ion recombination in dense gaseous Xe

ELSEVIER

International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 451-467

Electron/ion Masatoshi

Ukai”>‘,

recombination

andIonProcesses

in dense gaseous Xe*

Takahiro Odaka”, Hitoshi Yamadaa, Keiko Isodaa, Kyoji Shinsakab, Noriyuki Kouchi”, Yoshihiko Hatanoa>*

“Department of Chemistry, Tokyo Institute of Technology, Meguro-Ku, Tokyo 152. Japan bDepartment of Electronics, Kanazawa Institute of Technology, Nonoichi-machi, Ishikawa 921. Japan

Received 16 June 1995; accepted 27 June 1995

Abstract The electron mobility pL, and the electron/ion recombination rate constant k, in dense gaseous xenon at 0.9, 1.6, and 5.0 x 102’ atom cmp3, near the critical density of 5.1 x 102’ atom cmm3 at 292 K, have been measured as a function of an external electric field using a pulse-radiolysis d.c.-conductivity method. Although the values of pe are much smaller than those for previous measurements in CH4, Ar, and Kr, k, has been found to be well below the diffusion-controlled recombination rate constant indicated by the reduced Debye equation. By comparison with theories, possible reaction-control stages involving the relaxation processes of excess energy, which emerges upon recombination of ion clusters with electrons via resonant capture, and their dependence on gaseous media are discussed. Keywords:

Electron/ion

recombination;

Xenon

1. Introduction

Electron/ion recombination in dense molecular media is an important charge annihilation process in both fundamental and applied chemical physics [l-3]. Previously this was explained by a diffusion-controlled process, where measured rate constants, k,, were in good agreement with those, kD, given by the reduced Debye equation [l-4] using an * Dedicated to Professor David Smith FRS on the occasion of his 60th birthday. * Corresponding author. ’Present address: Department of Applied Physics, Tokyo University of Agriculture and Technology, Naka-cho, Koganei-shi, Tokyo 184, Japan.

electron mobility pe: kD = ‘he/Le/c

(1) where e is the electron charge and E the dielectric constant of the medium. Recently, however, we have shown that the Debye (or Langevin-Bates) theory for k, breaks down in high pe media such as high pressure gaseous CH4, Ar, and Kr near the critical points or the liquids [5-81. The ratio of observed rate constants to those calculated using the Debye equation, k,/kD, was shown to be much smaller than unity for high pe media. The deviation from the diffusioncontrolled reaction clearly represents the aspect of microscopic transport phenomena

0168-I 176/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-l 176(95)04276-8

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based on an electron/ion collision process, i.e. the probability of electrons escaping from recombination or attractive coulombic forces due to an ion is enhanced by the extended mean free path which is proportional to pL,. Also the extended mean free path, or more exactly the reduced electron-collision frequencies, can easily “heat” electrons above thermal energy in the electric field, invalidating the assumption of thermal electron transport. The recognition of this departure in those previous results for the diffusion-controlled reaction has also led to various theoretical studies [9-181, such as the theory of a partially diffusion-controlled reaction, Monte Carlo simulations of the Fokker-Planck behavior of electrons [9,10], molecular dynamics (MD) simulations [ 11,121, the transition state theory of the steady state recombination rate constant [ 131,fractal analysis of electron “random walk” trajectories [14-171, and a semiempirical theory that takes into account both the diffusioncontrolled recombination rate and the energyexchange-controlled recombinaion rate [ 181. The effect of an external electric field on recombination rate constants has also been investigated theoretically [ 19,201. However, the agreement between experiments and theories is not consistent. Also the atomic or molecular properties of the media have rarely been taken into account in the above theories. With respect to the microscopic recombination behavior, the intermediate neutral state initially formed by the encounter of an electron and an ion possesses a certain amount of excess internal electronic energy. The internal relaxation of the excess energy, which is in competition with re-emission of the electron, determines the fractional recombination rate constant k, among the initial encounter rate given by electron diffusion. The macroscopic deviation of k, from the diffusion-controlled reaction further gives information on microscopic aspects of kr/kD depending both on the external electric field strength and the density of the

media), such as the electron-thermalization process, the relaxation process of the excess energy in an initially formed intermediate state, and the character of ions in dense media [l]. It is thus of great importance to investigate the process systematically, with respect to both the character of the gas media and the strength of the external electric field, to reveal the dynamic behavior of electrons both macroscopically and microscopically. In the present paper, we present an experimental study of ,LL~ and k, in dense Xe as a function of both the external electric field and the gas density. Although pe is much smaller than the values for CH4, Ar, and Kr, k, is found to be well below the Debye rate constant. We place emphasis on the relaxation process of the excess energy which emerges upon recombination and controls the behavior of k,.

2. Experiment 2. I. Apparatus

and procedure

The measurements of pe and k, are made for purified xenon gas in a high pressure cell using a pulse-radiolysis, d.c.-conductivity technique [4-8,211. Careful control of the temperature and densities of xenon was important in the present investigation, as was described in previous papers [5-81. For the purification of xenon gas, a grease-free gas-sampling system was employed after evacuation to 1O-6 Torr. Commercially obtained xenon gas (stated purity >99.9%) was passed through an oxygen absorber and molecular sieve 5A, bubbled through a liquid Na-K alloy, and the transferred to a conductivity cell equipped with parallel plate electrodes. The cell was made of stainless steel and resistant to pressures up to 140 atm. The pressure of the xenon gas sealed in the cell was monitored by a capacitance-type pressure

