IONIZING COLLISIONS OF LASER-EXCITED RARE GAS ATOMS

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IONIZING COLLISIONS OF LASER-EXCITED RARE GAS ATOMS

W. Bussert, T. Bregel, J. Ganz, K. Harth, A. Siegel, M.-W. Ruf, H. Hotop, H.

Morgner

To cite this version:

W. Bussert, T. Bregel, J. Ganz, K. Harth, A. Siegel, et al.. IONIZING COLLISIONS OF LASER- EXCITED RARE GAS ATOMS. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-199-C1-214.

�10.1051/jphyscol:1985120�. �jpa-00224492�

JOURNAL DE PHYSIQUE

Colloque C l , suppl6ment au nO1, Tome 46, janvier 1985 page Cl-199

IONIZING C O L L I S I O N S O F LASER-EXCITED R A R E GAS A T O M S

W. Bussert, T. Bregel, J. Ganz, K. Harth, A. Siegel, M.-W. Ruf, H. Hotop and H. ~or~ner'

Fachbereich Physik, U n i v e r s i t a t Kaisers Zautern, 6750 KaisersZautern, F . R. G.

+ ~ a k u ~ t a t fur Physik, U n i v e r s i t a t Freiburg, 7800 Freiburg, F.R.G.

Resume : Nous avons utilise la spectrometrie de masse et la spectrometrie d'electrons pour Ctudier l'ionisation d'atomes d'argon et de krypton dans des collisions, aux energies thermiques, avec des atomes de Ne B courte duree de vie (2p53p, J = 1,2,3) excites par laser. Les sections efficaces dependent fortement de l'dtat excite ; leur comportement est bien repro- duit par des calculs fondes sur les courbes theoriques d'energie potentiel- le et sur l'existence d'un seul etat autoionisant B decroissance exponen- tielle. Les rendements total et partiel d'ions et les spectres d'electrons presentent des effets de polarisation imporfants ; on ne peut les expliquer que par des probabilites d'autoionisation dQpendant de 0 et favorisant le transfert df61ectrons CI --> o.

Abstract: Using mass spectrometry and electron spectrometry, we have studied ionization of Ar and Kr atoms in thermal energy collisions with laser-excited short-lived Ne(2p5 3p J=1,2,3) atoms. The cross sections show a strong state- dependence, which is reproduced in calculations based on theoretical poten- tial energy curves and a single exponential autoionization width. Significant polarization effects have been observed in the total and partial ion yields and in the electron spectra; they can only be explained with R-dependent au- toionization probabilities favouring o + o electron transfer.

1. Introduction

The availability of tunable lasers, especially of stabilized cw single mode dye la- sers, has made possible detailed studies of electronic and atomic collisions /e.g.

1-18/. In the last years, we have started a program to investigate ionizing colli- sions of state-selected heavy rare gas metastable atoms x(mp5(m+l)s 3 ~ 2 O ) (x=Ne,Ar, Kr,Xe) /l 1,12/ and of laser-excited, short-lived states x(mp5 nll) /13-18/ by high resolution electron spectrometry and mass spectrometry. It is our goal to obtain in- sight into the ionization mechanism in collisions with states of medium to very high excitation (Rydberg states nzlO) and to test potential energy curves for such multi- state systems. For this purpose, we compare the results obtained for many multiplet states, which are excited or state-selected by laser optical pumping of intense col- limated metastable rare gas beams. We study the dependence of the cross sections on collision energy and on the polarization of the pumping laser with respect to the axis of the (average) relative velocity of the collision system. For the excited heavy rare gas atoms x(mp5 ni) it is of interest that polarization will be trans- ferred to both the valence electron @to the core. Especially the polarization of the orbital angular momentum of the core may play a decisive role for the autoioni- zation of the collision system. In this paper, we report in detail the results ob- tained for ~ e ( 2 ~ ~ 3p J=1,2,3)+Ar together with calculated potential energy curves;

in addition, we present first results for ~ e ( 2 ~ ~ 3p J=1,2)+Kr.

2. Experimental

Fig. 1 sho-ds a' schematic drawing of the apparatus. A thermal energy, mixed metastable

~ e ( 2 ~ ~ 3s 3 ~ 2 0 ) beam, originating from a separately-pumped cold cathode discharge

source /I l /, : S highly collimated ( 5 1 : 100) at the entrance to the reaction region,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985120

JOURNAL DE PHYSIQUE

where it is transversely excited by a stabilized single mode dye laser, tuned to the 'O~e(3s+3p) transition of interest (Fig. 2). The velocity distributio? of the

Ne(3s 3 ~ 2 0) atoms has been studied by time-of-flight techniques; under normal opera tion of t&e source (current 10 mA, source pressure 10-30 mbar, wall temperature around 300 K) the average metastable velocity v was found to be 800 m/s with a FWHM of about 30% of T. Typical Ne* intensities from our source are (1-2).10~~/s-sr. Ad- mixture of He gas results in a shift of the Ne* velocity distribution towards higher

v, accompanied by a small increase in Ne* intensity. With the addition of He at an amount comparable with the normal Ne pressure, we obtain a Ne beam with 7=1200 m/s (FWHM 30%) and a He* fraction below 3%. The latter does not produce problems in the interpretation of electron spectrometric data.

to Mass Spectrometer

Fig. 1 : Schematic Drawing of Experimental Setup

In this paper we present data obtained with

NEON two different setups:

E (103 c m - ' ) E ( e V 1

155 - -

l50 -

-

145 -

(L0 - I

l 3 5

1 &;: of the average relative velocity between the Ne* and the target beam, tilted away

0 from GNe. This apparatus has been used be-

fore for photoelectron spectrometry and in- corporates two separate, rotatable two-stag Fig. 2 : Neon Energy Levels hemispherical condensers, allowing the mea-

i) In the first (Fig. l), we use a static J.0 J.1 J z 2 J - 3 - target gas (density (2-6). 1012/cm3) for elec

tron spectrometry, S lol l/cm3 for ion mea-

-\rF

2 p 5 3~

640.2nm

2 p 5 3s

73.6nrn 3p2

surements). Here, the Ne* velocity is the

le5 the relevant polarization quantization dependence. axis for A studies 12T0 cylin- of drical condenser 111-151 or a two-stage he- mispherical condenser / 16,181 have been used

-180 for electron spectrometry. A quadrupole

mass spectrometer /15,17/ or a time-of- 1 flight mass spectrometer sample the ions.

