesis

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002
400

800
(a)

(d)

32S + 208Pb

32S + 232Th

300

D(E)

D(E)

600
400

200

200

100

0

0

0.6
0.5
_
M 0.4
0.3
0.2

33

0.6
0.5
_
M 0.4
0.3
0.2

(b)

(c)

(e)

(f)

0.4 < M < 0.6

4.0
3.0
A

A 3.0
TSM
2.0
2.0
No coupling
1.0
130

140

150

160

TSM
1.0
130

140

150

160

170

180

E c.m. (MeV)
E c.m. (MeV)
Figure 2. The barrier distribution (a) for 32 S + 208 Pb together with (b) the centroids of the fission mass-splits (symmetric fission is indicated by thedashed line) and (c) the energy dependence of the fission angular anisotropy. The predictions of the TSM with and without the inclusion of couplingsin capture are given by the dashed and full lines respectively. Similar quantities for 32 S + 232 Th are shown in (d), (e), and (f), the results for symmetricmass-splits between 0.4 and 0.6 of the compound nucleus mass being indicated by triangles. For both reactions, coupled-channels calculations of thecapture barrier distributions show that the inclusion of wide barrier distributions does not allow reproduction of the measured anisotropy values.

ward angle, and the anisotropies as a function of beam energy
for each reaction. In both cases, the anisotropies calculated assuming fusion-fission using the transition state model (labeledTSM) are small, whether the width of the barrier distribution is
included (full lines) or not (dashed lines). These anisotropies are
small because the calculated saddle-point shapes are very compact for such fissile compound nuclei, allowing fission far fromthe plane normal to the angular momentum vector.
For both reactions, the measured anisotropies A lie well above
the calculations, indicating that the fission occurs close to theplane normal to the angular momentum vector. This implies
that compact shapes are not generally reached in these reactions,consistent with previous conclusions11, 12 that quasi-fission predominates. The energy dependence of A for the two reactions
is, however, very different. For 32 S + 232 Th, A rises as the energy
falls below the average fusion barrier energy, as observed forlighter projectiles incident on deformed heavy targets, for example 16 O + 238 U (Ref. 14) and even 12 C + 238 U,232 Th (Ref. 15, 16).
In contrast with the reactions induced by lighter projectiles,
which only show small changes (see Figure 1(b)), the energy
dependence of the shape of the fission mass-distributions for32
S + 232 Th shows marked changes in shape and centroid, as
demonstrated in Figure 2(e). For 32 S + 208 Pb, however, theanisotropy falls monotonically with decreasing energy, and themass-distributions show essentially no change in shape or centroid, unlike those for the 232 Th target. Thus there is no indication in the 32 S + 208 Pb data of a significant change in the character or probability of quasi-fission which is dependent on theenergy of the barrier encountered, unlike reactions with statically deformed heavy nuclei. This is most likely correlated withthe high frequency of the vibrational excitations of 208 Pb, as opposed to the low frequency associated with collective rotational
excitations of 232 Th.
In reactions involving heavy statically deformed nuclei, theconfiguration found at the capture barrier is likely to remain essentially unchanged up to the time the two nuclei start to merge
together, and so influences the subsequent fission dynamics. For
vibrational nuclei, a configuration resulting in a low energy fusion barrier will not necessarily translate into an elongated com-posite nucleus, due to the high frequency of the collective vibrational modes.
3.2. Dependence of Evaporation Residue Yield on Contact Configuration. The energy dependence of the fission behaviour in the two 32 S-induced reactions discussed above thus
indicates a specific influence of static deformation of the system before contact on the subsequent reaction dynamics. A
general increase in quasi-fission associated with contact barriers with larger radii (lower energy) than average is not indicated. The data do support the hypothesis originally developed
to explain the anisotropies for the 16 O + 238 U reaction. At thattime, it was suggested that the orientation-dependence of thequasi-fission probability would lead to suppression of evaporation residue yields at sub-barrier energies, whilst it may leadto enhancement at above-barrier energies. In terms of eq 1,
this occurs because the orientation-dependence of the quasifission probability also defines the complementary probability
Pcompact (E ∗ , l, EC) of reaching the equilibrium deformation.
Recently, measurements of evaporation residue cross sections
have been made at JAERI, for the 60 Ni + 154 Sm (Ref. 17) and76
Ge + 150 Nd (Ref. 18) reactions, where both target nuclei havelarge prolate static deformations. It was found that there was
essentially no evaporation residue yield in the lowest 10 MeVof the calculated fusion barrier distribution, corresponding only
to those collisions where the projectile makes contact with the
tip of the target nuclei. This result, complementary to studies offission properties in the same low energy regime, is consistent
with the above picture of orientation-dependent quasi-fission.
4. Dependence of Quasi-fission on Entrance Channel
Mass-asymmetry
It has long been recognised that the probability of quasifission depends on the entrance-channel mass-asymmetry. A
number of comparative measurements, where the same compound nucleus has been formed with different pairs of projectile and target nuclei, have shown19, 20 that for the reaction withthe more symmetric entrance-channel masses, the fission properties show signatures characteristic of quasi-fission (for example, broader mass distributions).

