Integral cross sections for free electron production in atom-atom collisions

Chemical Physics Q North-Holland

41 (1979) 245-255 Publishing Company

INTEGRAL CROSS SECTIONS IN ATOM-ATOM COLLISIONS

Received

crossing

12 February

FOR

FREE

ELECTRON

PRODUCTION

1979

model.

It will be shown that our eaperirnental results are fully interpretable in terms of this model. Experimental information on the subject is availabte, but not in a form to allow a conclusive comparison with the theory. Collisional detachement, A- + 3 + A + e + B. has been the subject of a number of experiments in the last years. This process also involves a discrete to continuum transition. Due to the absence of Rydberg states below the conrinuum limit, however, it requires a different theoreticul approach [2]. Electron energy spectra have been measured for a number of atom-atom and ion-atom systems (see, e.g.. ref. [3]). The interest has been concentrated upon the marked structures, which are observed in some of these spectra. and which indicate an indirect ionization mechanism (i.e. production of intermediate autoianizin_r states). The Demkov-Komarov model describes il direct mechanism. The electron energy spectrum in this case is predicted to be a smooth (exponential) function, peaked at zero electron energy. Such spectra seem to be diflicult to distinguish from experimental background and have therefore not yet been accurately measured. Measurements of the total charse production cross section in atom-atom collisions have been reported for some systems [4]_ It has turned out [S, 6-j that charges are often produced in quite different mttss combinations. for instance in the present case:

1. Introduction Inelastic processes in collisions between 3toms or ions have been explained with much success by a small number of basic models. Most of them assume a localized transition repion, that is a small region of interatomic distances. in which the inelastic rransition is supposed to take place. Welt-known models of this type are that of two crossing potential curves with radial (Landau-Zener mode:) or rotational coupling or the Demkov model of charge exchange. They ail refer to transitions between discrete scntes of the diatomic system in question and are applicable to processes like atomic excitation. ion pair formation, and others. A different type of process, which is nor covered by such well-established mod&s, is that of free electron formation in collisions ofgroand state atoms.

AtB+A’+e+B. It involves a transition from a discrete state of the diatomic system A + B to a continuum state. and therefore requires a dimerent type of model description_ Such a model has been proposed by Demkov and Komarov [I]_ They ascribe free electron formation to an intersection between a discrete potential curve of the quasimolecule AB and a continuum limit, and they derive an exphctt formula for the probability of a transition to the continuum. 245

H+M-,H’+e+M, 4H

+e+M’,

4 H-

-I- M+,

which have comparable magnitudes of the cross sections. As long as these channels are not measured separately, a conclusive comparison with theory is not possible. In the present experiment, integral cross sections for diffzent processes like the ones listed, are indeed separated. They are measured as a function of the collision energy. In all cases, the experiments are not only performed with normal hydrogen (H) atoms, but aiso with deuterium (D) atoms. When it is assumed that the diatomic system has only one discretexontinuum crossins point, the theory yields a simple prediction not only for the energy dependence of the integral ionization cross section, but also for its variation under isotope substitution. This assumption can be reasonably made only for one of

YAG

the two possible free electron channels, namely for that one, which has its apparent threshold at the lower collision energy. For these channels, the agreement between experimental resuits and the theoretical predictions turns out to be very good in all cases.

2. Experimental

The neutral hydrogen beam is generated by laser photodetachment from a H- or D- beam. An intensity of 10” atoms/s through 10 mm’ can be obtained, the typical energy spread is 1 eV. The particle energy is variable between 10 eV and 1 keV. The principle of the experimental setup is shown in fig. 1. Negative ions are formed in a hot cathode discharge, accelerated to 500 eV. mass selected by a Wien filter, focused by means of electrostatic

laser

head

scattering

volume

beam monitor

!~n deflection

secondary beam sourw

electrostatic lens

Fig. 1. Principle of the experimental setup. The nestive ion beam is focused by the first lens upon the exit diaphragm of the Wien filter and approximately to the scattering center by the second lens. The detection system is shown in greater detail in lig. 2.