:17.5 The target chamber temperature was (295-

300) K; for the system ~ e * + ~ r with i ~ e

- 4 0 0 m/s, an average collision energy

-170 re1=58 mev results.

ii) In the second setup, an effusive target

;16.5 beam (target density around 5 * 1 0 ~ ~ / c m ~ cros

ses the ~ e * beam at right angle. Here, the

quantization axis is given by the vector

surement of electron angular distributions /19/

In both setups i) and ii) an electron energy resolution of (20-30) meV was employed by appropriate choice of the constant pass energy. The energy dependence of the over- all transmission of the electron spectrometers was determined by WV photoelectron spectrometry of 02. CO and NZ /e.g. 12/. The electron spectra shown below have been transmission-corrected. All spectra were measured by multichannel scaling techniques as described before /11,12/.

Next,we discuss the important aspects of the laser excitation of the metastable ~ e * beam. Using a metastable state selection method involving multimode dye lasers /11, 201, we have repeatedly determined the 3~2/3~o-composition of the normal Ne* beam

(without He seed gas) as 5.1 :l and the 3~2/3~o-ionization cross section ratio for A r at vNe=800 m/s as 0.81+10% /l l/. Therefore, the 3 ~ 2 / 3 ~ -ratio of the product "den- sity* ionization cross section" is given by n202/n0007~r)=4.1. Similar ratios are calculated for the target atoms K r , Xe, Hg /?l/.

In the measurements, we have always excited the 20~e(3s 3~2)-fraction ( 7 6 % ) of the Ne* beam. We first discuss the transition 'ONe(3s 3~?+3p 3 ~ 3 6 2pg Paschen notation) at 640.2 nm; it is unique because spontaneous electrlc dipole decay from the upper level leads always back to the pumped state. Therefore, a substantial quasi-statio- nary upper state population can be achieved together with a well-defined polariza- tion of both the upper and lower state. In pumping this transition, we have used a nearly parallel beam (diameter about 4 mm) of 100-200 mW power from a stabilized single mode dye ring laser (Coherent 699-21, dye DcM). Under these conditions, the pumped 'ONe(3s 3 ~ 2 ) atoms spend about 5 us in the laser beam and undergo 250 sponta- neous emissions. With linear laser polarization only even state multipole moments are present with a rank up to 2.5. As we could show by photoelectron angular distribution studies of Ne(3p 3 ~ 3 ) , ionized by 351.1 nm radiation /16/, the theoretically expec- ted alignment is actually achieved under our excitation conditions. We note, that the saturation broadened linewidth is typically 100- 150 MHz (FwHM) ; therefore, the influ- ence of the Doppler effect (FWHMz520 MHz for a collimation ratio of 1 : 100) is negli- gible in the absence of beam scattering, i.e. for very thin target conditions, as met in the ion measurements. Here, almost 50% of the pumped 20~e(3s 3 ~ 2 ) atoms are pre- sent in the 2pg-state (excitation fraction f=(45+5)%). For electron spectrometry, the target density has to be increased to such a level that elastic.scattering of t'e Ne* beam between the collimating aperture and the reaction region leads to a non-ne- gligible broadening of the effective Doppler profile and a reduction of the 2pg-frac- tion. Even here, values of f=25% are easily obtained, however, resulting in ~ e ( 2 p ~ ) - induced electron counting rates which are comparable with those due to Ne(3s 3~2).

In Fig. 3, we have sketched the different choices of laser pola5izatio.n applied in the present work with the 2p9-state. In transverse excitation (kL 1 vNe,tre ) + with linearly-polarized lighi, we have the extreme cases rill (k ^{I l Yrel) and v 1} 1~~ ^vre$

In coaxial excitation (kL I I vNe), the use of circularly polarized light (all ) re- sults in a pure asymptotic state; coaxial excitation is velocity-selective to a de- gree determined by the saturation-broadened excitation width (under our conditions Av/vzlO%). The numbers given in Fig. 3 for the relative asymptotic R=lmJI and mR-pc- pulations correspond to the diagonal elements of the respective density matrix and illustrate the polarization-induced variations in the boundary conditions for the collision system. As a result of the non-perfect kinematics of our experiment, espe- cially for the beam-gas configuration i), some averaging occurs and will result in a reduction of the polarization effect /21/. More importantly, we emphasize that our measured quantities represent averages over all contributing impact parameters

(typically 0-8 ao).

We now discuss the procedure to study ionizing collisions with ~ e ( 3 ~ 3=1,2) states.

As is clear from Fig. 2, laser excitation to the ~e(3p 5=1,2) levels suffers from

their spontaneous decay to non-pumped Ne(3s)-states. Therefore, the "effective resi-

dence time" reff in these truly short-lived Ne(3~) states is comparable with their

natural lifetime T ' ( z 20 ns /22/). Compared with the Ne(3p 3 ~ 3 )-state, we expect a

loss in signal(assuming comparable cross sections) of two orders of magnitude. By

Cl-202 JOURNAL DE PHYSIQUE

careful reduction of background (e.g. due to scattered metastables and VUV fluores- cence Ne(3s J = l ) + ~ e ( 2 ~ ~ 'so)), using two-stage condensers, we have succeeded in mea- suring electron spectra due to the short-lived Ne(3p J=1,2)-states with adequate signal-to-background ratio.

