.- . 

INTRODUCTION TO DISSOCIATIVE RECOMBINATION 

Steven L. Cuberman 

Institute for Scientific Research 

33 Bedford St., Suite 19A 

Lexington, MA 02173 

and 

J. Brian A. Mitchell 

Department of Physics 

The University of Western Ontario 

London, Canada N6A 5B9 

Dissociative recombination (DR) of molecular ions with electrons has 

important consequences in many areas of physical science. Even though 

almost 40 years have elapsed since the first experimental and 

theoretical investigations of DR, it continues to present great 

challenges to the investigator. 

For the diatomic or polyatomic molecular ion AB+, DR is described by , 

AB+ + e- + A + B 

where e' is an electron and A and B are atoms or molecules that may be 

in their ground states or vibrationally and/or electronically excited. 

The last decade has seen something of a revolution in the study of 

DR, since ab initio calculations coupled with resonant scattering 

theory and multichannel quantum defect studies have produced detailed 

results illuminating the role of ion vibrational excitation, the 

quantum yields of the DR products, and the role of Rydberg states. The 

old assumption that for most molecules the DR rate coefficient is about 

cm3/sec is clearly no longer adequate. Indeed, it is now clear 

that the simplest ions, e.g. H; and He;, have considerably slower total 

(NASA-CR-184950) INTPOWCTION TO N 89- 2 48 89 

DISSOCIATIVE RECOMBINATION (Institute for 

Scientific Research) 13 p 

CSCL 20H 

Unclas 

~1/72 0201505 
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DR rate coefficients from their ground vibrational levels. H3, the most 

important ion in hydrogen plasmas, has been shown theoretically and 

experimentally to recombine much more slowly when vibrationally cold 

than once believed. Deep narrow resonances associated with Rydberg 

state interact ions have been predicted and observed. New decay 

channels have been found and the effects of vibrational excitation are 

being clarified as theorists probe the details and experimentalists 

obtain better control of their experiments. 

I. Theory 

The early experimental results of Biondi and Brown'] and Holt et 

a1.*] on rare gas afterglows coupled with the need to explain the 

electron concentrations in the earth's i0nosphere3~ led Sir David Bates 

to first propose a mechanism for DR in 19504] in a seminal paper that 

was less than one full page in length. The mechanism'has stood the test 

of time and is still the basic mechanism used to describe DR in the 

absence of the higher order role due to Rydberg states. The proposed 

mechanism was several years in the making because it had to overcome 

two important obstacles. First, due to the mass mismatch, a collision 

with an electron could not be expected to cause a massive molecule to 

fall apart. The transfer of electronic energy to the nuclear motion iS 

improbable. However, in Bates's proposed mechanism, the electron energy 

is transferred entirely to the electrons of the target molecule and a 

neutral state is formed in which the nuclear motion leads to the 

dissociation of the molecule. The process is illustrated in Figure 1 

where a molecular ion, AB', shown by the solid potential curve captures 

an electron of energy E: into repulsive state AB. Once the interparticle 

distagce between A and E? becomes sufficiently large, the electron can 

no longer be ejected and the process is said to be stabilized. The 

second obstacle, as pointed out in the paper in this volume by 

O'Malley, is the non-crossing rule which requires that curves of the 

same molecular symmetry do not cross. According to this rule, the 

repulsive state labelled AB in Figure 1 could not reach the Ion 

c 
IN'IERNUCLJMR DISTANCE 

Fig. 1. Dissociative Recombination Mechanisms 

cause it would have to cross through an infinite number of Rydberg 

ates of the same symmetry as AB and having the ground state of the 

jn as a series limit. It is now understood however, that the repulsive 

;ate, AB, is a diabatic state, i.e., it is not an adiabatic solution 

P the full Schroedinger equation and therefore does not violate the 

3n-crossing rule. 

The first detailed calculations of DR were done by Bardsley5] who 

,sed the configuration mixing (CM) or resonant scattering theory 

ipproach. Bardsley also introduced Rydberg states into DR via indirect 

In this process, the electron is captured directly 

into a vibrationally excited Rydberg state by Born-Oppenheimer 

breakdown (vibronic coupling). In Figure 1, this process is illustrated 

for an electron of energy E'. The Rydberg state is then predissociated 
by the neutral AB repulsive state. 