247 einzellenses, and decelerated to the desired energy_ Before entering the scattering region, the beam passes through the cavity of a 1.06 jcrn YAG laser. where up to 80% of the ions are neutralized. The detached electrons are collected on a plate. The combination of electric and magnetic lields. which is applied to the neutralization region for this purpose, is strong enough to guarantee the collection of all electrons, the deflection of the ions before neutralization, however, is still negligible. This electron signal

is used as the measure of neutral beam intensity. To avoid systematic errors in the cross section determinations, one has to make sure that all neutrals produced get into the scattering volume. Control of the beam dimensions is therefore obtained by means of diaphragms, which are placed in the ion beam before it enters the laser cavity, and by the focusing properties of the ion optics. Because the beam profile is energy dependent. it is measured behind the scattering volume. The CuBe secondary electron multiplier used BSa monitor. gives ;i signal down to about 15 eV hydrogen atom energy. To account for the presence of B --background beam” of energetic neutrals formed by collisional detachment with residual gas atoms, the laser beam is chopped, and forward-backward counting techniques are applied to all signals.

The hydrogen atom beam is crossed by a secondary beam effusing from a multichannel array. From the dimensions of the array and the working pressure, it can be concluded [7] that the secondary beam extends only a few millimeters along the primary beam axis, and that its density is constant across the primary beam for at least 10 mm. As even at the lowest energies used the primary beam is conlined in a region 6 mm wide, the integral cross section for any process is proportional to the number of processes occurring in the scattering volume per unit time, divided by the primary beam flux, i.e. the current of detached electrons. Charged collision products are created in pairs. Simultaneous mass determination of both products is obtained by a delayed coincidence time-of-flight technique (fig. 2). Charged partictes are accelerated by ;Lhomogeneous electric Lield (3-5 kV/lS mm) to both sides of the scattering

Icm

Fig. 2. Delayed coincidence time-of-flight mass spectrometer. The shaded arex in the center represents the secondary beam source 20 mm below the scattering center. The secondary beam in the scattering volume is not much wider. The multipliers I and II are of the vcnetian blind type and have 24 mm x 14 mm sensitive surfaces.

volume. according to the sign of their charge. After further acceleration up to 5 keV and total travelling distances of 40 mm, they pliers on either side. The coincidences between the is rgistered as a function

hit the cathodes of multinumber of delayed pulses from both detectors of the delay time. As the

Fig. 3. Delay time spectrum for H + Kr at 100 eV collision energy. Thu area under the peaks is divided by the primary beam intensity to give the integral various channels.

cross sections

for the

W Aberlg et d/Free

248

electrot! prodrcctiotl irl MOW-ufom colksions

time delay between two pulses equals the difference of times of flight of the two products, it depends on both product masses. Therefore, different mass combinations will, in general, appear at different delay times. allowing to meakure their intensities separately. Fig. 3 shows a typical delay time spectrum. It is seen that the resolution is amply suliicient to separate all channels. The main advantage of the present method over a separate determination of positive and negative particle intensities is that the intensities of all channels ure obtained directly, without the need to compute difference signals. Further, whenever there is more tl!an one possible positive product ion and more than two negtive ones (or vice versa) a separate measurement of all charged channel intensities is not possible by any other than a coincidence method. The most dificult problem with the coincidence apparatus is to make sure that all ions and electrons produced are detected - or at least a fraction indcpendcnt of the collision energy. The problems arise mainly with H t and H- ions. They are produced with a kinetic energy only slightly less than that of the incident neutral hydrogen atom. For the GtSe of forward scattering. for instance, the initial ion velocity is directed perpendicular to the axis of the detector. tind can be overcome only by a

suficiently

large extraction voltage. For free elec-

trons and for the heavy ions, there are no such Even for the most unfavourable cases, D + Ar -. Ar * + D-. Ar’ + D + e with backward scaltering of the deuterium product. the Ar ion energy is only 20% of that of the incident atom. Electrons from atomic collisions are known to have problems.

energies below 50 eV, in general [3].