34

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Hinde

A recent study at the ANU, reported in Reference 21, showed
for the first time the presence of quasi-fission, and the simultaneous suppression of the evaporation residue yield, for massasymmetric reactions. These results are described below.
4.1. ANU Experimental Studies of Reactions Forming
216
Ra. Three combinations of projectile and target nuclei wereused to form 216 Ra: 12 C + 204 Pb, 19 F + 197 Au, and 30 Si + 186 W. The
evaporation residue (ER) cross sections were measured, as wellas the fission cross sections and properties. Although the fission may previously have been expected in such reactions toresult only from fusion-fission, in principle it also includes contributions from the quasi-fission process (if present) in which noevaporation residues are produced. Measurements were made atten or more beam energies, from the Coulomb barrier upwards
for each reaction. The energies were chosen such that the 216 Ra
nuclei were formed at the same excitation energy in the threereactions.
The 14UD tandem electrostatic accelerator at the ANU provided pulsed beams which bombarded thin isotopically enrichedtargets. The 204 Pb target was enriched to 99.7%, which was confirmed by the absence of α lines from the lighter Pb isotopes.
To determine the cross sections for ERs, aluminum catcher foils
were placed immediately behind the target to stop the ERs.22
The catcher foils were 1.5–2.5 times thicker than the average
range of the ERs for each reaction. All the ERs undergo subsequent α decay from their ground-states, with lifetimes from 1.9 s
to 3.5 h. The α particles resulting from the decay were detectedin an annular solid-state detector as shown in Figure 3(a). Repeat measurements for the 30 Si reaction with a thicker catcher
gave the same cross sections, confirming that all ERs were
stopped. Measurements were made both during and after irradiation. Together with the use of a sophisticated peak-fitting
program, this allowed determination of the individual yields ofalmost all evaporation channels
Measurements of fission were carried out in separate experiments, the two fission fragments being detected in twolarge area, position-sensitive multi-wire proportional countersarranged as shown in Figure 3(b). Each covered an angularrange of 75◦ , allowing determination of the cross section in
250

(a)
200

Monitor detector
Catcher foil
Beam
Annularalphaparticle
detectorRa
CountsTarget

150
100

Rn

Alpha-particle
Fr

50
Monitor detector
5.0

(b)

5.5

6.0 6.5 7.0
Energy (MeV)

7.5

4

Fissionfragment 1

Beam

Target10

Monitordetectors(out of plane)