In this work we have used the following excitation conditions: a cylindrical lens (f=50 cm) produces a line waist of the laser with a width of about 0.2 mm, located in the center of the reaction region (width seen by the electron detector about 2mm). Thereby, excitation outside the detection volume is ruled out, and the atoms spend about 250 ns (12 T) in the laser beam, allowing for complete removal of the pumped magnetic sub-states by subsequent absorption-spontaneous emission cycles. Un- der these circumstances, the background-corrected, energy-integrated electron inten- sities are proportional to the respective ionization cross section and to the effec- tive residence time

in the upper state k. .reff may be expressed as the product of the natural lifetime rk times an efficiency factor Q, which accounts for the de- tails of the transition, i.e. which percentage of the magnetic substates mi in the lower state i can be pumped for a given laser polarization and which fraction of the spontaneous decays from the upper state k leads back to the pumped state i. The na- tural lifetimes are precisely known / 2 2 / , and we have calculated the efficiency factor n for all the 3s+3p transitions and polarizations of interest, using the rate equation approach. Magnetic fields are assumed to be absent, i.e. below 1 0 - ~ T for practical purposes; in our apparatus, a double mumetal-shielding reduces the magne- tic field to values around 1 0 - ~ T/l9/. Measurements with linearly-polarized excita- tion have been carried out, yielding significant changes between nil and .rrl for Ne(3p J=2)+Ar, as will be discussed elsewhere. Here we deal only with excixation by unpolarized light, which was realized by using a Hanle-type polarization scrambler

(Fa. Halle, Berlin). In this case, the efficiency factor n is simply given by:

riki=l/(l-Aki/Ak), where Aki is the spontaneous transition rate from the upper state k to the pumped state i -here: Be(3s 3 ~ 2 ) - and Ak=l/.rk is the total spontaneous transition rate from the upper state k, as listed in /22/.

Asymptotic m, - Population of R =lm,l- Population

I Y ( X ) I ~ lv13p)12 ^3p - ^{electron (zp-hole)} of j = 3 State

1% 1

ON,

6,:

i

i;;

e-

0-,

A

VNe = quantization axis Fig. 3: The three different polarizations and their corresponding asymptotic

ml- and Q =ImJI-populations

3. Experimental Results

3.1 Polarization Dependence of the Ion Production in Ne(3p 3 ~ 3 ) Collisions

With a time-of-flight mass spectrometer, which could also be used to measure the to- tal ion yield in an effective way, we have studied the polarization dependence for ionizing collisions of Ne(3p 3 ~ 3 ) (YNe=800 m/s) with several static target gases Y.

Fig. 4 illustrates the procedure and the total ion results for Y=Ar. Without the pumping laser ("laser off"), we obtain a reference ion intensity, containing known contributions due to Ne(3s 3 ~ 2 ) (see above). With saturated (f=(4525 ) % ) transverse laser excitation of 'ONe(3s 3~2), the total ion signal increases significantly; the increase is found to depend strongly on the angle €3 between the electric vector of the linearly-polarized laser and the average direction of the relative velocity

(=FNe in this case). The 3~,-fraction remains unaffected, of course. From electron spectrometry with state-selected, polarized ~e(3s 3 ~ 2 ) we know that the polarization dependence of the Ne(3s 3~2)+Ar cross section is very small ( S 1%); for the evalua- tion of the present ion data, we neglect it. With the excitation fraction f=0.45(5) the Ne(3s 3~2)-contribution to the "laser on" data can be easily calculated from the known "laser-off" contribution, as indicated in Fig. 4. Using formulae given in /15/, one can then easily deduce the relative ionization cross sections for Ne(3s 3 ~ 2 ) and Ne(3p 3 ~ 3 ) and the polarization ratio Q=o(nl l)/o(n - l ) of the latter.

A Fourier analysis of the ~olarization angular dependence of the Ne(3p 3~3)+h ion yield (Fig. 4)

3

I(@) = 1 ^{Rn COS (2n6)}

n=O (3.1)

can be used to derive the [mJ/-dependence of the cross section /23/, as will be dis- cussed elsewhere in detail. Here, we just note that R2,R3 were found to be negli- gibly small for all the studied targets; the ratio RI/Ro is then related to Q simply by Q=( l+R1/Ro)/(l-~l/~o). For all the rare gas targets Ar, Kr, Xe a clear polariza- tion effect was found in the total ion yield with Qz4/3 (see Table 1). We have also investigated the polarization dependence of the partial cross sections, e.g. Ar+- formation (Penning ionization PI) and NeAr+-formation (associative Penning ioniza- tion AI). The AI-channel always shows a much more pronounced polarization effect than the PI-channel. For the target Hg, whose electron spectrum exhibits a very strong polarization dependence /14/, the total ion yield was found to be practical- ly independent of the polarization direction. Weak polarization effects (Qs1.05) have been observed for Y=N2, CO, and 02.

a: Average of o(nll ) and o(nl - ), measured relative to Ne(3s 3 ~ 2 ) /l 1,15/

Table 1: 'Ratio ~=o(rr,~)/o(n~) of the total and partial ionization cross sections for the systems Ne(3p 3 ~ 3 )+Ar ,Kr,~e. (YNe=800 m/s) .

3.2 Polarization Dependence of the Ne(3p 3 ~ 3 ) + ~ r Electron Spectrum

$ I 1.22 5 0.03 1.29 -1- 0.04 1.25 + ^0.05

QTOTAL 1.33 0.07 1.40 + ^0.09

1.33 0.06 TARGET

Ar K r Xe

We have previously reported on a polarization dependence of the electron spectra for Ne(3p 3~3)+Ar, Kr, Xe /13/, using transverse Ne* excitation ( a 0 0 m/s) in a beam- gas setup. In the meantime, we have also measured spectra with coaxial excitation, which is facilitated by the use of the intense ring laser output.