The voltages applied

and the geometry of the up to 100 eV kinetic energy and originating in the scattering volume follow trajectories which end on the cathodes of the multipliers. As a preventive measure, the scattering center is shifted backward with respect to the detection axis by 4 mm, in order to make sure &at any systematic deviation from this expected behaviour does not affect the dominant [S] forward scattered part of the hydrogen ions. The ratio be&en the number of particles detected by one of the multipliers and the number system are such that all particles

of particles produced in the scattering volume is the transmission factor for the particle in question. The actual transmission hctors have at Ieast three possible components: non-unity transmission of grids, non-unity detection probability at the multipliers, and discrimination due to too high an initial energy. Whereas the lirst two components are not dependent on the collision energy, the third one certainly is. Reliable determinations of the energy dependence of cross sections are therefore only possible in the absence of the third component. Two types of experimental tests have been performed to obtain information on the transmission behaviour: (1) saturation of counting rates was tested by varying the three acceleration voltages independently for a number of representative channels at high collision energy (100 eV for channels containing a hydrogen ion, 500 eV for the other ones). Saturation was always obtained at or below the voltages expected. (2) When there is only one channel and no background signal. transmission factors for both products can be determined experimentally. Let N be the rate of production of pairs of charges and (ii and q_ the transmission factors. The counting rate of negative particles is then rl_iV, that of positive particles q,N. When the particle loss mechanisms on the two sides are statistically independent, the coincidence rate is q+q_N. Measurement of the three counting rates q_ N, q+N, and q+q-N yields the two transmission factors. The method can be extended to cases with

more than one channel, but it becomes rather complicated. We applied it therefore only to the process H + Ne + Hi

+ e + Ne at 70 to 120 eV There is no competing channel observed in this energy range. The measured results for the transmission factors of protons and electrons are shown in fig. 4. They are reasonably constant. When the values are corrected for the transparency of the grids. one obtains numbers which should represent the detection probabilities for tlie multipliers. The WdheS found are 0.18 for protons and 0.33 for electrons. Literature values for H + [9-l I] are a factor two to three larger. Since our multipliers are in general rather Lr from an optimum state, we regard this as a good agreement. The low value for the electrons is caused by the high energy of impact upon the multiplier cathode [12]. We conclude that collision energy.

0.0

!

,

L

50

1

I

100ev kinetic

energy

-

Fig. 4. Transmission t%aors of thr two arms of the detection system for protons and for electrons. The values arc obtained by dividing, for the process H f Ne + H’ + e + Ne. the coincidence counting rate by the single arm counting rates. The transmission factors do not depend on the energy of the incident H atom.

reliable determinations of the energy dependence of crosssections are possible up to 100 eV collision energy for channels containing B hydrogen ion. and up to at least 500 eV for the other channels.

Chum& from an H atom to a D atom beam requires a change of the gas in the discharge chamber. a new setting of the Wien lilter, and minor readjustments of electric voltages. The whole procedure is performed in such a short time (< 30 min) that the secondary beam intensity can be held constant without problems. The primary beam intensity is reliably determined for both types-of beams. Therefore for channels of the type H,D+M-tH,D+M++e, the H and the D cross sections obtained as a ratio of coincidence counting rates and beam intensities are in the same units and need no correction. For channels of the type H,D+M-+H’.D’+e+M, one has to take into account that the detection probabilities of H _ and D’ ions might be different. We used the ratio q(H+)/q(D’)

= 1.27.

This is an experimental result for the ratio of secondary electron yields [I I], obtained for the same type of cathode material, CuBe, as used by us. under similarly undefined surktce conditions as in our case. and at un ion energy of 5.1 keV. The secondary electron yield is not identical to the detection probability needed here. As the values are known to be small [9? lo], they can be expected to be close to each other. The value 1.27 is reasonably intermediate between two limits, that of pure energy dependence of the detection probabilities and that of linear dependence upon the velocity [9], corrcsponding to the values 1.0 and 1.4. As the difference between H and D nuclei is of a very simple nature. the value used might be expected to be in better agreement in different experiments than is usual with such numbers. Tentativeig, we ascribe an error of 10 ‘;;, to this number.

Absolute values of the cross sections are not obtained with our method, because the secondary beam density is unknown. There exist however for all H + M (noble gas) collisions reliable determinations of the absolute values of the total charge production cross sections [4], i.e. the sums of the cross sections of all channels measured by us. They are used to derive absolute scales for the present results. In our experiment the detection probabiiities for the various channels of one reaction are different. Therefore, our result for the total charge production cross section is given by a weighted sum of individual cross sections: the weighting factors are inversely proportional to the detection probabilities. We obtain the necessary information upon the detection probabilities by comparison with one more experiment. Van Zyl et al. [s] measured the absolute values of individual cross sections for H + Ar. Their results are shown in fig. 5. Our results can be made fo agree with these only when the foliowing ratios of detection probabilities are used to correct the measured relative magnitudes: q(H+)/cl(Ar’)

= 1.10,

q(e)/rl(H-)

= 0.41.