M. Ukai et al./International Journal of Mass Spectrometry and Ion Processes 1491150 (1995) 451-467

transducer. The temperature of the gas was kept at 292 f 1 K, which was monitored by a thermocouple near the inner electrode in the cell. Since the critical temperature of xenon is 289.73 K, the precision limit of the control does not create a significant error in the measurements. The densities of the xenon gas (0.9, 1.6, and 5.0 x lo*’ atom cme3) at the measured pressure and temperature were obtained by referring to the table by Vargaftic [22], which allowed the evaluation of the dielectric constant using the ClausiusMossotti equation. The field strength was altered by the application of a negative high voltage through an 8 kHz low pass filter to one of the rectangular parallel electrodes with a gap of 3.95 mm and an area of 19 x 40 mm*. To generate excess electrons in the xenon gas, pulsed X-rays were employed; these were emitted from a tungsten foil of 0.1 mm thickness by irradiation with a nanosecond electron beam pulse of maximum energy 0.6 MeV from a Febetron 706 [4-8,211. The pulsed X-ray dose was controlled by the transmission of the X-rays through lead plates of known thickness. This irradiation procedure induced a transient electron current which, after being transmitted through a 30 or 10 MHz noise filter, was amplified and recorded by a 1 GHz storage oscilloscope. The measurements were made with pulsed X-rays of low (approx. 5 x 10” eV 7-l) and high doses (approx. 5 x lo’* eVg- ). For measurements at high doses the magnitude of the transient electron current was sufficiently great that amplification was not required. 2.2. Analysis The decay curve of the transient signal was analyzed as previously described in detail [4-8,211 but briefly is as follows. For measurements with low X-ray doses, the probability of an encounter between electrons and ions was negligible so that the

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transient electron current I(t) was well fitted with a first-order decay equation: I(t) = lo(l - p$t/d)

exp(-k,,t)

(2)

where IO is the peak current, E the applied electric field strength, d the distance between the parallel electrodes, and k,, the first-order decay rate constant for the electrons. In the case of high X-ray doses, because the probability of encounters and recombination between electrons and ions was significantly increased, the transient current obeyed the following equation: IQ> = lo[(l - ~eUtld)l(l x exp(-W)

+ no&>1 (3)

where no is the initial number density of excess electrons. The electron/ion recombination rate constant k, was obtained by fitting the transient signal to Eq. (3) using the ,LL~and kt, obtained by Eq. (2) at a low dose. The error limits in the values of pe and k, were 10% and 15% respectively.

3. Results 3.1. Electron mobility

The electron mobilities, pL, obtained at the densities of n = 0.9, 1.6, and 5.0 x lo*’ cmP3 are shown in Fig. 1 as a function of the applied density-normalized electric field strength E/n. Almost the same dependence of pe on E/n is apparent for the results at n = 0.9 and 1.6 x lo*’ atom cmh3. Typically, at n = 1.6 x lo*’ atom cmP3 nearly constant values of pe M 15 cm* V-’ sei are obtained in the region of E/n < 10 mTd. In the region of E/n > 10 mTd, the value of pe increases with increasing E/n but with further increase in E/n, pL, decreases, which results in a peak in ~_l~ M 80 cm* V-’ s-l at around E/n = 70 mTd. This strong variation of pe indicates the

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E/n (mTd) Fig. 1.Electron mobility pClein gaseous Xe at 0.9 x 102’ atom cm-3 (O), 1.6 x 102’ atom cmm3 (O), and 5.0 x 102’ atom cmm3 (0) as a function of the density-normalized external electric field strength E/n (mTd).

heating of the excess electrons in which the electron energy gained by the external field is not compensated for by the collisional energy loss. Although it is difficult to estimate the effect of heating in the region of electron energy near thermal energy, the value of E/n = 10 mTd where pe starts to increase may be a measure of the limit of the thermal equilibrium of the mean electron energy, which is referred to as the critical field strength in the following description. The difference in the absolute values of pe in Fig. 1 for different n is explained by the variation of the collision frequencies with n, which is seen by the almost overlapping curves of the densitynormalized mobilities npe in Fig. 2 at IZ= 0.9 and 1.6 x 1021 atom cmP3. The present results of np, are very similar to the results at n = 0.06 and 0.29 x 102’ atom cme3 by Huang and Freeman (see Fig. 4 in Ref. [23]). The maximum pe value at n = 0.9 and 1.6x 1021 atom cmP3 may be ascribed to the Ramsauer-Townsend minimum of the momentum transfer cross-sections of electrons in liquid and dense rare gases [24], although further investigations on this kind

Fig. 2. Density-normalized electron mobility npe in gaseous Xe at 0.9 x 102’ atom cmm3 (O), 1.6 x 1021 atom cmm3 (O), and 5.0 x 102’ atom cmm3 (0) as a function of E/n.

of maximum are still needed, as described below. Although the result for pe at n = 5.0 x 1021 atom cm -3 is limited to the region 30 < E/n < 100 mTd, somewhat different features are obtained from those at II = 0.9 and 1.6 x 102’atom cmP3. The value of pe increases slightly in the region 30 < E/n < 45 mTd and decreases with increasing E/n for E/n > 45 mTd, which results in a peak maximum of pe = 50 cm2 VW1s-l around E/n = 45 mTd. However, Fig. 2 shows that the value of np, in the whole region of E/n as well as at the maximum value is much greater than those at n = 0.9 and 1.6 x 102’ atom cmm3. This is due to the inapplicable normalization or scaling simply with respect to the electron collision frequencies with isolated atoms. Otherwise, the different result for pe at it = 5.0x 1021 atom cmW3 implies a different electron transport process due to the structural change in the gas medium slightly below the critical density of it, = 5.1 x 1021 atom cmP3 namely in a supercritical condition. Accordmg to the table by Vergaftic [22], the compressibility is much greater in this region of y1 than in the region of n < 2 x 1021 atom cme3 due to the van der

M. Ukai et al./Iniernational Journal of Mass Spectrometry and Ion Processes 1491150 (1995) 451-467

E/n(mTd) Fig. 3. Electron/ion recombination rate constant k, in gaseous Xe at 0.9 x lo*’ atom cme3 (O), 1.6 x lo*’ atom cmm3 (a), and 5.0 x lo*’ atom cmd3 (0) as a function of E/n.

Fig. 4. k,/kD in gaseous Xe at 0.9 x 102’ atom crnm3 (O), 1.6 x lo*’ atom cmm3 (O), and 5.0 x 102’ atom cme3 (0) as a function of E/n.