A recent important development is the application of multichannel 

quantum defect theory (MQDT) to DR by Lee71 and Giusti-Suzor.81 In the 

first article in this volume Giusti-Suzor reviews the main features Of 

both the CM and MQDT approaches and describes the role played by 

vibrationally excited Rydberg states which appear as resonances in the 

DR cross sections. These Rydberg states participate in DR by both a 

non-Born-Oppenheimer coupling described above and by an electronic 

coupling. For the non-Born-Oppenheimer coupling, the largest matrix 

elements involve a change of unity in the vibrational quantum number. 

In practice, this can usually be satisfied by high principal quantum 

numbers near about seven. On the other hand, the electronic coupling 

between the Rydberg and dissociative valence states is largest for the 

lowest Rydberg state and decreases approximately as n*-3'* where n* is 

the effective 3ydberg principal quantum number. In this mechanism, 

Rydberg states with low principal quantum numbers but considerable 

vibrational excitation can play a role. This electronic coupling 

mechanism has been the subject of important studies by O'Malleygl and 

Hickman,lO] and Hickmanf0l has shown that the electronic coupling can 

be considerably larger than the vibronic coupling. 

In the second paper in this volume, O'Malley reviews the use of the 

resonant scattering theory approach to Dr' with the assumption that the 

various processes that drive DR are localized in the internuclear 

distance coordinate. This approximation is especially applicable if the 

dissociative state does not have a steep slope. O'Malley finds that the 

electronic coupling mechanism leads to the surprising result that the 

cross section for the case of a single isolated resonance has a dip at 

the energy of the Rydberg state vibrational level. 

The electronic coupling mechanism between the Rydberg and 

dissociative states is explored in the paper by Hickman. He shows that 

the capture is given by a matrix element of a Green function and is 

second order in the electronic coupling between the electron-ion and 

dissociative states. These higher order couplings are present in the 

second and higher terms on the right side of Eq. (5) in the paper by 

Giusti-Suzor. Hickman also compares the CM and MQDT approaches and 
points out that for the case of a single isolated resonance, the 

I resonant scattering theory approach in the Independent Resonance 

, . Approximationlo] and the MQDT approach lead to the same expression for 

the DR cross section. The expression takes the form of a Beutler-Fano 

profile with a non-zero q. A study of DR in H$ shows that the net 

effect of the indirect process depends upon whether the direct process 

is fast or slow. 

f 

Large scale ab initio results for DR potential curves for 02 and N2, 

and electron capture widths and DR rate coefficients for 02 are 

reported in the paper by Guberman. He finds that for 02, out of the 11 

states that can produce O(lS), the upper state of the green line, only 

a single state is important for the lowest 9 vibrational levels of the 

ion. The DR rate coefficient is very sensitive to vibrational 

excitation. The maximum rate coefficient for generating O(lS) is from 

v=2 and is 78 times greater than the rate coefficient from v=O. For 

O(lD), three states are important for generating the upper state of the 

red line from the lowest three vibrational levels of the ion. The O('D) 

rate coefficients are less sensitive to vibrational excitation than the 

O(lS) rate coefficients with the rate coefficient from v52 being a 

factor of 2 less than the rate coefficient from v=O. The calculated 

O(lD) rate coefficients are in good agreement with rate coefficients 

deduced from satellite measurements. For N2, DR from v=O is dominated , 

by four states and an inspection of the dominant configurations 

indicates that the 311u states may have the highest rate coefficients. 

Large scale CASSCF calculations are reported by Kraemer and Hazi on 

the potential curves which describe the DR of HCO'. Their approach 

leads to rather accurate values for electronic excitation energies in 

CO and HCO and an accurate dissociation energy for HCO'. Since a 

favorable recombination rate coefficient would require a similar 

geometry for the linear ion and the neutral state containing the 

captured electron, they hold the CO internuclear distance at the 

separation found in HCO' while varying the CH distance. In a linear 

geometry, none of the neutral states give likely dissociative routes 

from the lowest vibrational level of the ion. While two of the 

potentials drop significantly after relaxing the CO separation, a 
favorable dissociative route is still not found in spite of the fact 

that the laboratory DR rate coefficients are high. They suggest several 

possible indirect mechanisms. 