Our accordingly corrected results are included in fig,. 5 and show excellent agreement. We assume in

a factor of two. The curves G,JE) from our experiment and the directly determined ones agree ;is hr as the energy ranges overlap.

We present in this paper the results for the integral cross sections of the reactions H.D+M-+H+,D’+e -t H, D

+ M-

t M

(type I),

ie

(type?),

with M the noble gas atoms Ne, Ar, Kr, Xe. For the fast three, we observe in addition the ion pair chonncf H-, D- + M’. The results will be presented and discussed in a subsequent paper. Ion pair cross sections with H atoms have been reported

in ref. [IS].

20

50

100

kinetic

energy

eV

500

*

.

Fig. 5 Charsed channel cross sections for H + Ar. The solid lines show the results of ret [5]; they arc in absolute units. The symbols are our results. They are originally in arbitrary units, and have been multiplied by adjustement Factors to agree as well as possible with the former ones. The factors are.diffcrent for the three different channels. They allow a conclusion on the detection probabilities for the vaious charged particles in our experiment.

addition bility

that

us Ar’,

q(Kr’)/q(Ar’)

KrT

has the same

and

D-

= 1.00,

detection

has the same q(D-)/q(H-)

proba-

one as H-, = 1.00.

The four quantities are suflicient to determine an absolute scale for alf reactions observed. Their values ure not unreasonable when compared with literature values [3-l l]. Again like in section 2.2, a small value for the electron detection probability is found. Unfortunately, Van ZyI and coworkers regard their absolute scale for the ion pair channel (H + Ar + H- + Ari) as not fully reliable. This makes our value q(e)/fl(H-) = 0.41 questionable and may result in an error in our absolute SC&S of up to

The results are shown in fig. 6. The cross sections are shown as a function of the hydrogen or deuterium atom velocity in a double logarithmic plot. Open circles are D results, filled ones refer to H atoms. A second abscissa scale gives the H atom energy in eV. The D atom energy for the Snme velocity is twice as large. Therefore, a plot of the cross sections as a function of atom energy is obtained by shifting the D results to the right by an amount, which is indicated by the arrow in fig. 6b. D cross sections are larger than H cross sections, when compared at the same velocity. When compared at the Fame energy, they are smaller. The error bars represent two standard deviations of the statistical uncertainty of the number of coincidence counts and of the current of photodetached electrons. Further uncertainties, concerning the relative and absolute magnitude of the cross sections, have been discussed in the foregoing section. We would like to stress the point that the relative magnitudes of the H and D cross sections are fully reliable for reactions of type 2 and contain a sys.Jematic error of probably not more than 10% for type 1. For Kr and Ar, we observe both types, I and 2, of free electron producing reactions. For Ne only type 1 and for Xe only type 2 is observed. When comparing with theory, it is more convenient to group the channeIs according to their energetic order. Out of the two channels of one reaction, that

50

H.t& -

100

---cK-e

10%112

100 e”

L

-

-

100

ev

500

50

(H-otomsl 100 e”

50

H.Kr-H’.e J’ _

r

10~*cmz

- 10%n* ä

100 50

-

100

ev

50D

H.Xe -Xe’.e

x c

530

4

L

H.Ar- Ar-.e

5.0

H-Ar -W.e

kinetic energy 50

ev

H.Kr-Kr;e

Fig. 6. (a) Velocity dependence of the integral cross sections ol the first free electron channels observed in collisions of H atoms (filled circles) and D atoms (open

circles) with noble gas atoms. The solid lines are the theoretical results obtained by integration over the impact parameter of Demkov and Komarov’s formula. The values of three free parameters (cross section scaling factor, velocity scaling factor. and a curve form parameter) are needed to select one pair of H and D cross section curves from the serveral theoretical isUIt of fig.8. (b) Cross sections for the second free electron channels. In collisions with Ne and with Xc, no second channel is observed. For Kr, B reasonable fit with a pair of theoretical curves is

possible, the deviation in the D cross section at low energy is, however. beyond the range of experimental uncertainty. For Ar, no reasonable tit is possible. The energy scale at the top is valid only for the H results. To use it for the D experimental points, these have to be moved to the right as indicated by the arrow.