Waals non-ideality of the gas. This is the result of a strong attractive interaction between xenon atoms, which enhances the formation of van der Waals clusters. Thus it is difficult to explain the peak of pe only by the Ramsauer-Townsend minimum in the momentum transfer cross-section of the isolated xenon atom [25,26]. We conclude that pe at n = 5.0 x 1021 atom crnw3 is not the result of electron collisions with isolated xenon atoms, as are those at n = 0.9 or 1.6 x 1021atom cme3, but involves a large contribution from collisions with large van der Waals clusters. Also much greater values of npe suggest more highly mobile electrons enhanced by a different transport mechanism.

n = 0.9 x 102i atom cmP3 further increases, whereas k, at 1.6 and 5.0 x 102t atom cme3 decreases with increasing E/n. The increase of k, at lower E/n is ascribed to the enhanced diffusion process corresponding to the increased pe. Fig. 4 shows the ratio of k, to the theoretical value of electron/ion recombination rate constant obtained by the Debye equation (Eq. (1)) as a function of E/n. It should be remarked that the values of k,/kD for Xe gas below unity clearly indicate the breakdown of the Debye theory based on the diffusion-controlled reaction. This is obviously different from the previous conclusion that the values of k, in dense media for ale < 100 cm’ V-’ S-’ are generally explained well by the diffusioncontrolled reaction [ 1,3].

3.2. Electron/ion recombination rate constants Fig. 3 shows the electron/ion recombination rate constant k, as a function of the applied electric field strength E/n obtained in the present study. The value of k, increases with increasing E/n and then decreases. In the region E/n < 30 mTd almost the same values of k, are obtained at both n = 0.9 and 1.6 x 102’ atom cmP3. The value of k, at

4. Discussion The breakdown of the Debye theory for diffusion-controlled electron/ion recombination observed in k, indicates possible reaction-control stage(s) existing in the whole recombination processes. It is necessary to

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hf. Ukai et al./International

Journal of Mass Spectrometry

and Ion Processes 1491150 (1995) 451-467

Table 1 Comparison of experimental values of k,/kD in high density xenona, argonb, kryptonC and methaned media with theoretical valuese-i Element

T (W

nj (IO” cmm3)

Ek

A’

rem

A

(nm)

(nm)

(cm2 V-’ s-l)

k,lkI, (ew)

k,lkD (theory)

TC

Sf

LQg

Mh

W’

GClS Xe

291

1.6

1.09

1.1

52.6

1Y

0.25a

1.0

1.0

0.93

0.93

Xe

293

0.9

1.05

1.8

54.4

25a

0.20a

0.97

0.99

0.89

0.89

Ar

296

2.4

1.06

61.6

53.3

860b

O.Olb

0.06

0.09

0.19

0.19

Kr

291

1.2

1.04

4.9

55.3

70”

o.05c

0.87

0.94

0.75

0.75

CH4

285

1.2

1.04

18.3

56.4

260d

0.19d

0.47

0.54

0.45

0.45

21

1.49

19.0

128

490b

O.llb

0.72

0.85

0.65

0.65

4.8 x 1O-4 (150) 3.8 x 1O-4 (130) 5.7 X 10-5 (52) 3.4 x 10-4 (120) 4.0 X 10-s (398)

Liquid

Ar

87

Kr

200

10.8

1.39

21.0

60.2

357c

0.61’

0.46

0.51

0.44

0.44

CH4

123

15

1.60

19.4

84.9

420d

0.60d

0.63

0.70

0.54

0.54

0.083 (251) 2.9 x 1O-4 (70) 0.81 (3750)

a Present work; b Ref. [8]; ’ Ref. [6]; d Ref. [S]; e Tachiya [9]; ’Sceats [13]; g Lopez-Quintela et al. [14]; h Mozumder [16]; ’Warman [18]. The values in parentheses below k,/kD are Ets (in V cm-‘) (see Ref. [18]). ’The values of n are obtained from Ref. [22]. Ir Calculated using the Clausius-Mossotti equation. ’Mean free paths are obtained using the Lorentz equation A = (3/2e)(rmkBT/Z)“‘p,. * Onsager lengths are obtained by the relation rc = k2/ekB T.

examine how the diffusion-controlled recombination process indicates the zero escape probability of an electron encountering an ion. Thus the breakdown, or k,/kp < I, observed in the previous experiments for high pu, media such as CH4, Ar, and Kr, at high pressures near the critical points or in liquids [ l-8,2 l] has stimulated various theoretical studies [g-20]. In this section we discuss the trends observed in k, in the present experiment. In Section 4.1 we compare the experimental results at E/n M 0 mTd with the theoretical values because, in principle, the Debye equation is only applicable to a recombination process in the absence of an external electric field. In Section 4.2 we discuss microscopic properties of ions in dense

gases. Finally in Section 4.3 we discuss another key point involved in electron/ion recombination. 4. I. Comparison

with theories

Table 1 shows the list of experimental results of kr/kD at E/n M 0 mTd in comparison with the theoretical values for Xe, Ar, Kr, and CH4. A systematic comparison between experiments and theories for Ar, Kr, and CH4 was given in our previous papers [1,8]. Tachiya [9, lo] discussed the inapplicability of the Debye equation based on the Smoluchowski equation in the case of a weak interaction between the electrons and the media and suggested the importance of the Fokker-Planck equation. Instead of solving

M. Ukai et al./International Journal of Mass Spectrometry and Ion Processes 149/150 (1995) 451-467

the Fokker-Planck equation he calculated k,/ko as a function of A/Y~ by a Monte Carlo simulation. In the present comparison we employ the Onsager length rc as a measure of a reaction radius. Sceats [13] extended Tachiya’s treatment and derived a theoretical formula for the steady state recombination rate constant by taking into account a transition state theory for an electron/ion pair. As shown in Table 1, however, systematic agreement is not obtained for the present k,/kp results for Xe nor for those for Ar and Kr in the gas phase. Good agreement is obtained only for liquid CH4 and Kr. Lopez-Quintela et al. [ 14,151. considered the influence of the differential fractal dimension of the electron random-walk trajectories on the rate of diffusion-controlled bulk recombination. Mozunder [ 16,171 further considered the influence on the escape probability, mean recombination time, and homogeneous recombination rate. Almost the same values of k,/kn were obtained by Lopez-Quintela et al. and by Mozumder. Their results are in relatively good agreement with the previous experimental results for liquid Kr and CH4 but these are again much greater than the present results. Warman [ 181 presented a semiempirical theoretical formula for the recombination rate constant by taking into account the diffusion-controlled recombination rate constant and the energy-exchange-controlled recombination rate constant. To evaluate the efficiency of electron energy loss he introduced the critical field strength El0 where the electron drift velocity deviates by 10% from the value expected for the thermal electron mobility. Although the agreement with the experimental results is good both for liquid Ar and CH4, the theoretical values in the gas phase are much smaller than the experimental values. It would be difficult to define El0 for gas media with a Ramsauer-Townsend minimum, which implies underestimation of El0