Ni + Au
Yield

Fission fragment
detector 1

C + PbF + AuSi + W

3

10

Fissionfragment 2

Fission fragment
detector 2

0.8
0.2
0.4
0.6
Normalised fission fragment mass

Figure 3. Experimental configurations for the two types of measurement and typical measured spectra. (a) A schematic diagram of theconfiguration of the ER measurements with a typical α-particle energy
spectrum from the annular α-particle detector, and the fit to the spectrum (full lines). This spectrum shows that the α particles from Ra canbe very clearly identified. (b) Configuration for the fission measurements, with three normalized mass spectra (defined as the mass of one
fragment divided by the total mass) measured for fission of 216 Ra at thesame excitation energy in the three reactions. The peak for elastic scattering of 58 Ni from 197 Au shows the good experimental resolution.

a single measurement. The coincident detection of both fragments allowed the determination of the fission fragment massratio through reconstruction of the velocity ratio.14
In both ER and fission measurements, cross sections were
determined by normalizing to the yields of elastically scattered
beam particles measured in monitor detectors located at ±22.5◦ .
It was essential that reliable absolute cross sections were obtained in order to make meaningful comparisons between reactions. This could be achieved, without requiring determination of transmission efficiencies through a complex apparatus,
because the cross sections were sufficiently large that the ERs
could be identified when stopped at the target location. Thus
accurate absolute detector normalisation could be obtained simply by measuring elastic scattering both in the monitor detectors
and in the α-particle and fission detectors, at low beam energies
where the elastic scattering cross sections will be Rutherford.
The individual ERs, identified by their decay α-particle energies and lifetimes, were mainly Ra isotopes, formed after theemission of x = 3, 4, 5, ... neutrons.
4.2. Experimental Results for 216 Ra. The ratio of the yieldof a given xn channel to the total xn cross section was determined at each energy for the three reactions, the results being
shown in Figure 4, as a function of excitation energy in 216 Ra.
Bohr’s independence hypothesis23 states that compound nuclei
with the same excitation energy and angular momentum will decay independently of their method of formation. The data showthat for the ER, this is the case, the peak in the ER yield foreach isotope occurring at a value of E ∗ essentially independentof the reaction. This confirms that the actual excitation energiesof the 216 Ra nuclei formed in the three reactions are indeed essentially the same, and that pre-equilibrium neutron emission is
not significant, as expected at low beam energies.
The sum of the fission and ER cross sections defines the capture cross section. Both are shown, for all three reactions, inFigure 5 and Figure 7(a). In each case, the ER cross sections
peak at a certain beam energy, then fall, whilst the contribution

1.0
0.8
0.6
0.4
0.2
0.0
1.0
σxn 0.8
Σ σ xn 0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0

3n

4n

19 F

5n

12 C

5n

6n

7n

50 60
E * (MeV)

70

80

30 Si

20

30

40

90

Figure 4. The ratio of individual xn channel cross sections to the total
xn cross section, for the three reactions forming 216 Ra. Statistical model
calculations are shown by the curves. The xn excitation functions arealmost identical in the three reactions.

Role of Entrance-channel Dynamics in Heavy Element Synthesis

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

35

103
102
σ
(mb)
101

FusionFission
ER

D(E)

100

19F + 197Au

30Si + 186W

70 80 90 100 110 120
Ec.m. (MeV)

100 110 120 130 140 150
Ec.m. (MeV)

12C + 204Pb

800
600
400
200
0
-200
50

60 70 80
Ec.m. (MeV)

90

Figure 5. cross sections and capture barrier distributions for the three reactions 12 C + 204 Pb, 19 F + 197 Au, and 30 Si + 186 W. The upper frames show thesum (closed circles) of the measured fission (open circles) and ER (triangles) cross sections. For the 30 Si + 186 W reaction the different triangle symbols
represent ER measurements using different stopper foil thicknesses. The lower panels show the experimental capture barrier distributions D(E). Thelines represent the results of the coupled-channels calculations using known target and projectile excitations.