one which has its apparent threshold at the lower collision energy is called the “first” and the other one is called the “second channel. The first channels are collected in lig. 6a, the second ones in fig. 6b. It should be noted that the observed order of the channels is closely related to the sequence of ionization potentials of the particles, IP(Ne) > IP(Ar) > IP(Kr) > IP(H) z=-IP(Xe). For Ne, no Ne’ is observed; for Ar, Ar’ formation is observed,

but at much higher energy

than H +, Di formation; for Kr, the Kri channel begins at only slightly larger energy than the hydrogen ion channel; with Xe finally, the order is reversed: Xe+ appears ttt low energy, but Hi is not observed below 100 eV. This means that for all collisions the first channel (i.e. the one with the lower apparent threshold) is that one which has the lower actual threshold.

252

W. Aberle et aLlFree electron prodmiotr

3. Theory

ia utotn-utottl

collisions

potentials and finally pdSSeSinto and continuum states are labeled by the quantity E, the vertical distance to the continuum limit. For the Rydberg states, E -Z 0 is the binding energy of the electron to the molecular ion, for the continuum, E > 0 is the kinetic energy of the free electron. The transitions from the initial state to the upper part of the Rydberg series (say for E > E,,) and to the continuum SvdteS are treated in a unified manner. Regard a collision with definite impact parameter_ and assume that the system has probability p,, to stay in the initial state beyond the crossing with the Rydberg state Q,. According to Demkov and series of Rydberg

the continuum. Rydberg

3.1. The Den&or-Komaroo

model

According to Demkov and Komarov [I], the process of free electron formation in a collision between atoms can be ascribed to an intersection between a discrete State potential curve and a continuum limit. For a collision between neutrals, the model unavoidably involves the complication that the continuum is preceded by an infinite series of Rydbers states. The corresponding potential curves are more or less parallel to the continuum limit and crowd towards it. They all have to be crossed by the one particular curve. The situation is illustrated in fig. 7. One potential curve crosses a

Komarov,

beyond

the probability

the crossing

p, = pCOexp [-(t:

to stay in the initial state

with state E is then

- I:~)(X./i&)].

(1)

Here, L = const. is a characteristic width of the crossing region, and u, is the velocity of radial approach orthe two nuclei at the crossing, u, = F(1 -

VJE -

b’/r:)‘;‘,

(2)

with t’ the relative velocity at infinite distance, E the kinetic energy, 6 the impact parameter, and V, and r, the potential energy and internuclear separation at which the crossing is located. From eq. (I), the probability for the system to pass the continuum limit, is found to be PO = p.,, exp [-2L~e,[/k+].

(3)

At not too larse velocity, and provided that L 4 rcr it cdn be assumed that p,, is identical to the ionization probability. Under these conditions, the probability for the system to decay into a continuum state after having passed the limit is close to unity, and the probability of recapture from a continuum State to the discrete

‘c

internuclear

distance

-

Fig. 7. Intersection of a discrete molecular potenrial curve with a continuum limit and the preceding Rydberg series. r, and V, measure the position of the crossing region. The energy scale has its zero at the level of the initial state at infinite internuclear distance.The quantity E is the verlical disrance of Rydberg as well as continuum states to the limit and is used to identify these states.

one is negligible (the lirst property is easily seen by analyzing eq. (1) for E > 0, the second one is derived in Demkov and Komarov’s paper). The value of the Factor p_ in eq. (3) is governed by the crossings with those Rydberg curves, which are not covered by the unified treatment, as well as by other possible crossing points. When the coupling is always radial, pm is simply given by a product of kUIdaU-Zener probabilities of the form p,, = exp [ - u,,/q]_ The radial velocity II, in the

253

IV Aberle er &/Free elecrrol, protfucfion it1 U~OIII-0110111 collisiorls denominators is different from one crossing point to the other. As long as these differences are negligible, eq. (3) simplifies to p.