457

due to the marked reduction in the momentum transfer cross-section at the minimum, in comparison with the case where the strong variation of the momentum transfer crosssection is absent [27]. To conclude this comparison, appropriate theoretical evaluation of k,/ko of the dense gases measured in the present or previous experiment has not been obtained. Good agreement is only obtained with our early result for liquid CH4. Poorer agreement is obtained for gaseous CH4, liquid Ar and liquid Kr. Concerning this, we notice that by the application of these theories, the experimental value of k,/ko in gaseous CH4 is greater than that for Kr whereas this tendency is generally reversed in the theoretical values, except for the results by Warman [ 181.Because these theories, based mainly on the diffusion process of charged species, were motivated by our early result on CH4, it is not surprising that these theories can also give good or comparable agreement with the results for these media. It is possible that the inapplicability of these theories to dense rare gas media lies in the different surroundings of the ions. 4.2. Encounter of an electron with an ion and its escape, in dense gaseous Xe

To aid further consideration of the actual theoretical aspects, we summarize the macroscopic recombination in dense gaseous media by the following cycle of microscopic stages: + e-+ M+ t

M*

(Sl)

M’ + M”‘, M, + M2 M* + c- . . . M+ !_ e- . . . Mf

+

M+e-

(=A) (SW

(S3)

These microscopic stages are as follows: (Sl) electron capture to form an intermediate neutral state by the encounter with an ion;

M. Ukai et al./International

458

Journal of Mass Spectrometry

(S2) relaxation of a certain amount of excess electronic energy present as internal energy in the intermediate neutral state due to the competing processes of internal energy relaxation into the different nuclear-configurational states well below the ionization threshold of M, forming, for example, a ro-vibrationally excited state or a dissociation pair (S2A), or re-emission of an electron (S2B); (S3) escape or release of re-emitted electrons from the ionic coulombic potential. This cycle can be understood as the random walk of an electron in the vicinity of an ion. For ease of understanding we present in the following a schematic formula of a recombination cycle through the above stages. The mean distance of each random walk, i.e. the mean free path A, which is a measure of the escape from the coulombic potential, can be compared with the Onsager length rC = e2/ckBT. An electron approaching an ion via diffusion is captured by the ion in stage (Sl) with a crosssection CJ, or simply scattered with cross-section gs. The intermediate neutral state formed in the electron capture by the ion decays via internal relaxation with a rate of rtR in stage (S2A) or via re-emission of an electron with a rate of YEMin stage (S2B). The probability of internal relaxation per collision, PIR, can be represented by the product of the ratio of the cross-sections, a,/a,, and the ratio of rlR to the total decay rate YEM+ YIR as PIR

YIR DC = as YEM + hR

and the probability P EM

UC =

% rEM

(4)

of re-emission

as

rEM (5) + rIR

For the case of a low value of R/rc, electrons unable to escape from the coulombic potential are recaptured (Sl). The competition between recapture (Sl) and escape (S3) of an electron is expressed by the ratio of the rate of electron to that of other scattering capture, YCAP,

and Ion Processes

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processes, rs, so that ture, FRC is given by

the fraction

of recap-

rCAP FRC

= rCAP

+ rS

where rc/h gives the number of collisions required for transmission through the effective length of the interacting coulombic potential if represented by the coulombic interaction. The continuation of the stages as iterative cycles results in the macroscopic recombination rate constant defined by k,, where k,/kD is given by k

-L=_

0,

‘b

US

rIR rEM

+ rIR

x (1 +f

+f2 +f3..

rEM

.f =

FRC rEM

+ rIR

.)

(7) (8)

Only if an insignificant escape probability is given by a negligibly small A/rc value, do the iterative cycles finally yield zero escape probability of the electron after an encounter with an ion, irrespective of the electron capture cross-section for stage (Sl) or the competing rates between internal relaxation and re-emission for stage (S3). In this case, k, obeys a macroscopic diffusion-controlled reaction rate constant or k,/kD = 1 as observed for nonpolar media with pL, < 150cm2V-‘s-’ in Fig. 3 of Ref. [l]. By contrast, k,/kD < 1 for greater pu, is understood as the natural behavior of escape where A/rc is large enough to break the cycle at stage (S3). It appears that the previous theories summarized in Section 4.1 considered mainly the

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probabilities of encountering and the escape of electrons under the control of A defined by pL, but did not consider the relaxation probability, especially the relaxation of the internal energy possessed by the intermediate neutral species which could lead to recombination by the internally rearranged species energetically incapable of re-emission of electrons (S2A). We will comment in later sections on the internal relaxation process. However, even the rates of encounter and escape do not appear to be correctly described in the theories when applied to the recombination processes in gas-phase media. The theories treat ions as “free” positive charges surrounded by a homogeneous dielectric medium. At the Xe densities of n = 0.9 and 1.6 x 102’atom cmP3 in the present experiment, the macroscopic electron transport is under the control of collisions with isolated neutral atoms in the gas phase, which is confirmed by referring to the table by Vergaftic [22] and evidenced by the present measurement of nap. It is clear, however, that there is no reason to consider the homogeneous density of the dense rare gas media, because isolated monoatomic ions are unlikely. Instead they form ion clusters having molecular potential surfaces. Judging from termolecular ion/molecular reaction rate constants [28] and thermochemical constants [29,30], ions produced in the present condition are immediately stabilized as large clusters, which induces a strong density fluctuation only in the vicinity of the ion core. Although it is difficult to estimate the actual distribution of cluster sizes using limited thermochemical constants obtained only for smaller clusters [29,30], the mean size of ion clusters, m, can certainly be assumed to exceed 1000 for Xe. Fig. 4 further presents the dependence of k,/ko on the Xe density, suggesting that relaxation of the internal excitation energy possessed by the intermediate neutral states is easy. This is explained by the structural difference between