Nakamura, Takagi, and Nakashima report results for the DR of Hi (and 

isotopes) and CH". For H;, an interesting isotope effect is reported 

from the v=3 vibrational level of D;. At about 0.5 eV electron energy, 

the cross section for Di is very small compared to the cross sections 

for Hi and HD". The shape of the window resembles the DR Franck-Condon 

type windows found in model calculations.l'] For vibrational excitation 

from the v=l state of HD", they show that the energy dependence of the 

cross section is similar to that for DR indicating that the repulsive 

states are the intermediate states. Above the threshold energy, the V5l 

to 2 vibrational excitation cross section is of comparable magnitude to 

the DR cross section. For CH", they find that the DR rate coefficient 

is about 1 x 10-7 cm3Jsec at T=120K in agreement with the result of the 

merged beam experiment. 2] 

Associative ionization (AI), is related to DR by detailed balance 

and many of the same theoretical techniques developed for DR can be 

used for AI. Urbain describes some recent MQDT calculations on AI in H2 

and several recent experimental developments. For the case where the 

separated atoms limit lies below the lowest vibrational level of the 

ion, the AI cross section increases with energy above threshold as new 

vibrational ahannels become accessible. Above the ion asymptote, 

Penning ionization competes and the AI cross section decreases. For the 

case of H" colliding with H-, the entrance channel asymptote is above 

the lowest vibrational level of the ion and the cross section is large 

at zero energy decreasing inversely with the increasing energy. 

Experiments are described which provide for a measurement of the AI 

cross section by detection of either the emitted electron energy 

spectrum or of the vibrationally excited product ion. The generation Of 

H(2s) and H(38) atoms for AI experiments is described. 

Since the neutral excited states of HeH lying beneath the ground 

state of HeH" all have the attractive ion core, there are no excited 

repulsive states which can lead to DR of the ion ground state. The 

paper by Michels describes the calculation of dissociative routes which 

1 

. 
- can potentially lead to DR of excited states of HeH'. The lowest ion 

excited state is only weakly bound and the calculated series of quartet 

states do not appear to offer favorable routes for DR. An additional 

doublet series is difficult to calculate since it can autoionize to the 

ion ground state. A second quartet Rydberg series which can provide DR 

routes for three higher excited states of the ion but which can also 

autoionize to a lower ion state is also discussed. 

* 

.I 

c 

11. Experiment 

The merged beam technique is described in the paper of Mitchell and 

Youssif. Recent measurements of the total DR cross sections for H;, 

H$, HeH', and Ni and of the branching ratio for H$ recombination are 

discussed. A new channel leading to H; has been identified in the 

latter measurement. HeH' has been measured to have a nonnegligible 

recombination cross section, although the state of excitation of the 

ions used in the experiment has yet to be determined. Deep resonant 

structures have been observed in the cross sections of HS, HeH' and 

N; . 

Adams and Smith have brought the Flowing Afterglow Langmuir Probe 

(FALP) technique to the forefront of recombination research in recent , 

years. An important advantage of this technique is the fact that ion 

formation and decay occur in different regions of the flow apparatus 

and so the ions have time to relax internally before their 

recombination rate is studied. Measurements of H; recombination with 

this technique have shown that the rate coefficient for de-excited ions 

is less than 10-8cm3/sec. This has been confirmed by recent merged beam 

experiments. (See Mitchell and Yousif, this volume). Subsequent studies 

have found that measured values for He',HeH+ and H; rate coefficients 

are indistinguishable. In a plasma, collisional radiative recombination 

(CRR) must be considered. In the FALP method where electron densities 

of 1010Cm'3 are encountered, CRR can proceed with a rate coefficient of 

about 10-9cm3/sec, thus setting a lower limit to the measurable 

dissociative recombination rate coefficient. CRR may also have 
contributed to recently measured high values of H$ recombination 

published by Amano.'3] The FALP technique has been extended to the 

determination of recombination rate coefficients for a wide variety Of 

protonated species and efforts are underway to introduce UV absorption 

spectroscopy and laser induced fluorescence techniques to measure 

branching ratios for DR. 