&AI 2.3 + ^0.3

2.7 5 1.0 3.0 + ^1.8

oa _TOT [g2]

2 3

2 3

29

C1-204 JOURNAL DE PHYSIQUE

m T

' ( U

N -

From t h e beam-gas e l e c t r o n s p e c t r a we o b t a i n Q=1.30 i n agreement w i t h t h e i o n d a t a

a able 1 ) . F i g . 5 shows t h e ~ e ( 3 ~ - ~ D ~ ) + A r e l e c t r o n s p e c t r a o b t a i n e d with t h e beam- beam a p p a r a t u s f o r VNe=1200 m / s (Erel=l10 meV). The e l e c t r o n s a r e d e t e c t e d perpendi- c u l a r t o t h e ~e*-beam i n a p l a n e which c o n t a i n e d a l s o t h e l a s e r beam. P r e l i m i n a r y measurements a t o t h e r e l e c t r o n d e t e c t i o n a n g l e s ( r e l a t i v e t o t h e Ne" beam) y i e l d e d

s p e c t r a w i t h e s s e n t i a l l y t h e same shape and only weak t o t a l i n t e n s i t y changes. The s p e c t r a i n F i g . 5 show a v e r y c l e a r p o l a r i z a t i o n dependence w i t h a continuous t r e n d from 0 1 1 ( o n l y Im 1 =R=3 populated a s y m p t o t i c a l l y ) v i a n l (dominant R=3 p o p u l a t i o n ) t o n l l (dominant A=o p o p u l a t i o n ) , s e e F i g . 3. As h a s a l s o been observed a t

T=800 m/s, t h e A ~ + ( ' P ~ / ~ ) / A ~ + ( ~ P ~ / ~ ) branching r a t i o d e c r e a s e s , whereas t h e h i g h energy p a r t of b o t h f i n e - s t r u c t u r e peaks i n c r e a s e s from

v i a n l t o n l l The l a t - t e r o b s e r v a t i o n i s compatible with t h e s t r o r g p o l a r i z a t i o n dependence o f t h e Ne Ar+- channel, which corresponds t o t h e high energy p a r t o f t h e e l e c t r o n peaks w i t h Eel-E0>Ere1 ( E ~ : r e s p e c t i v e nominal energy of peaks, s e e e . g . / l 1 /).

From t h e " 1 1 - and n l - s p e c t r a i n F i g . 5, one o b t a i n s t h e p o l a r i z a t i o n r a t i o

Q=1.57(4). The i n c r e a s e r e l a t i v e t o t h e VNe=800 m/s d a t a may be i n p a r t due t o t h e b e t t e r d e f i n e d kinematics a t 7 =l200 m / s . For a d e t a i l e d understanding of t h e pola- r i z a t i o n dependence of t h e ele!fron s p e c t r a it i s n e c e s s a r y t o know t h e p a r t i c i p a - t i n g p o t e n t i a l energy c u r v e s i n o r d e r t o c a r r y o u t model c a l c u l a t i o n s o f t h e s p e c t r a There a r e f o u r p o t e n t i a l curves Q=0-,1,2,3 f o r Ne(3p 3 ~ 3 ) + A r and t h r e e i o n i c curves f o r NeAr+('~f / 2 , 211 3/2, 'R 1 / z ) ; moreover, t h e a u t o i o n i z a t i o n width, which may depend on R , e n t e r s t h e problem. Here, we only g i v e a q u a l i t a t i v e d i s c u s s i o n ( s e e below) and postpone t h e d e t a i l s t o a l a t e r p u b l i c a t i o n .

3.3 E l e c t r o n S p e c t r a f o r Ne(3p J = 1 , 2 ) + A r , K r

Using s e t u p i ) we have o b t a i n e d r e s u l t s f o r s i x N e ( 3 ~ 5=1,2) s t a t e s a t 7 =800 m/s, a s r e p o r t e d l a s t y e a r /18/. With t h e improved beam-beam a p p a r a t u s i i ) weNRave mea- s u r e d s p e c t r a f o r t h e same s i x s t a t e s a t YNe=1200 m/s f o r Y = A r , K r and - f o r compari- son and c a l i b r a t i o n purposes - a t TNe= 800 m / s f o r N e ( 3 ~ J=2; pp8, 2p6 ) + ~ r . The r e - s u l t s f o r TNe=1200 m/s a r e shown i n F i g . 6; u n p o l a r i z e d r a d i a t i o n was used f o r e x c i - t a t i o n . I n Table 2 , we have l i s t e d t h e r e l a t i v e c r o s s s e c t i o n s deduced from t h e Ar- s p e c t r a i n Fig. 6 t o g e t h e r w i t h t h e e a r l i e r r e s u l t s f o r vNe=800 m/s /18/. The abso- l u t e s i z e of t h e c r o s s s e c t i o n s c a l e was chosen t o b e compatible w i t h t h a t of t h e e a r l i e r d a t a , which was based on a N e ( 3 ~ 3 ~ 3 ) + A r c r o s s s e c t i o n o f 19.7 8' (average of rill ^and nL). This v a l u e i s about 15% lower t h a n t h e more c a r e f u l l y determined average v a l u e i n Table 1 , b u t we n o t e t h a t t h e experimental u n c e r t a i n t y i n t h e de- t e r m i n a t i o n of t h e Ne(3p J = l , 2 ) c r o s s s e c t i o n s r e l a t i v e t o t h e Ne(3p 3 ~ 3 ) c r o s s sec- t i o n from t h e i r r e s p e c t i v e e l e c t r o n i n t e n s i t i e s s o f a r amounts t o about + ^{50%. This}

u n c e r t a i n t y t r a n s f e r s t o t h e a b s o l u t e s c a l e of t h e c r o s s s e c t i o n s i n Table 2.

As i s c l e a r from Fig. 6 and Table 2 , t h e t o t a l c r o s s s e c t i o n s show a very s t r o n g s t a t e dependence, both a t tNe=800 m/s and 1200 m / s . The r e l a t i v e i n t e n s i t y f o r t h e t w o . i o n i c f i n e - s t r u c t u r e channels a l s o s t r o n g l y v a r i e s from s t a t e t o s t a t e ; analo- gous d i f f e r e n c e s have been found i n t h e behaviour of t h e m e t a s t a b l e Ne(3s 3 ~ 2 , 3 ~ 0 ) s t a t e s /11/. For some s t a t e s , a s i g n i f i c a n t v e l o c i t y dependence o f t h e t o t a l c r o s s s e c t i o n s i s observed. As f o r t h e Ne(3p ~ = 1 , 2 ) + K r systems, F i g . 6 shows t h a t t h e y be- have q u a l i t a t i v e l y i n t h e same way a s Ne(3p J=1,2)+Ar.