459

the ions. Because the mean value of m increases with increasing Xe density below the critical point, the ease of the internal relaxation is affected by the mean size of the ion clusters. The iterative cycle in the dense Xe gas is as follows: e- + Xe+(Xe,)

+ [Xe(Xe,)]*

(Sl’)

Xe(Xe,)]* + [Xe(Xe,)]*‘, Xe* + (Xe,) . . . (S2A’) (S2B’)

[Xe(Xe,)]* + e- . +. Xe+(Xe,) ._.._ e- . . . Xe+(Xe,) --t Xe+(Xe,) + e-

(S3’) The density fluctuation or inhomogeneity in liquid Xe is not restricted to the vicinity of ion cores but is more dispersed in the media where neutral atoms are also under a much stronger van der Waals interaction than in the gas phase. In this sense good or comparable agreement of the theories with experimental results as discussed in Section 4.1 is not surprising. In the gas phase, however, the fluctuation can enhance the difference between microscopic electron transport near the ion core and the macroscopic transport dominated by electron collisions with neutral atoms. The Onsager length Y, becomes reduced due to the increased density around the ion core by about 30%. The mean free path A of electrons should also be altered near the ion core. It is natural that the rates of reduction or alteration of these quantities are not identical. By the simple increase of density, a much greater decrease of A results in a further increase in the predicted k,/ko in the above theories, which causes further disagreement with the experimental results. However, if the clusters are regarded as micro solid particles and if the behavior of pu, in the previous measurements of CH4 and Ar in the gas and solid phases [571 is considered, pu, near the ion core can be greater than that in the gas by one order of

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magnitude. This can reduce the discrepancy between the theories and the experiments [31]. It should further be noted that density fluctuation imports a strange property to rc, i.e. yc is much greater than the size of the clusters. Because yc is defined in a homogeneous dielectric medium, the yc in the dense gas or the 30% reduced TC corresponds to the size m > 10’ microparticles. As far as we know, such large clusters of Xe have not been observed. Also at a distance of yc from the ion core the polarization force is not enough to bind atoms against thermal energy collisions with the surrounding atoms, inducing evaporation of outer sphere atoms. On the other hand, outside the outermost sphere of a cluster, gas-phase electron collisions are allowed by the significantly decreased Xe density. It is necessary to consider the effective distance for the evaluation of the coulombic interaction. As described in Section 4.1, electron transport at n = 5.0 x 1021 atom cmP3 is more similar to that in the liquid phase. 4.3. Internal relaxation of recombined-

intermediate superexcited states The theories summarized in Section 4.1 treat the recombination as an encounter between positive (ion core) and negative (free-moving electron) charges where both charges do not have internal electronic structures. This is a bold assumption to describe recombination in the gas media. These theories considered that electrons in the coulombic potential can escape or can be re-emitted by obtaining thermal energy from the media. In this context the Onsager length has an important meaning in recombination. As described in Section 4.2, however, electron transport in the present condition at least at IZ= 0.9 and 1.6 x 1021 atom cmP3 should not be treated as electrons in dielectric media but as electrons colliding with atoms and molecules in the gas phase. In the latter treatment, many neutral excited

states should exist in the vicinity of the ionization level [32]. An electron with the same energy as such an excited state is captured by the ion core to form a recombined intermediate state, which is understood as resonant electron capture into a superexcited state [32]. This is a natural assumption because, during the traverse time of a thermal electron (about 1 fs) passing over a molecular dimension, only l/ 100 of a collision occurs between the ion and neutral under the present density conditions. Also it is an unlikely nonadiabatic energy exchange, a termolecular reaction in which a free moving electron directly loses as much kinetic energy as when being captured in an electronically bound state. The stepwise energy degradation of electrons due to multiple collisions in the clusters is inefficient in forming bound levels of captured electrons. The small amount of energy loss in momentum transfer collisions requires about 10’ collisions to reduce the initial thermal energy of an electron, which is unlikely judging from the mean free path and the above-mentioned cluster size. Energy loss due to (ro)vibrational excitation of a cluster is possible but seems to be insufficient to explain the magnitude of the energy relaxation, owing to the small vibrational spacings and small inelastic crosssections for a nonpolar target. It is only possible to enhance the inelastic scattering cross-section via the resonant effect due to the strong polarization force from the ion core, which is otherwise described as resonant electron capture. Thus, without resonant states which have a certain cross-section for electron capture and a certain lifetime for internal relaxation, electrons can easily transmit through the neighbourhood of ions. Sceats [ 131 treated the relaxation rate of electrons in the transition state between an electron and an ion. We note the necessity of further consideration of the formation and relaxation of the transition state, as well as the character of such a transition state. The nature of the

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transition state [ 131 is close to a shape resonance with a temporarily trapped electron in the centrifugal barrier due to the electron angular momentum [33]. However, the transition state ought to be quantized as a kind of Rydberg state instead of a simple continuum state. This model also considers only electron re-emission due to the exchange of thermal energy with the media. Failure to consider the internal relaxation process in this model as well as in other theories [9-12,14-181 appears to result in a considerable overestimation of k,/kD in dense gaseous media. Possible internal relaxation processes for excess electronic energies are internal conversion into different isomeric structures, into vibrationally excited states, and neutral predissociation. They are dominated by nonadiabatic transitions. If a closely located repulsive state is available, direct dissociation is also possible. Rather floppy structures of ion clusters [34] can give large probabilities of internal conversion. With respect to energy stabilization, however, isomerization, vibrational excitation, or predissociation emitting a neutral atom from outer spheres of a cluster, i.e. evaporation, only reduces the amount of internal energies by about kB T. On the other hand, the media investigated which showed a diffusion-controlled reaction (k,/k, = 1) consisted of organic molecules such as n-C5Hi2, neo-CsHiz, n-C6Hi4, cycle-CgHi2, and Si(CH3)4 [l-3, 211. The ground state ions formed by the elimination of an electron from the highest bonding orbital of hydrocarbons [35,36] have a repulsive potential surface. This reduces the Franck-Condon factor for the transition between a bound intermediate (or superexcited) state and an electronically free state, which restricts the production probability of recombined intermediate states and also the rates of re-emission. In the case of these organic media, the mean free path of a re-emitted electron is much smaller than rc due to the small pe, which allows zero escape