of ERs to the capture cross sections decreases as the projectile
becomes heavier. Calculations using nuclear potential parameters consistent with many other reactions,9 and coupling parameters from the known properties of the collective modes in eachnucleus, reproduced the present capture cross sections and barrier distributions D(E) for the three reactions, typically to within
2%, indicating that the three systems behave as expected. These
calculations are shown by the lines in Figure 5. From these calculations, the capture angular momentum distributions were obtained for each beam energy, for the three reactions. As the beamenergy increases, the projectile can bring in higher angular momenta l h̄. As the height of the fission barrier falls proportional
to l 2 , this leads to the observed rapid fall in the ER probability. Fitting these data with a statistical decay simulation showsthat the fission probability exceeds 98% at l = 30. This restricts
ER survival to low l values, allowing a simple and essentiallymodel-independent comparison of the measured ER yields forthe three reactions, which is described below.
4.3. Reduced ER cross sections σ̃ER . At a given beam energy E, the total ER cross section is the sum of the cross sections
from each l, these being the products of the capture cross sections and the probabilities of surviving fission (1 − Pf (l, E ∗ )).
Initially it is assumed that Pf (l, E ∗ ) is independent of the entrance channel. Thus

calculations24 (using Tl (E) from the coupled channels calculations which reproduced the measured capture cross sections) indeed show this behaviour, as illustrated in Figure 6(a), where
the three lines corresponding to each reaction converge when
all reactions fully populate the angular momenta leading to ERs(Tl (E) = 1 for all l below 30). By comparison, the experimental
ER data do not converge, but show a systematic difference foreach reaction, with the yield of ERs being largest for the light-

10 3
all ER

(a)
102

~
σ
ER

12

204

19

197

C+

1

10

F+

(2)

l=0

where Tl (E) is the probability of capture for l, and λ is the reduced deBroglie wavelength, determined by the beam momentum. Division by πλ2 gives the reduced cross section σ̃ER . Although the coupled-channels capture models can reliably predict Tl (E), reliance on a particular calculation can be eliminated.
This is because all such models show that at beam energies sufficiently high above the Coulomb barrier, Tl (E) is essentiallyunity for all l which lead to ERs. At these energies Tl (E) can be
dropped, giving∞

σ̃ER (E) = ∑(2l + 1) (1 − Pf (l, E )).
∗

(3)

l=0

Thus at the same E ∗ , the three reactions should give the sameσ̃ER , as long as Pf (l, E ∗ ) is independent of the reaction, in accordance with Bohr’s hypothesis. Monte Carlo statistical model

Au

30Si +186 W

10

0

(b)

Ra isotopes
xn ER

∞

σER (E) = πλ2 ∑(2l + 1) Tl (E) (1 − Pf (l, E ∗ )),

Pb

10 2

~
σ
ER
10

1

10 0
20

30

40

50

60

70

80

90

E * (MeV)
Figure 6. Reduced cross sections for ERs as a function of excitation energy for (a) all ERs and (b) radium ERs. Monte Carlo statistical model calculations, based on Bohr’s independence hypothesis, areshown by the curves, which converge at the higher energies. In contrast,
the measured ER reduced cross sections for the heavier projectiles are
inhibited compared to those for 12 C.

36

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Hinde

est projectile. The yields could be affected by the recognizedphenomenon of breakup of the lighter projectiles into α-particle
clusters,25 leading at high l to incomplete fusion, resulting in increased ER formation rather than fission. Contributions from incomplete fusion can be eliminated by summing the yields for Ra
isotopes alone, which can only be formed when all the protons in
the projectile are captured. These yields, plotted in Figure 6(b),still show a strong dependence on projectile mass, those for 19 F
and 30 Si being respectively 0.64 ± 0.09 and 0.57 ± 0.08 of thosefor 12 C at the two highest energies. This cannot be explained by
the low values of Tl (E), since the measured capture cross sections for all three reactions can only be reproduced with Tl (E)values close to unity. The only reasonable conclusion is thateither Pf (l, E ∗) depends on the reaction, in disagreement with
Bohr’s hypothesis, or that fission is not all from the fully equilibrated compound nucleus. Then the right hand side of eq 2 mustbe multiplied by the probability of passing from the contact tothe compact shape, as in eq 1, allowing for inhibition of true
fusion for the heavier projectiles. Fusion with light projectiles(such as 19 F) has previously implicitly been assumed to proceedwithout any inhibition. We believe that this is the first observation of fusion inhibition for such a light projectile.
4.4. Fission Mass Distributions. If the inhibition is causedby the presence of quasi-fission, as in reactions forming super-