(4)

= exp [ - L;,/L;,~,

with ~7,a constant parameter typical for the whole series of crossings. Eq. (4) is very similar to the ordinary LandauZener formula, and it is tempting to explain it by regarding all the crossing points as isolated LandauZener-type crossings. Though this gives a good qualitative insight into what is happening, it is not a correct explanation. The effective coupling regions or the various crossings are so strongly overlapping that an isolated treatment is wrong. The quantity u, in eq. (4) remains unaltered under isotope substitution. This is the same behavior as is shown by the corresponding

Landau-Zener

The ionization integration

GirtI= 27L

quantity in the

formu!a.

cross section is obtained parameter,

by

over the impact

b db exp

(-

u,/c,).

(3

s 0

Like in the Landau-Zener case, the integral can be expressed by tabulated functions [ 131, Ginl

=

nr:F(E/EC,

K/E,),

05)

with EC = $fm$ III the reduced F = ?(I -

VJE)E,[(E/E,

-

mass.

K/E,)- “‘1,

(7)

and I&(z) an exponential integral [14]. The possible resulting cross sections curves are shown in lig. 8. F = Gfm$ is drawn for various values of the parameter Vc.E, as a function of the velocity v in units of I;,, a second abscissa scale gives E/E,. The ScdkS are double logarithmic, such that the theoretical curves and the experimental results of fig. 6 are directly comparable. Under isotope substitution H --f D, the potential curves, and therefore V, and r,, remain the same as well as the coupling parameter u,. The effect of isotope substitution upon the theoretical cross section

is therefore

fully described

by the substitu-

Fig. 8. Theoretical cross sections for free electron production according to the Demkov-Komarov model. Possible cross section curves are given in units of nrz as a function of the velocity in units of rC (upper scale) or as a function of the energy in units of $awz (lower scale). The quantity V,/~~& plays the role of a curve form parameter. When the velocity scale is used, the only effect of H + D isotop substitution is to reduce this partlmeter by a factor of two.

tions

all practical masses is 2.)

(For

4. Comparison

purposes,

of experiment

the ratio of the reduced

and theory

and

discussion

For all of the lirst free electron channels (fig. 6a), we have chosen the parameters r,, VC/E,, and v, in such a way that the best possible agreement between experiment and theory is achieved. These

II! Aberle et ok/Free electron prodrtctio,l it1ufonz-utom collisiom

254

Table 1 The tirst three columns give the values of the parameters, which have been used to select the theoretical curves in IQ. 6. V, in the fourth column is the height of the crossing region above the level OF the incoming channel as calculated from VJE, and uC. Note that the error marges are rather large. In the best case, Xe + Xe’. the experimental error of the potential parameters is about 30% &llJ)

KW)

0.05

0.090 0.136 0.125

20.2 23.1 19.5

0.10 0.10

0.134 0.125

13.8 39.0

WE,

(H atoms) Ne-H+ Ar+H” Kr+H+ Kr - Kr-

0.95 0.62

Xe -+ Xe+

1.13

0.30

0.10

1.20

0.05

electron channels certainly suffer from a competition of the first ones. Moreover, the second Ar channel. which is observed only at energies larger than 150 eV, has a good chance to be disturbed by other channels, which are not detected in the present experiment. The qualitative agreement of experiment and theory for the second Kr channel has to be ascribed to a smaller influence of such competitions_ The ion pair channel which is observed in three of the four collision systems at low collision energies might influence the first free electron channels. Most probably [ 151, however, this state is populated indirectly from one or more of the Rydberg states preceding the grst continuum limit. The competition included

parameters are given in the first three columns of table 1. The resulting cross section curves for both H and D reactions are included as solid lines in fig. 6a. They agree with the experimental points within the range of the experimental uncertainty. For the second Kr channel, a rather good iit is also possible. The parameters are also included in table 1, and the resulting cross section curve is shown in fig. 6b. For the second Ar channel, no EasOwdbk tit is possible. Column 4 of the table gives the potential energy vc of the crossin’g resion as calculated from the fitting parameters VJE, and v,. The width parameter L (eq. (1)) can be estimated from the value of u,. For all systems, L 5 0.1 A is found. Thus, the condition L < I-, for the applicability of the theory is Fulf?lled rather well. For the first channels of Ne, Ar, and Kr, a rather wide range of fit parameters will lead to a reasonable agreement between theory and experiment. The uncertainties in the relative magnitude of H tind D cross sections and in the absolute scaling, and the rather small energy ranges of these measurements result in a large uncertainty for the potential parameters. For the first Xe channel, the situation is better; the parameters V, and nc cannot be changed by more than about 30 “/, without destroying the agreement. The integral cross section curves of Iig. 8 have been derived for a case with only one curve crossing region. These results can therefore be applied only to systems in which no competition from other inelastic processes is to be expected. The second free

of this channel

in the theory.