Earlier experiments performed using the microwave afterglow 

technique have been re-examined by Johnsen. It has been found that (a) 

the presence of molecular additives in a plasma leads to a lowering of 

the mean electron temperature, and (b) heat conduction in a plasma is 

insufficient to produce a uniform electron energy distribution over the 

whole volume. The consequence of these findings is that some of the 

earlier values for measured recombination rate coefficients must be 

treated with suspicion. This is particularly true for cluster ions. A 

reassessment of previous Ni studies is given in the light of recent 

research on the vibrational deactivation of diatomic ions. Although it 

is concluded that previous studies applied to vibrationally excited 

ions, skepticism is expressed concerning the new merged beam results 

discussed by Mitchell and Yousif. Mention of new studies concerning 

electron-ion recombination at elevated gas densities and of recent 

ion-ion recombination work is also given. 

following the DR of NS, 05, CO;, and H20' in a flowing afterglow, as a 

function of the initial vibrational excitation of the parent ions, have 

been performed by Rowe and Queffelec. The H20' results support the 

conclusions of HerbstIs statistical analysis of branching ratios rather 

than Bates' theory based on bond breaking. 

Spectroscopic measurements of the product state branching ratios , 

Translational spectroscopy in which measurement of the kinetic 

energies of dissociation products allows a determination of their 

excitation state is a powerful tool which could be used for DR 

branching ratio measurements, The paper by van der Zande, Koot, Los, 

and Peterson provides an example of this elegant technique. A study of 

the energy spectra of the products of 0; + Cs dissociative electron 

capture is presented. The high resolution inherent in the technique 

allows the Rydberg states into which the electron is captured to be 

. 
-. identified . . , A proposed experiment to demonstrate laser stimulated radiative 

. 

b recombination of electrons and protons is described by Morgan and 

Mitchell. The experiment will employ the Merged Beam Apparatus at the 

University of Western Ontario and will employ field ionization 

detection of the highly excited recombination products. The technique 

also has applications to the measurements of DR branching ratios and 

dielectronic recombination cross sections. 

Recent theoretical and experimental studies by Lundeen on H2 Rydberg 

states with high angular momenta have shown that the energies of these 

states may be accurately calculated using models employing long range 

interactions only. This is in contrast to the case for low 1 states 

where short range interactions dominate and MQDT theories are necessary 

for energy calculations. Furthermore, long range interaction theories 

predict short autoionization lifetimes (lO'gsec) for the high 1 states. 

Short range interaction theories, on the other hand, predict lifetimes 

of the order of tens of seconds. This implies that long range 

interactions play a crucial role in the dynamics of high 1 Rydberg 

states. 

The paper by Graham addresses the subject of electron and ion 

temperatures in plasma discharges. A knowledge of these is important in 

order to determine the conditions under which DR acts as a major ion 

loss mechanism. Generally it is overshadowed by ion diffusion to the 

walls. DR, however, does play a major role in the production of excited 

atoms and so a knowledge of product branching ratios is important for 

the interpretation of plasma spectra which provide diagnostic 

information concerning the state of the discharge. DR also competes 

with dissociative attachment for low energy ions and so must be 

included in models of negative ion sources. 

It is generally accepted that the primary formation mechanism for Hions in a pure hydrogen discharge is the dissociative attachment Of 

electrons to vibrationally excited H2 molecules. The source of this 

vibrational excitation is only partially understood. Hiskes and Karo 

have examined the role of wall collisions involving H; and H$ in 

producing vibrationally excited hydrogen molecules. A description of 
the processes involved in the neutralization of these molecules at 

surfaces is given and the authors find that collisions of vibrationally 

excited Hi and H$ produce copious numbers of H2(v11) molecules. Indeed, 

this mechanism appears to be the dominant source of H2(v10 at low 

plasma densities. 

Bahns and Stwalley provide a review of antimatter cluster ion 

formation principles. The impetus for this work is to produce 

antihydrogen in a condensed form for easy transportation and storage. 

The concept of the pseudowall, a cold, trapped, high density plasma 

within which many collision processes can occur leading to cluster ion 

buildup, is discussed. Experimental manifestations of the pseudowall 

are proposed. 

Spectroscopy is an important tool in plasma diagnoses since it is 

generally non-perturbative, Interpretation, however, requires a good 

knowledge of the atomic processes leading to photon emission. 

Shoemaker, Canguly, and Carscadden describe how a study of the Stark 

broadening of spectral lines from highly excited Rydberg states within 

the plasma can provide information on local electric fields. A 

description of the application of this technique is given. 

' 

111. Applications 

DR can yield translationally hot products which may have energies 

that exceed those needed for planetary escape. The role of DR in the 

escape of N isotopes from Mars is discussed in the paper by Fox. Among 

several processes that contribute to planetary escape, DR of N': is the 

major process at high and average solar activities and is the most 

important process contributing to the isotope enhancement ratio. The 

isotope enhancement role of DR disappears for v>O. DR of 0; is an 

important process in planetary atmospheres, where it generates O( 'SI 

and O('D), the upper states of the green and red lines, respectively. 