I n o r d e r t o understand t h e s t r o n g s t a t e dependence o f t h e c r o s s s e c t i o n s , we have c a l c u l a t e d p o t e n t i a l energy curves f o r Ne(3p)+Ar, a s w i l l be explained i n t h e next s e c t i o n . Using t h e s e t h e o r e t i c a l p o t e n t i a l s , we have c a l c u l a t e d t o t a l i o n i z a t i o n c r o s s s e c t i o n s o f Ar f o r a l l t h e Ne(3p) m u l t i p l e t s t a t e s i n t h e t h e r m a l energy range, assuming - f o r s i m p l i c i t y - a s i n g l e a u t o i o n i z a t i o n width f u n c t i o n r ( R )

w i t h t h e c r i t i c a l parameter y optimized such t h a t t h e s t a t e dependence o f t h e expe-

r i m e n t a l c r o s s s e c t i o n s (Table 2 ) i s reproduced. The f a c t o r C p l a y s a minor r o l e ;

it i s found t o s c a l e t h e a b s o l u t e s i z e o f t h e c a l c u l a t e d c r o s s s 6 c t i o n s i n an almost

l i n e a r way f o r t h e d i s c u s s e d systems.

Cl-206 JOURNAL DE PHYSIQUE

&.

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El ^{.. 'A'}

^{5.:: L..} _:g; ^{ki. ,}

af"

V'.

4 _. 4.

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^9:. it

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Q!! ^''2

.. . . .

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(3-207

Table 2: Total Ionization Cross Sections [W2] for ~e(3p J=l,2) + Ar

a Theoretical values obtained with r ( ~ ) = 0.137 eV. exp(-0.9 R/ao).

N e ( 3 p ) - s t a t e Ne(3D,,2p8) Ne(3Dl ,2p7) Ne(lD,,2p6) Ne(lP1,2p5) lJe(3P2,2p4) Ne(3P1 ,2p2)

b The values in brackets were calculated with the adiabatic potential curves for the n=1 components, see text.

4. Calculation of Potential Ener~y Curves for ~ e ( 2 p ~ n l ) + Ar 4.1 the or^

EXPERIMENT

Ere, = 58 meV 110 meV 15.3 + 0.8 16.4 + 1.0

6.9 2 0.9 9.8 + 1.0 11.6 + 1.1 13.6 + 1.4

1.5 + 1.0 4.9 + 0.9 3.0 + 0.9 5.7 ⁱ 0.9

0.4 ? 0.4 + 0.8

- 1.2

We consider a slow collision between an excited rare gas atom X and a ground state atom Y with the respective conrigurations

T H E O R Y ~ Ere,= 58 neV 110 meV

18.3 16.2

4.5 ( 7 . 9 ) b 9.6 (12.2) b 15.8 (12.9) 15.0 (13.6)

3.7 ( 5 . 5 ) 3.7 ( 5 . 2 )

5.7 (4.5) 5.9 (4.8)

1.9 2 . 1

The total energy shall lie in the ionization continuum of Y+. In computing the corresponding potential curves we project out all configurations, which look like X(ls0) + Y+ + e-, where the electron may be in a bound or a continuum state. The very same method was u s e d i n ~ e few ab initio calculations that exist for Penning- ionizing molecular states le.g.24-26/. The continuum comes in again when computing the autoionization width of the resonance, which is not our purpose.

The symmetry of molecular states XY is fully described by the wavefunction of X, which in turn depends parametrically on the internuclear distance between X and Y.

The basis states for our treatment are the same as those which are used to treat the isolated x(mp5nl) atom. These states represent two electron (or one-electron-one- hole) wavefunctions. They have been discussed extensively by Condon & Shortley / 2 7 / , who define two basis sets which correspond to the LS coupling case and to the jj coupling case, respectively. We denote these basis states by ILSJ> and IKjJ>.

J is the total angular momentum of the atom, L the total orbital angular momentum and S the total spin angular momentum. K denotes the total angular momentum of the mp5 hole state and j the same quantity for the nl electron state. All electrostatic interactions in the atoms are diagonal in the ILSJ> basis, whereas spin orbit interaction can be parametrized as a diagonal matrix in the IKjJ> basis. The ne- cessary transformation between the two basis sets can be done with the aid of a ma- trix U, the elements of which consist essentially of 9j-symbols 1281. The parameters which are used for describing the electrostatic interactions and the spin orbit interactions are discussed in detail by Condon and Shortley /27/.

We define two matrices and A SO . contains all electrostatic interactions (ex- pressed by the proper parameters) and is diagonal in the I LSJ> basis. ASO describes the spin orbit interaction with the two conventional parameters 5 and , , c and is diagonal in the IKj J> basis. Then we define the matrix A by

Diagonalization of A yields the eigenvalues of the included configurations X(mp5nl),

nl variable. The employed parameters are taken from Condon & Shortley /27/. In this

Cl-208 JOURNAL DE PHYSIQUE

parametrization, configuration interaction within the atom is not included. There- fore, matrix A blocks into several submatrices A; which correspond to the single configurations x(mp5nl), x(mp5n'l' ) , . . . This simple method leads to very good re- sults for the rare gas configurations mp5ns and mp5nd. It was found, however, that mp5np configurations cannot be parametrized in this way with the same precision. In this case, the introduction of an effective operator a.L(L+l), which simulates the interaction with other configurations, improves the situation significantly (cf.

Feneuille et. al. /29/). At this stage, we resume that it is possible to construct a matrix A according to eq. (4.2), the eigenvalues of which represent the energy levels of the configurations ~ ( m p ~ n l ) of an excited rare gas atom.