is therefore

already

It ivill not affect the cal-

culated form of the free electron cross sections. From the good agreement between experiment and theory, which is found for all first channels, one has to conclude that the basic formula, eq. (4), is a correct reflection of what is actually happening. The formula results from the Demkov-Komarov theory. However, a conclusion on the validity of the entire theory cannot be drawn directly from our experiments. Any other explanation of eq. (4) would serve as well. A better test of the entire DemkovKomarov model would be obtained by trying to verify the much more detailed eq. (1) rather than eq. (4). This equation makes a prediction for the energy distribution of the free electrons and for the probabilities of producing Rydberg state atoms. Measurements of this energy distribution and of cross sections for the processes H + M -t H(rrl) + M are therefore desirable. It should be mentioned that the observed order of the two possible free electron channels is in a very natural way explained by the model: the lowest continuum limit at infinite internuclear distance will in general be the lowest one at finite distance and therefore the first one to be crossed. Strong support for the applicability of the Demkov-Komarov model to the present processes comes from a quantum chemical cdIcuIation. Butscher and coworkers [IS] find, in an adiabatic calculation for the system HAr, a well-localized region of strong radial coupling between the two states dissociating into H(Is) + Ar and H(2s) + ArThe appearance of the coupling matrix element and

It! Aberle et d/Free

electron prodwriorl in utom-atom collisiom

of the potentials is very similar to the LandauZener case, i.e. the cae of two crossing diabatic potential curves. The crossing is located at 1.2 A and at 7 eV above the ground state asymptote. The parameters ‘; and F obtained from the H + Ar + H’ + e + Ar experimental results are 1.2 A and 23.1 eV. The two sets of data are not directly comparable. The first set refers to a single crossing point, the second one to a weighted mean over the entire Rydberg series. Bearing this in mind and recalling the large uncertainties of the fitting parameters, it appears reasonable to identify the calculated crossing point as the first one in the series of crossings, which has been postulated to explain the experimental observation.

References [I] Yu. N. Demkov and LV. Komarov. [z]

23 (1966) 189. Yu. N. Demkov,

Sov. Phys. JETP

Sov. Phys. JETP 19 (1964) 762.

[3] [4]

255

A. Niehaus and M.W. Ruf. J. Phys. B9 (1976) 1401. H.H. Fleischnxmn and R.A. Young, Phys. Rev. 175 (1969) 254: R.C. Dehmel, R. Meger. H.H. Fleischmann and M. Steinberg. J. Chem. Phys. 58 (1973) 51 II. [S] B. van Zyl, T.Q. Le. H. Neumann and R.C. Amme, Phys. Rev. A15 (1977) 1871. -[6] W. Abe&. B. Brehm and J. Grosser. Chem. Phys. Letters 55 (1978) 71. [7] P. Zugenmaier, Z. Angew. Physik 70 (1966) 154. i-81 H.H. Fleischmann. CF. Barnett and LA. Pav.-. Pbvs. _ - - Rev. A10 (1974) 569. [9] M. Van Gorkom and R.E. Click, Intern. J. Mass Spectrom. Ion Phys. 4 (1970) 203. [IO] G.D. Magnuson and C.E. Carlston, Phys. Rev. 129 (1963) 2403. [l I] R.C. Lao, R. Sander and R.F. Pottic, Intern. J. Mass Spectrom. Ion Phys. 10 (1972) 309. [ 121 M. von Ardenne. Tabellen zur angewandten Physik I (VEB, Verlag der Wissenschaften, Berlin. 1962). [I31 R.E. Olson, Phys. Rev. A2 (1970) 121. [14] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover Publications. New York, 1970). [IS] W. Butscher, private communication. to be published.