σcap(mb)

1200

(a)

800
400
0

< L2 >

2000
1000

(b)
12C + 204Pb
19F + 197Au
30Si + 186W

heavy nuclei, there should be evidence for quasi-fission in thefission mass-distributions, since quasi-fission is expected tohave a broader mass-distribution than fusion-fission. The widthof the fusion-fission mass-distribution depends principally on
excitation energy, but may depend slightly on angular momentum. However, if the 216 Ra compound nuclei formed at the sameE ∗ in different reactions have the same angular momentum distributions, then according to Bohr’s hypothesis, the fission massdistributions should be identical. The angular momentum distributions can be reliably predicted26, 27 by the coupled-channels
calculations that reproduce the capture cross sections.9 Figure 7(a) shows the dependence of the deduced mean l 2 on E ∗ .
This demonstrates that the 12 C reaction matches the 30 Si reaction at one energy, and approaches the 19 F reaction at the highest energy. Qualitatively this must happen, as the heavier projectiles have a higher threshold E ∗ for capture, but carry moreangular momentum than 12 C. The measured variances of the fission mass-distributions for the three systems, presented in Figure 7(b), do not match at any energy, but rather show a systematic dependence on projectile mass, as well as the expected
increase with E ∗ . This result is consistent with the observed
inhibition of fusion for the heavier projectiles, indicating an increasing contribution from the quasi-fission process, in which no
ERs are produced, and for which full mass-equilibration is notexpected, leading to wider mass-distributions for the reactions
with heavier projectiles.
Having found convincing evidence for quasi-fission in the fission mass-distributions, as well as inhibition of fusion, we conclude that the combined results indicate that quasi-fission is not
only competing with fusion-fission at high angular momenta,
but is also competing at the low angular momenta leading toERs.
4.5. Interpretation in terms of Entrance-channel Massasymmetry. These results may be interpreted qualitatively byconsidering what can happen to the projectile nucleus when it
makes contact with the target nucleus. It may be swallowed upby the heavier nucleus, resulting in a compact compound nu-

0
(c)

(σM)2

0.004
0.002
0.000
20

40

60

0.09

(0)

216Ra

Potential Energy ( E s )

0.006

80

E*(MeV)
Figure 7. Experimental evidence for quasi-fission. As a function of
excitation energy we present the measured and calculated capture crosssections for the three reactions, shown in panel (a), whilst the calculated mean-squared angular momentum introduced in the three reactions, based on these fits, are shown in panel (b). The measured variances of the normalized fission mass-distributions are shown in panel(c). Experimental uncertainties are typically smaller than the size ofthe points. For the same excitation energy and mean-squared angularmomentum in 216 Ra, the mass distributions for the reactions are not
the same. The systematic dependence of the variance on the massasymmetry of the projectile and target is evidence for an increasing
contribution from quasi-fission associated with the projectile mass.

216

Ra

30 Si

19

F 12 C

0.07
0.05
0.03
0.01
0.5

0.6 0.7
0.8 0.9
Mass Asymmetry

1.0

Figure 8. Fission barrier energies for 216 Ra are shown as a function ofmass-asymmetry, defined as the difference between the masses of thetwo parts of the elongated nuclear system divided by their sum. The
barrier energies, calculated with the Liquid Drop Model, are expressedin units of the spherical surface energy Es(0) of 216 Ra. The initial massasymmetries for the three reactions are indicated. The shapes at contact
corresponding to these asymmetries, and others, are sketched above.