If we wish to obtain information on the molecular states of x(mp5nl) + y(lSO) we must add those interactions which arise when X and Y approach each other. These interactions can be assumed to be of purely electrostatic nature. Thus, they are ad- vantageously described in the ILSJ> basis. We conceive now a matrix B which contains the interactions specific for the molecule X + Y in the ILSJ> basis. Diagonalization of the sum of the two matrices A + B will then lead to the eigenvalues and eigen- vectors of the molecular states X + Y. The molecular interactions include those which couple different configurations mp5nl and mp5n 'l ' . This causes off-diagonal elements in B which couple different blocks Ai and Aj within the matrix A. At this stage, diagonalization of the sum A + B leads to more accurate results since both spin orbit and (molecular induced) configuration interaction are taken into account.

Now we start to explicitly construct the matrix B. We first treat the elements of B which couple states within the same configuration. Let ILSJ> and ILISJ'> be two states belonging to the same configuration mp5nl. The coupling operator shall be denoted by v. Since v is purely electrostatic the spin quantum numbers of both states must be identical. With respect to the nuclear axis, L,S,J shall have the projection quantum numbers ML, MS and M, resectively. The coupling matrix element can be written as

<LSJMIQIL'SJ'M'> =E C(LSJ;M~M$) C(L'SJ';M M M') ~ ~ M ~ I V I L ' M > srnl

L S L (4.3)

MLMS

Usually nothing is known about the matrix element < L M L ~ Q ~ ~ ' ~ L > . In order to arrive at a practically useful expression we replace the operator Q by the sum QC + 0 , . 7 , shall act only on the wavefunction of the valence electron nl. Coupling between the wavefunctions is neglected. Let 1, be the resultant orbital angular momentum of the core electrons and me, m the projections of 1, and 1 onto the internuclear axis Then we express the bracket in eq. (4.3) by

7

The definition of VC and 9 , makes these operators diagonal in m, and m, respectively.

The wavefunction Ilm> can be considered to describe a molecule X'(n1) + Y(~so).

X' shall be an atom with a nuclear charge increased by 1 with respect to X but with an additional electron filling the hole in the mp5 shell of X. The wavefunction Ilm>

can be taken as describing C, IL, . . . molecular states of Xf(nl)+y, depending on the absolute value Iml. Interaction with other atomic states n'l' is neglected so that

Ilm> is avalencebond type of molecular wavefunction for X'+Y (cf. Fano and Fano /30/). Going from X'+Y to X+Y requires (at first order perturbation theory) that the splitting is taken into account which is caused by lmcl taking on different values.

Since for mp5 one has lc = 1 , m, can take the values - 1 , o, 1. In order to conserve the center of gravity of terms we require that

< . , m c I V I 1 m > = o

-. C C C (4.5)

Thus < l c m c l ~ Ilcmc> does not describe the potential curves of the molecular ion

x+(mp5) + Y(?S~), but merely the splitting between the C and IL state potentials VC,

VIL. We can identify

Thus we have found a form f o r t h e coupling m a t r i x element i n e q . ( 4 . 3 ) which a l l o w s t o make use of a v a i l a b l e , sometimes even experimental i n f o r m a t i o n : <lmlvvllm> s h a l l be t a k e n a s a p o t e n t i a l curve f o r atom Y and t h e a l k a l i atom next t o X i n t h e p e r i - odic system. It must be kept i n mind, however, t h a t it i s t h e valence bond p o t e n t i a l curve and not t h e exact one which i s r e q u i r e d a s i n p u t d a t a f o r < l m l v v l l m > .

Now we c o n s i d e r t h o s e elements of m a t r i x B which couple d i f f e r e n t c o n f i g u r a t i o n s mp5n1 and m p 5 n ' l ' . We d e f i n e an o p e r a t o r which d e s c r i b e s t h e e l e c t r o s t a t i c i n t e r - a c t i o n between t h e one-electron s t a t e s I n l > and I n l l ' > which i s caused by t h e ap- proach of t h e atom Y. $l i s d i a g o n a l i n t h e p r o j e c t i o n quantum number m, i . e . t h e ma- t r i x element < n l m l v l n ' l ' m ' > v a n i s h e s u n l e s s m=m'. The m a t r i x element of B can be w r i t t e n a s

( 4 . 7 )

<nl;LSJMlftln'l';L'SJIM> = C(LSJ;MLMSM) C(LISJ';M M M) < n l ; m L I R l n ' i ' ; I ' M L >

L S

where M ~ " ~

< n l ; ~ ~ ~ i f t l n ' l ' ; ~ ' ~ L > = ~ C ( l c l L ; m c m M L ) C ( l C 1 ' I ' ; m c mM L ) t n l m l P i n ' l ' m > . ( 4 . 8 ) mcm

4.2 Computation o f t h e P o t e n t i a l Curves f o r Ne(2p53s,3p) + Ar

We apply t h e formulae from t h e preceeding s e c t i o n t o t h e computation o f t h e molecu- l a r s t a t e s o f ~ e * + Ar which d i s s o c i a t e t o Ar and ~ e ( 2 ~ ' 3 s , 3 ~ ) . We i n c o r p o r a t e t h e c o n f i g u r a t i o n s 2p5 3s and 2p5 3p i n t h e t r e a t m e n t .

The f i r s t s t e p c o n s i s t s i n c o n s t r u c t i n g t h e m a t r i x A according t o e q . ( 4 . 2 ) . A l l ne- c e s s a r y i n f o r m a t i o n can be found i n /27,29/. The parameters used a r e l i s t e d i n Table 3. The terms o b t a i n e d by d i a g o n a l i z a t i o n of A d e v i a t e o n l y v e r y l i t t l e from t h e experimental v a l u e s /31/. For t h e c o n f i g u r a t i o n zp53s t h e d i f f e r e n c e n e v e r ex- ceeds 0.06 meV, f o r t h e c o n f i g u r a t i o n 2p53p t h e d e v i a t i o n i s always below 0.9 meV.