Fox discusses a detailed model of these emissions as a function Of 

altitude in the nightside ionosphere of Venus. The model results for 

the green line emission are consistent with the measurements made by 
- the Venera space probe. 

I Yee, Abreu, and Colwell discuss the modelling of the O(lS) and O(lD) 

t 

b 

- emissions which result from DR of 0; in the Earth's ionosphere. For the 

vibrational distribution of the ion they use five models developed by 

Fox. For the specific rate coefficients yielding lD and lS atoms, they 

use the values calculated by Guberman. In order to calculate yields for 

a distribution of vibrational levels, one must have a specific rate 

coefficient and a total rate coefficient for each level. Since total 

rate coefficients have not been measured or calculated for v>O, they 

use the laboratory v=O coefficient for higher v. The adequacy of this 

assumption must await the results of future calculations or 

experiments. Their theoretical model shows that the 'D (IS) quantum 

yield decreases slightly (increases strongly) with vibrational 

excitation. A calculation of the quantum yields using the measured 

volume emission rates from the Atmosphere Explorer E satellite 

indicates that at high vibrational excitation, the calculated 'S 

quantum yields are higher than the authors' theoretical model results 

but the lD results are in good agreement with the theoretical model. 

The products of the DR of polyatomic molecules are important 

components of the chemistry of dense interstellar clouds. Herbst 

discusses three methods which have been used to determine these yields 

and comparative examples are given for H30+, HCNH', and C4H2'. The 

abundances of neutral complex molecules and of small molecules such as 

OH are sensitive to the model that is used. It is known that the ratio 

of singly deuterated species to their hydrogenic analogues is often 

higher than the deuterium to hydrogen ratio in the dense clouds. It is 

possible that the product branching ratios for DR reactions may account 

for this, but a definitive statement must await the independent 

determination of the DR branching ratios. 

The role of DR in diffuse interstellar clouds is discussed by Black 

and van Dishoeck who point out that the concentrations of neutral 

species can be intimately affected by the products of DR reactions. 

They stress the need to determine the quantum yields of products 

resulting from DR of CHS, C$i, C3H3, and H30'. In diffuse clouds, 

where the fractional ionization is high, the DR rate coefficient for H$ 
significantly affects the column density of H$, but in dense molecular 

clouds the column density is less sensitive to the DR rate coefficient. 

For HeH', the predicted model concentration is greater than the 

recently observed upper limit, indicating that an important sink is 

missing from the models. 

Several approaches for determining the small ionization fraction in 

dense interstellar clouds based on deuterium fractionation are 

discussed by Turner. Reliable values of the DR rate coefficients of H3 

and CH3 are needed for these models. The chemistry of cyanopolyynes is 

discussed and several possibilities are presented to account for the 

difference between the observed and model values for the ion to neutral 

concentration ratios. A model of the DR of H3C@ is presented. Turner 

argues that the model supports the prediction of Bates for the likely 

quantum yields of the DR products. 
IV. References 

1. M. A. Biondi and S. C. Brown, Phys. Rev. 3, 1700 (1949); M. A. 

Biondi and S. C. Brown, Phys. Rev. 76, 1697 (1949). 

9 

la+ 

DW - 

2. R. B. Holt, J. M. Richardson, B. Howland and B. T. McClure, Phys. 

Rev. 77, 239 (1950). 

3. D. R. Bates and H. S. W. Massey, Proc. Roy. SOC. - A187, 261 (1947). 

4. D. R. Bates, Phys. Rev. - 78, 492 (1950). 

5. J. N. Bardsley, J. Phys. B - 1, 349 (1968). 

6. J. N. Bardsley, J. Phys. B 1, 365 (1968). 

7. C. M. Lee, Phys. Rev. - A16, 109 (1977). 

8. A. Ciusti, J. Phys. B 13, 3867 (1980). 

9. T. F. O'Malley, J. Phys. B - 14, 1229 (1981). 

10. A. P. Hickman, J. Phys. B 20, 2091 (1987). 

11. S. L. Guberman, Can. J. Phys. - 64, 1621 (1986). 

12. J. B. A. Mitchell and J. W. McCowan, Astrophys. J. - 222, L77 (1978). 

13. T. Amano, Ap. J. - 329, L121, (1988).