Role of Entrance-channel Dynamics in Heavy Element Synthesis
cleus (fusion). Alternatively, it may gain mass from the heavier nucleus, and the system will approach the entrance channel configurations of more and more mass-symmetric collisions.
Although it may still fuse from these configurations, passing
inside the unconditional saddle-point deformation, the system
may also separate, leading to quasi-fission.
Though this seems qualitatively to be a reasonable interpretation, we must consider an alternative explanation, related tothe orientation dependent quasi-fission picture described above
for statically deformed nuclei, where increased elongation of thesystem at contact increases the quasi-fission probability. 204 Pb isessentially spherical, and the small oblate deformation of 197 Au
results in contact shapes only 2% longer than average at most.
The larger prolate deformation of 186 W can result in contact
shapes over 7% longer than average. The largest change in theeffect of deformation is thus between 197 Au and 186 W, whilst thelargest change in ER yields is between 197 Au and 204 Pb. Furthermore, the comparison of σ̃ER must be made at energies above
the fusion barrier region, where all orientations of the deformed
nucleus contribute. Hence this mechanism seems unlikely to
explain the observed difference between the 204 Pb and 197 Au reactions.
Fusion and quasi-fission competition has previously been discussed in terms of the dependence of the calculated heightsof the mass-asymmetric fission barriers,28–30 or in terms of the
mass-asymmetry dependence of the energy of the contact configurations.31 In Figure 8 the conditional fission barrier energies(interpolated from calculations of Reference 32) for 216 Ra areshown as a function of the mass-asymmetry. The projectile willtend to be absorbed if the mass-asymmetry is to the right of thepeak, whilst if to the left, it will preferentially gain mass. The
three reactions studied span the peak, with only the 12 C reaction
on the side favouring rapid compound nucleus formation. It may
seem surprising initially that the calculated potential energies forthe fission shapes appear to agree so well with the experimental
data, as the potential maximum for the contact shapes (which areless elongated than the conditional fission saddle-point shapes)
occurs at smaller asymmetries. However, after contact, the development of a neck between the two nuclei causes the potential
maximum to shift back to larger asymmetry,33 similar to thatfound for the saddle-point shapes. Our results are consistent
with the mass-asymmetry being a crucial variable determining
the dynamics of these reactions, though of course the dynamics
will not only depend on the the potential energy surface, but also
on the dissipation and inertia tensors. A quantitative understanding of the effect of mass-asymmetry, and other important variables such as the deformation of the symmetric fission barrier
and the elongation of the system at contact,14 will require further
experimental and theoretical studies. To describe theoreticallythe complex fusion dynamics after capture, multi-dimensionalmodels31, 34, 35 are being developed. Their future application tofusion reactions leading to new super-heavy elements promises
insights into possible advantages of using short-lived neutronrich nuclei, for which extensive experimental surveys will not
be practicable.
5. Conclusions
A large static deformation of the heavy partner in a nuclear
collision has been demonstrated to affect the probability ofquasi-fission. Experimental data indicate that collisions at thelowest beam energies that result in contact between projectile
and target favour quasi-fission, and thus must inhibit true fusion. This is related to the elongation of the combined system,and the low frequency of the collective rotational motion whichis induced. In contrast, collisions involving heavy spherical nuclei show no evidence of enhancement of quasi-fission at low
beam energies, which is argued to be due to the high frequencies of the collective vibrations excited during the collision.