461

probability from the coulombic potential of the ion or FRc = 1 in Eq. (6), yielding enhanced probabilities of recombination. With respect only to the electronic structure of molecular ion cores, the competition between relaxation stages (S2) in the case of CH4 is similar to those for other organic molecules. However, the extended mean free path of electrons, being comparable with the Onsager length, allows higher escape probabilities. However, in further comparison with high density rare gases, the recombined intermediate states undergo much faster dissociation. As shown by the photoionization quantum yields of isolated molecules [32], the dissociation probabilities of these superexcited states are as high as unity around the ionization threshold. We consider, due to the fast relaxation of a large amount of excess internal energy by the bond dissociation of the molecular ion core, that reasonable agreement was obtained for CH4 with theories which disregard molecular properties. It should also be noted that in the case of recombination in molecular media, a large amount of energy is released by the dissociation of superexcited states. Upon degradation of the released energy, recombination of fragment radicals in the media is unlikely. On the other hand, emission of a rare gas atom through various internal relaxation processes such as evaporation and internal conversion (predissociation) releases much less energy, which can be gained by the thermal collisions to make it possible to reproduce the parent intermediate state of a neutral cluster and to re-emit an autoionizing electron. Together with the limited pathways to emit nonionizing fragment atoms and restricted efficiencies of excited-atom migration into vacuum, the probabilities that electron/ion recombination will occur in dense rare gas media is very low. Consideration of the potential energies for superexcited states and other possible excited

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and Ion Processes 149/150 (1995) 451-467

V(r)= -e2/ & r - Xe+(2Pij2) 20

Y 1

r (Angstroem)

V(r) = -e2/ E r + Xe+(2P3/2) Xe* 6s

_

V(r)

=

-e2/r

/ Xe

5p6

Spheres Fig. 5. Coulombic potential between an electron and an ion in the vicinity of the ion core. In potential curve in the vacuum is employed, whereas at a distance of an electron from the ion the the outer spheres of a cluster and reduced by the dielectric constant. Because of the high density core in a cluster, the dielectric constant is evaluated at the maximum value of n = 9 x 102’ atom

the vicinity of the ion coulombic interaction of neutral atoms in the cmm3 indicated in the

core a coulombic is well shielded by vicinity of the ion table by Vergaftic

P21.

states is of great help in describing the intermediate neutral states and their internal relaxation pathways. Hiraoka and Mori [29,30] showed that rare gas ion clusters with sizes larger than m = 3 are composed of an m = 3 cluster ion core with a localized charge and outer surrounding spheres of neutral rare gas atoms. Although potential surfaces for large ion clusters are not available, they are representatively considered in the following by the potential curves of Xe,f and the potential surfaces of Xet. Ab initio calculations show only one bound potential surface of Arr which correlates with Ar+(2P3,2) [34,37]. As far as we know there is no potential surface showing

Xe;. However, the similar electronic properties and similar potential structures of Xe and Ar allow us to assume naturally that a cluster ion in dense gas is in one of the ro-vibrational levels on the potential surface involving the ground state Xe+(‘Psj2). The relative energies of the potential surfaces involving Xe+, Rydberg atom, or lower excited atom are the following. The ionization potential (IP) for emission of an electron into vacuum in condensed (solid) Xe was observed at 9.8 eV [38-401. An ion produced in the present experiment immediately forms a large cluster, which reduces the total electronic energy by the stabilization due to the polarization inter-

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463

1

condensed Xe IP 1

Xe+Xe+(2P3,2)I

; I2t:A11 [W3/2)11 [W3/2)12 Xe+Xe*

Internuclear Distance (A) Fig. 6. Potential energy curves for the interaction of Xe+ and Xe’ with an Xe of dimer ions are employed from Refs. [42] and [43] for the estimation of both ionic potentials are lowered by the difference between ionization potentials number of Rydberg states exist below the ionic potential curves converging

action. By contrast, Woermer et al. [41] have shown that the 6s lowest exciton band does not shift significantly. This means that the van der Waals interaction does not have a strong influence on the electronic levels of neutral clusters involving the ground state atom or the 6s excited atom, for which the electron clouds are located at a distance smaller than atomic distances. Fig. 5 shows the coulombic potential between an electron and an ion in dense Xe gas. According to the above, and using the information on gas phase Xe2 [42,43], Fig. 6 shows the potential energy curve for the Xe

atom in a cluster. Relative energies for the potential curves ionic and excited neutral curves. The dissociation limits of in the condensed and gas phases (see text). Note that a to these ionic states.

dimer which naturally represents the relative location of the potential surfaces of Xez correlated with Xe+(‘P3ir) and Xe+(*P1i2) and those for Xe; involving an Xe [6s] atom in large clusters. Reimann et al. [44] presented a similar dimer potential curve in condensed Ar. One can suppose that the candidates for the intermediate neutral states formed by the adiabatic capture of a nearly thermalized electron, are the Rydberg states involving Xe** converging onto Xef(2P,,2), i.e. Xe** (2PI,2n& those converging onto Xe+(2P3,2), i.e. Xe**(2P3,2nl), and lowest electronically excited states involving

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Xe**Xe,

Resonant electron capture

7

Internal conversion

Electron penetration

Xen

Xe*Xe,

e* Q

Fig. 7. Schematic

representation

of the encounter

of an electron

an Xe*[Gs] atom. A large number of Xe**(“Pr12nT) Rydberg states were observed in the gas phase as superexcited states in the region of the spin-orbit interval of 1.3 eV between Xe+(2P3,2) and Xe+(‘Pt,z) [45]. According to Fig. 6, however, the repulsive states of superexcited clusters involving Xe**(2P1,2nl) formed in the adiabatic electron capture by the ion cluster involving the lowest electronic state of Xe+(2P3,2), readily dissociate to produce an Xe*(2Pt,2nl) autoionizing atom. Re-emission of an electron from the autoionizing atom means a further continuation of the iterative recombination cycles. The Xe**(*P3j2nZ) Rydberg states appear to be the more likely candidate. The potential surfaces of these Rydberg states are located below the ionic surface. However, as described above, the bound potential surface of Xe: correlates with Xef(2P3,2). This forms

with an ion cluster and successive

relaxations

(see text).