It f o l l o w s t h a t t h e a c c u r a t e asymptotic l i m i t s a r e guaranteed f o r t h e p o t e n t i a l curves we a r e about t o c a l c u l a t e . The remaining t a s k i s now t o f i n d t h e p r o p e r i n p u t d a t a f o r t h e m a t r i x elements < n l m l ~ l n ' l ' m > , <lmlvvllm>, and < l c m c l v c l l , m c > . We s t a r t w i t h t h e l a t t e r , a s d e f i n e d i n e q . ( 4 . 6 ) . We need t h e s p l i t t i n g between t h e C and t h e Il p o t e n t i a l f o r A r ~ e + ( 2 * ~ ) a s a f u n c t i o n of i n t e r n u c l e a r d i s t a n c e . Hausamann and Morgner /32/ compute t h i s q u a n t i t y w i t h a semiempirical method and f i n d t h a t it i s w e l l r e p r e s e n t e d by an e x p o n e n t i a l i n t h e r e l e v a n t R-range (4-7ao). I n t h e p r e s e n t c a l c u l a t i o n we have used Vn-VC = 230 eV . exp(-1.73 R/ao).

Table 3: Numerical Vdlues f o r t h e ~ e ( 3 ~ , 3 ~ ) 2 ~ ~ Atomic Parameters

Config. parametera) Numerical Value (meV1

2p5 3s b, _{d )} 16,743.760

G1 276.456

64.208

C ) d )

2p5 3p F. 18,583.26

F2 19.49

Go 95.01

G2 4.61

' 52p 64.22

<3p 0.967

C1 3.93

a ) D e f i n i t i o n s a s i n r e f . /27/

b ) F i t of p a r a m e t e r s : t h i s work c ) Parameters t a k e n from r e f . /29/

d ) The v a l u e s of F, have been ad-

j u s t e d t o reproduce t h e term

v a l u e s o f ~ e * r e l a t i v e t o t h e

Ne ground s t a t e

JOURNAL DE PHYSIQUE

4 5 6 7 8 9 1 0 1 1 1 2 1 3

Internuclear Distance R [a01

Fig. 7 : C a l c u l a t e d a d i a b a t i c p o t e n t i a l s f o r ~ e ( 2p53p )+AI-.

The zero p o i n t of t h e energy s c a l e i s s e t t o E(2p9)=18.555 eV.

Now we t r y t o f i n d r e a s o n a b l e i n p u t d a t a f o r t h e m a t r i x elements <nlmltSln'l'm> (eq.

4 . 8 ) and < ~ m l ? ~ l l m > ( e q . 4 . 4 ) . Here we use r e s u l t s of Diiren e t a 1 /33/ f o r ~ a ( n 1 ) + Ar; t h e y a p p l i e d a p s e u d o p o t e n t i a l method and f i t t e d t h e parameters of t h e pseudopo- t e n t i a l t o experimental s c a t t e r i n g d a t a /33,34/. T h e i r q u a n t i t i e s v' , ( R ) ( a s de- f i n e d , e . g . , i n /33-35/) a r e r e l a t e d t o our m a t r i x elements t h r o u g h . f-l

<nlmlQln'l'm> w i t h 1#1'

f ⁼ 1 ^(-1)' ~ ( 1 ~ l ' ; o o o ) C(l'pl;mom) v y l , ( ~ ) { .

< n l ~ n I ? ~ I n l m > w l t h 1=1'

U

Fig. 7 shows t h e c k l c u l a t e d Ne(3p)+Ar p o t e n t i a l energy c u r v e s . I n t h e r e l e v a n t R- range 5-8ao, t h e curves with dominant 3pn-character a r e a t t r a c t i v e , whereas t h o s e with dominant 3po-character a r e r e p u l s i v e . I n some c a s e s , n i c e avoided c r o s s i n g s show up, e.g. between t h e Q = 1 p o t e n t i a l s f o r pp6 and 2p7. The c h a r a c t e r of t h e d i f f e r e n t c a l c u l a t e d p o t e n t i a l curves p r o v i d e s an immediate q u a l i t a t i v e understand- i n g of t h e experimentally-found s t a t e dependence of t h e c r o s s s e c t i o n s : f o r c o l l i - s i o n e n e r g i e s i n t h e range 50-loo meV, t h e p o t e n t i a l curves f o r t h e 2p10-2p6 s t a t e s a l l o w t h e p e n e t r a t i o n t o r a t h e r s m a l l d i s t a n c e s (R=5a0), where t h e a u t o i o n i z a t i o n r a t e i s v e r y l a r g e ; i n c o n t r a s t , t h e p o t e n t i a l curves f o r t h e 2p5, 2p4 s t a t e s , and e s p e c i a l l y f o r t h e 2p3-2pl s t a t e s , prevent c l o s e r d i s t a n c e s t o be reached t h a n about 7a0, r e s u l t i n g i n s m a l l e r c r o s s s e c t i o n s t h a n f o r t h e 2p10-2p6 s t a t e s .

5. Discussion

5 . 1 Comparison of Experimental and T h e o r e t i c a l T o t a l I o n i z a t i o n Cross S e c t i o n s f o r

Using t h e a d i a b a t i c p o t e n t i a l energy c u r v e s o b t a i n e d i n s e c t i o n 4, we have c a r r i e d o u t c l a s s i c a l c a l c u l a t i o n s of t h e t o t a l i o n i z a t i o n c r o s s s e c t i o n s ( f o r t h e formulae, s e e e . g . /36/), making t h e f o l l o w i n g assumptions:

1 ) each $2-state i s weighted with a s t a t i s t i c a l f a c t o r Sn according t o : .T

with S, = 1 / ( 2 J + 1 ) f o r $2=o and SQ = 2 / ( 2 J + 1 ) f o r $221. J i s t h e t o t a l a n g u l a r momentum of t h e Ne(3p J ) - s t a t e i n q u e s t i o n .

2 ) T r a n s i t i o n s between Q - s t a t e s ( r o t a t i o n a l c o u p l i n g ) and between neighbouring N e ( 3 p ) - s t a t e s ( r a d i a l and/or r o t a t i o n a l c o u p l i n g ) a r e ignored. I n view of t h e s h a r p avoided c r o s s i n g s between t h e R=l s t a t e s f o r 2p7/2p6 and 2ps/2p4, it i s more adequate t o u s e t h e corresponding d i a b a t i c p o t e n t i a l c u r v e s i n c a l c u l a t i o n s of t h e r e s p e c t i v e c r o s s s e c t i o n s . A Landau-Zener a n a l y i s /37/ showed t h a t t h e c r o s s i n g p r o b a b i l i t y i s above 80% even a t t h e low e n e r g i e s of 50-100 meV. I n Table 2 , we have a l s o l i s t e d ( i n b r a c k e t s ) t h e c r o s s s e c t i o n s o b t a i n e d i f t h e . a d i a b a t i c Q=l curves a r e used i n t h e c a l c u l a t i o n .