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

37

The comprehensive data set obtained for three massasymmetric reactions leading to the compound nucleus 216 Ra indicates that the mass-asymmetry affects the probability of quasifission already for extremely asymmetric reactions (19 F + 197 Au),
even at low angular momenta. These experimental results provide a quantitative test of the physics incorporated in theoretical models of ER formation, through focusing on the boundary
between the simple fusion process envisaged by Bohr, and thecomplex and delicate dynamical process required to coax two
heavy nuclei together.
Acknowledgement. M.D. acknowledges the support of anAustralian Research Council QEII Fellowship.
References(1) S. Hofmann and G. Münzenberg, Rev. Mod. Phys. 72, 733(2000), and references therein.
(2) Yu. Ts. Oganessian, A. V. Yeremin, A. G. Popeko, S.
L. Bogomolov, G. V. Buklanov, M. L. Chelnokov, V. I.
Chepigin, B. N. Gikal, V. A. Gorshkov, G. G. Gulbekian,M. G. Itkis, A. P. Kabachenko, A. Yu. Lavrentev, O. N.
Malyshev, J. Rohac, R. N. Sagaidak, S. Hofmann, S. Saro,
G. Giardina, and K. Morita, Nature 400, 242 (1999).
(3) Yu. Ts. Oganessian, V. K. Utyonkov, Yu. V. Lobanov, F.
Sh. Abdullin, A. N. Polyakov, I. V. Shirokovsky, Yu. S.
Tsyganov, G. G. Gulbekian, S. L. Bogomolov, B. N. Gikal,
A. N. Mezentsev, S. Iliev, V. G. Subbotin, A. M. Sukhov,
O. V. Ivanov, G. V. Buklanov, K. Subotic, M. G. Itkis,
K. J. Moody, J. F. Wild, N. J. Stoyer, M. A. Stoyer, R.
W. Lougheed, C. A. Laue, Ye. A. Karelin, and A. N.
Tatarinov, Phys. Rev. C 63, 011301(R) (2001).
(4) C. H. Dasso, S. Landowne, and A. Winther, Nucl. Phys. A
405, 381 (1982); 407, 221 (1993).
(5) N. Rowley, G. R. Satchler, and P. H. Stelson, Phys. Lett. B
254, 25 (1991).
(6) J. R. Leigh, M. Dasgupta, D. J. Hinde, J. C. Mein, C. R.
Morton, R. C. Lemmon, J. P. Lestone, J. O. Newton, H.
Timmers, and J. X. Wei, Phys. Rev. C 52, 3151 (1995).
(7) A. M. Stefanini, D. Ackermann, L. Corradi, D. R. Napoli,
C. Petrache, P. Spolaore, P. Bednarczyk, H. Q. Zhang, S.
Beghini, G. Montagnoli, L. Mueller, F. Scarlassara, G. F.
Segato, F. Soramel, and N. Rowley, Phys. Rev. Lett. 74,
864 (1995).
(8) C. R. Morton, M. Dasgupta, D. J. Hinde, J. R. Leigh, R.
C. Lemmon, J. P. Lestone, J. C. Mein, J. O. Newton, H.
Timmers, N. Rowley, and A. T. Kruppa, Phys. Rev. Lett.
72, 4074 (1994).
(9) M. Dasgupta, D. J. Hinde, N. Rowley, and A. M. Stefanini,Ann. Rev. Nucl. Part. Sci. 48, 401 (1998).
(10) W. D. Myers and W. J. Swiatecki, Phys. Rev. C 62, 044610(2000).
(11) B. B. Back, R. R. Betts, J. E. Gindler, B. D. Wilkins, S.
Saini, M. B. Tsang, C. K. Gelbke, W. G. Lynch, M. A.
McMahan, and P. A. Baisden, Phys. Rev. C 32, 195 (1985).
(12) W. Q. Shen, J. Albinski, A. Gobbi, S. Gralla, K. D.
Hildenbrand, N. Herrmann, J. Kuzminski, W. F. J. Muller,
H. Stelzer, J. Toke, B. B. Back, S. Bjornholm, and S. P.
Sorensen, Phys. Rev. C 36, 115 (1987).
(13) D. J. Hinde, M. Dasgupta, J. R. Leigh, J. C. Mein, C. R.
Morton, J. O. Newton, and H. Timmers, Phys. Rev. Lett.
74, 1295 (1995).
(14) D. J. Hinde, M. Dasgupta, J. R. Leigh, J. C. Mein, C. R.
Morton, J. O. Newton, and H. Timmers, Phys. Rev. C 53,
1290 (1996).
(15) J. P. Lestone, A. A. Sonzogni, M. P. Kelly, and R.
Vandenbosch, Phys. Rev. C 56, R2907 (1997).
(16) J. C. Mein, D. J. Hinde, M. Dasgupta, J. R. Leigh, J. O.
Newton, and H. Timmers, Phys. Rev. C 55, R995 (1997).