the vibrationally excited Xes*, located above the Xe$ surface, by the resonant capture of a free electron assisted by a nonadiabatic transition. The resonant electron capture is followed by internal relaxation or predissociation into repulsive states which leads to a nonautoionizing Xe*[6s(3/2)] atom (see the schematic diagram in Fig. 7): Xez + e- +

Xeg (Ryd) -+ [Xe;]

---t Xe*[6s(3/2)] + Xe,_ I This process involves two-step nonadiabatic processes which only give a small probability of recombination, whereas the excitation onto the same potential curve involving Xe*[6s(3/2)] followed by direct dissociation must be a more probable process (see also Fig. 7): Xez + e- + [Xe;] + Xe* + Xe,_ 1

M. Ukai et al./International Journal of Mass Spectrometry and Ion Processes 1491150 (1995) 451-467

This corresponds to the direct dissociation on the adiabatic potential surface of the recombined intermediate state involving Xe*[6s(3/2)] [46]. In both of the above cases an electron is transferred into the lowest excited state, in which the electron approaching an ion should penetrate the surrounding layers of neutral Xe atoms. This reduces the probability of re-emission. In both cases the penetration of Xe*[6s] through the outer cluster spheres is necessary to emit Xe* into the vacuum. However, the probability of penetration of Xe* via atomic migration is restricted by the expanded atomic dimension. Also the probability via exciton migration or excitation transfer is restricted by the nonequivalent energy levels of Xe* depending on the layer of spheres, which is unlike the condensed rare gases [47]. In most of the above theories [9-l 1,1317], the Onsager length rc was the measure of the reaction radius for recombination. However, it is a natural question whether or not rc obtained by a simple coulombic relation can be any measure of the reaction radius, which is also related to the abovementioned comment on the physical meaning of YC, Otherwise the reaction radius should be, quite phenomenologically, given by the efficiencies of each stage of the recombination cycle depending on the molecular properties. Although we tentatively employ yc in the present paper for the evaluation of the theoretical values, further consideration of the reaction radius and of the interaction distance between an electron and an ion is necessary.

5. Summary In the present paper, we have reported the results of an experimental study of pe and k, in dense gaseous xenon as a function of both the external electric field and the gas density.

465

Although the value of pu, is much smaller than those for CH4, Ar, and Kr, k, has been found to be well below the Debye rate constant. By comparison with theories and by proposing an iterative recombination cycle, possible reaction-control stages involving the relaxation processes of excess energy, which emerges upon recombination of ion clusters with electrons via resonant capture, and their dependence on gaseous media have been discussed. We have pointed out that the molecular dependence on the macroscopic recombination rate constant is the result of the competition between internal relaxation and the re-emission of an electron from (or autoionization of) the recombined intermediate superexcited states. On the basis of these viewpoints, we have discussed the molecular properties for rare gas media and molecular media.

References [1] Y. Hatano, in L.G. Christophorou, E. Blenberger and W.F. Schmidt (Eds.), Linking the Gaseous and Condensed Phases of Matter, Plenum, New York, 1994, p. 467. [2] K. Shinsaka and Y. Hatano, in J.W. Gallagher, D.F. Hudson, E.E. Kunhardt and R.J. Van Brunt (Eds.) Nonequilibrium Effects in Ion and Electron Transport, Plenum, New York, 1990, p. 275. [3] K. Shinsaka and Y. Hatano, Nucl. Instrum. Methods A, 327 (1993) 7. [4] T. Tezuka, H. Namba, Y. Nakamura, M. Chiba, K. Shinsaka and Y. Hatano, Radiat. Phys. Chem., 21 (1983) 197. [5] Y. Nakamura, K. Shinsaka and Y. Hatano, J. Chem. Phys., 78 (1983) 5820. [6] K. Shinsaka, M. Codama, Y. Nakamura, K. Serizawa and Y. Hatano, Radiat. Phys. Chem., 34 (1989) 519. [7] K. Shinsaka, M. Codama, T. Srithanratana, M. Yamamoto and Y. Hatano, J. Chem. Phys., 88 (1988) 7529. [8] K. Honda, K. Endou, H. Yamada, K. Shinsaka, M. Ukai, N. Kouchi and Y. Hatano, J. Chem. Phys., 97 (1992) 2386. [9] M. Tachiya, J. Chem. Phys., 87 (1987) 4108. [lo] M. Tachiya, J. Chem. Phys., 89 (1988) 6929. [11] W.L. Morgan, Phys. Rev. A, 30 (1984) 979. [12] W.L. Morgan, J. Chem. Phys., 84 (1986) 2298. [13] M. Sceats, J. Chem. Phys., 90 (1989) 2666. [14] M.A. Lopez-Quintela, M.C. Bujam-Ntifiez and J.P. PerezMoure, J. Chem. Phys., 88 (1988) 7478.

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[15] M.A. Lopez-Quintela, J.P. Perez-Moure and M.C. BujanNifiez, Chem. Phys. Lett., 138 (1987) 476. [16] A. Mozumder, J. Chem. Phys., 92 (1990) 1015. [17] A. Mozumder, Radiat. Phys. Chem., 37 (1991) 395. [18] J.M. Warman, J. Phys. Chem., 87 (1983) 4353. [19] M. Tachiya, J. Chem. Phys., 87 (1987) 4622. [20] K. Isoda, N. Kouchi, Y. Hatano and M. Tachiya, J. Chem. Phys., 100 (1994) 5874. [21] K. Shinsaka, Y. Nakamura, K. Endou, K. Honda, H. Yamada, K. Isoda, M. Ukai, N. Kouchi and Y. Hatano, Nucl. Instrum. Methods A, 327 (1993) 15. [22] N.B. Vergaftic, Tables on the Thermophysical Properties of Liquids and Gases, 2nd edn., Wiley, New York, 1975. [23] S.-S. Huang and G.R. Freeman, J. Chem. Phys., 68 (1978) 1355. [24] L.G. Christophorou and D.L. McCorkle, Can. J. Chem., 55 (1977) 1876. [25] M. Hayashi, IPPJ-AM-19, Institute of Plasma Physics, Nagoya University, 198 1. [26] Y. Sakai, in L.G. Christophorou, E. Illenberger and W.F. Schmidt (Eds.), Linking the Gaseous and Condensed Phases of Matter, Plenum, New York, 1994, p. 303. [27] We calculate k,/ko by employing the field strength where the momentum transfer cross-section shows a value, after passing through the Ramsauser-Townsend minimum [25], identical to the cross-section below the critical field strength, instead of using El0 from the context of Warman’s formula [18]. The calculated values are k,/ko = 0.57, 0.32, 3.2 x 10m4, and 0.15 for gaseous Xe (n = 1.6 x 102’ atom cmm3), Xe (n = 0.9 x 102’ atom cm-3), Ar, and Kr, respectively, in the order presented in Table 1. Although this may reduce mathematical reasons for En, in his theory, the values of k,/kD are significantly increased. It is interesting that the systematic alternation of k,/kD is strongly influenced by the magnitude of the momentum transfer cross-sections, in spite of the diminished collision frequency term in k,/kD in Warman’s formula (Eq. (11) in Ref. [18]). [28] Y. Ikezoe, S. Matsuoka, M. Takebe and A. Viggiano, Gas Phase Ion-Molecule Reaction Rate Constants Through 1986, Maruzen, Tokyo, 1987. [29] K. Hiraoka and T. Mori, J. Chem. Phys., 92 (1990) 4408. [30] K. Hiraoka and T. Mori, J. Chem. Phys., 90 (1989) 7143. [3 l] When considering a homogeneous solid Xe at 291 K, where A is tenfold greater and rc is reduced by 30% compared with those in the dense gas, the theoretical values of k,/ko derived by Tachiya [9], Sceats [13], Lopez-Quintela et al. [14], and Mozumder [16] are increased to 0.52, 0.60, 0.49, and 0.49, respectively (see Fig. 4 of Ref [9], Fig. 4 of Ref. [13], Eq. (7) of Ref. [14], and Eq. (18) of Ref. [16]). Another estimation of A using pL, by Huang and Freeman in the liquid phase [23] does not give a significant increase in k,/kD. It is, of course, difficult to employ these values for the estimation of k,/kD in the dense Xe gas, which does introduce errors from macroscopic electron transport dominated by collisions between electrons and neutral

[32] [33]

[34] [35]

[36] [37] [38] [39]

[40]

[41] [42] [43] [44]

[45]

[46]

and Ion Processes 149jl.50 (1995) 451-467 atoms. Also it is necessary to consider the electron transport at the surface with the fluctuating density. Y. Hatano, in K. Kuchitsu (Ed.), Dynamics of Excited Molecules, Elsevier, Amsterdam, 1994, p. 151. J.L. Dehmer, D. Dill and A.C. Parr, in S.P. McGlynn, G.L. Findley and R.H. Huebner (Eds.), Photophysics and Photochemistry in the Vaccum Ultraviolet, Reidel, Dordrecht, 1982, p. 341. T. Ikegami, T. Kondow and S. Iwata, J. Chem. Phys., 98 (1993) 3038. K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Iwata, Handbook of He1 Photoelectron Spectra of Fundamental Organic Molecules, Japan Scientific Society Press, Tokyo, 1981. M.B. Robin, Higher Excited States of Polyatomic Molecules, Vols. 1 and 3, Academic, New York, 1974, 1985. T. Nagata, J. Hirokawa, T. Ikegami, T. Kondow and S. Iwata, Chem. Phys. Lett., 171 (1990) 433. H.W. Biester, M.J. Besnard, G. Dujardin, L. Hellner and E.E. Koch, Phys. Rev. Lett., 59 (1987) 1277. W.F. Schmidt, in C. Ferradini and J.-P. Jay-Gerin (Eds.), Excess Electrons in Dielectric Media, CRC Press, Boca Raton, FL, 1991, p. 127. By subtracting the “Fe value” (the depth energy at the bottom of the conduction-band from the vacuum level) of 0.5 (solid, Ref. [38]) or 0.67 eV (liquid, Ref. [39]) from the IP in solid Xe, the 5p band gap energy in condensed Xe is given, it is almost the same as the IP in liquid Xe. This means stabilization due to the polarization interaction is almost the same irrespective of the phase of the Xe media. J. Woermer, V. Guzielski, J. Stapelfeldt and T. Moeller, Chem. Phys. Lett., 159 (1989) 321. W.R. Wadt, J. Chem. Phys., 68 (1978) 402. W.C. Ermler, Y.S. Lee, K.S. Pitzer and N.W. Winter, J. Chem. Phys., 69 (1978) 976. CT. Reimann, W.L. Brown, N.J. Norwakowski, S.T. Cui and R.E. Johnson, in G. Betz and P. Varga (Eds.), Desorption Induced by Electronic Transitions DIET IV, Springer, Berlin, 1990, p. 226. See for example, J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy, Academic Press, New York, 1979. The macroscopic behavior of k,/kD dependent on the external electric field strength E/n, implies other aspects of recombination, such as the electron-thermalization process and the electron capture process by the ion into the intermediate neutral states. The increase of k, at lower E/n is explained by the increased encounter probabilities of electrons with ions with an extended mean free path [19,20]. The decrease of k, at E/n greater than the critical electric field strength or E/n > 40 mTd is due to the “heating” of electrons in which the electron energies gained by the applied field are not compensated for by the energy loss process or the relaxation process. However, the remaining maximum in k,/kD at each Xe density at a certain E/n indicates the ease of recombination due to the cross-section energy of electron capture, Do, at the recombination balanced between the applied field and momentum

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Journal of Mass Spectrometry

transfer collisions. It is possible that oc reflects the FranckCondon overlap between the potential surfaces of the ground ionic state and repulsive Xek. In the region of E/n > 40 mTd, a strong dependence of k, jk, on Xe densities is not observed which can also be attributed to an inefficient energy loss and a small probability of resonant

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1491150 (1995) 451-467

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electron capture into the intermediate neutral states at the recombination energy. [47] See, for example I. Arakawa and M. Sakurai, in G. Betz and P. Varga (Eds.), Desorption Induced by Electronic Transitions DIET IV, Springer, Berlin, 1990, p, 246.