38

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002(17) S. Mitsuoka, H. Ikezoe, K. Nishio, and J. Lu, Phys. Rev. C
62, 054603 (2000).
(18) K. Nishio, H. Ikezoe, S. Mitsuoka, and J. Lu, Phys. Rev. C
62, 014602 (2000).
(19) C.-C. Sahm, H.-G. Clerc, K.-H. Schmidt, W. Reisdorf, P.
Armbruster, F. P. Hessberger, J. G. Keller, G. Münzenberg,
and D. Vermeulen, Nucl. Phys. A 441, 316 (1985).
(20) R. L. Hahn, K. S. Toth, Y. LeBeyec, B. Lagarde, and M. W.
Guidry, Phys. Rev. C 36, 2132 (1987).
(21) A. C. Berriman, D. J. Hinde, M. Dasgupta, C. R. Morton,
R. D. Butt, and J. O. Newton, Nature 413, 144 (2001).
(22) C. R. Morton, D. J. Hinde, J. R. Leigh, J. P. Lestone, M.
Dasgupta, J. C. Mein, J. O. Newton, and H. Timmers, Phys.
Rev. C 52, 243 (1995).
(23) N. Bohr, Nature 137, 344 (1936).
(24) J. P. Lestone, J. R. Leigh, J. O. Newton, D. J. Hinde, J. X.
Wei, J. X. Chen, S. Elfstrom, and M. Zielinska-Pfabe, Nucl.
Phys. A 559, 277 (1993).
(25) P. Vergani, E. Gadioli, E. Varciago, E. Fabrici, E. Gadioli
Erba, M. Galmarini, G. Ciavola, and C. Marchetta, Phys.
Rev. C 48, 1815 (1993), and references therein.
(26) N. Rowley, J. R. Leigh, J. X. Wei, and R. Lindsay, Phys.

Hinde
Lett. B 314, 179 (1993).
(27) A. B. Balantekin, A. J. DeWeerd, and S. Kuyucak, Phys.
Rev. C 54, 1853 (1996).
(28) J. Toke, R. Bock, G. X. Dai, A. Gobbi, S. Gralla, K. D.
Hildenbrand, J. Kuzminski, W. J. F. Muller, A. Olmi, H.
Stelzer, B. B. Back, and S. Bjornholm, Nucl. Phys. A 440,
327 (1985).
(29) V. S. Ramamurthy, S. S. Kapoor, R. K. Choudhury, A.
Saxena, D. M. Nadkarni, A. K. Mohanty, B. K. Nayak, S.
V. Sastry, S. Kailas, A. Chatterjee, P. Singh, and A. Navin,Phys. Rev. Lett. 65, 25 (1990).
(30) G. V. Ravi Prasad and V. S. Ramamurthy, Phys. Rev. C 54,
815 (1996).
(31) G. G. Adamian, N. V. Antonenko, and W. Scheid, Nucl.
Phys. A 678, 24 (2000), and references therein.
(32) K. T. R. Davies and A. J. Sierk, Phys. Rev. C 31, 915(1985).
(33) P. Möller and J. R. Nix, Nucl. Phys. A 281, 354 (1977).
(34) Y. Aritomo, T. Wada, M. Ohta, and Y. Abe, Phys. Rev. C
59, 796 (1999).
(35) V. I. Zagrebaev, Phys. Rev. C 64, 034606 (2001).