3 ) ^A s i n g l e e x p o n e n t i a l f u n c t i o n T ( R ) ( 3 . 2 ) i s assumed t o r e p r e s e n t t h e a u t o i o n i - z a t i o n width f o r a l l t h e m u l t i p l e t s t a t e s , i ~ d e p e n d e n t of Q. This simple choice with an optimized exponent y produces s u r p r i s i n g l y goodagreement w i t h experiment f o r t h e t o t a l u n p o l a r i z e d c r o s s s e c t i o n s ; it does not s u f f i c e , however, t o understand t h e p o l a r i z a t i o n e f f e c t s ( s e e below).

For comparison w i t h t h e experimental d a t a , t h e a p p r o p r i a t e k i n e t i c energy average of t h e c r g s s s e c t i o n s was-carried o u t . The average c o l l i s i o n energy f o r t h e beam-gas d a t a (vNe=800 m / s ) i s Ere1=58 meV, t h e one f o r t h e beam-bean d a t a (v=l2oo m / s ) i s Er l = l l o meV. We have v a r i e d t h e c r i t i c a l parameter y i n e q . ( 3 . 2 ) i n t h e range o.% y 2 1.2 a,-l with simultaneous adjustment of C t o s c a l e t h e a b s o l u t e s i z e of t h e c r o s s s e c t i o n s . The b e s t o v e r a l l agreement #as o b t a i n e d f o r y=o.9ao-l, with C=o. 137 eV (Table 2 ) , b u t t h e whole range (0.8-1.0) ao-l can be c o n s i d e r e d t o pro- duce s a t i s f a c t o r y r e s u l t s . It i s i n t e r e s t i n g t o note t h a t t h i s c h o i c e f o r y appears t o be a l s o adequate f o r reproducing t h e energy dependence of t h e m e t a s t a b l e

Ne(3s 3 ~ 2 , 0 ) + Ar t o t a l i o n i z a t i o n c r o s s s e c t i o n /38,39/ i n t h e range

10 meV 6 Erel S 200 meV. W e n o t e , however, t h a t t h e v a r i o u s experimental m e t a s t a b l e

c r o s s s e c t i o n s do not a g r e e v e r y w e l l , a s d i s c u s s e d i n /40/.

Cl-212 JOURNAL DE PHYSIQUE

5.2 Polarization dependence of Ne(3p 3 ~ 3 ) + Ar cross sections

In order to observe a dependence of the cross section on the asymptotically varied population of the magnetic substates, there has to be a Q-selectivity in the col- lision system. This may be due to strong differences in the potential energy curves or can also be due to a strong dependence of the autoionization width r on Q.

The first question, which has to be answered, is: what is the actual Q-population in the relevant range of distances, where autoionization occurs (5-8ao), for differ- ent asymptotic polarizations? Ifoneignores coupling to neighbouring multiplet states, the simplest model is that of "free evolution" for all impact parameters.

This model would be adequate in the absence of any energy-splitting between the dif- ferent Q-states, which, of course, is not the case. The next step of sophistication is the "critical radius" model /e.g. 4, 101. The system evolves freely until a crit- ical distance RC, at which the sudden transition from the lab frame to the close coupled body-fixed frame occurs. The system Na(3p)+Hg /4/ and especially ~ a ( 3 p )+~a+

/10/ appear to be good examples for this case. Ne(3p 3~3)+Ar , however, is more com- plicated. Close coupling calculations have been carried out /42/ to follow the evo- lution of the asymptotic Q-population on straight-line trajectories down to R=6a0

(the "average" distance of autoionization) in order to learn more about the relevant Q-population of the autoionizing quasi-molecule as a function of impact parameter b;

(for b>6a0, Ei=b was used). Couplings to the neighbouring 2p8-state were included, but found to be not very important (transfer to 2pg below 10%). When those quasi- molecular Q-populations were built into the calculation of the total ionization cross sections, a polarization ratio Q=1.03 was obtained at Ere.+=llo meV under the assumption of an Q-independent T(R) , using C=o. 137eV, y=o. 9 a , - (see above ) . ^The

experimental polarization effect (Q=1.57) is much larger, and we are forced to in- troduce an Q-dependence of T(R). This is not unexpected: one envisages (Fig.8) that autoionization will occur most likely if the Ne-core hole has U-orientation and is filled by transfer from a U-electron in Ar. Morgner /41/ has discussed Penning ioni- zation in terms of reduced amplitudes um+mc, where mc is the projection of the Ne- core orbital angular momentum, and m+ is the projection of the final-state &+-hole onto the internuclear axis. The previous statement then can be expressed by saying that uoo dominates. If one ignores all the other amplitudes, the Q=3 entrance chan- nel does not contribute to ionization, and this assumption leads to a polarization ratio of Q=1.55,i.e. gives the correct trend. One can show,however, that the experi- mentally-observed polarization dependence of the Arf ( 'p3 /' ) /Ar+( 'p1 / 2 ) intens5ty ratio requires contributions from (at least) ull at the 10% level.

electron

I ^hole

Fig. 8: Illustration of two of the reduced autoionization amplitudes the dominant amplitude is U ₀₀ .

3pd - 2pci transfer 3 p n - ^{2 p n transfer}

Finally,we briefly discuss the polarization dependence of the shape of the electron spectrum for Ne(3p 3 ~ 3 ) + Ar (Fig. 5) in the light of the calculated potential curves (Fig. 7). We have constructed semiempirical potential curves for Ne+Ar+ from available information /13, 43-45/ and expected analogies with ~e+Ar+, as will be discussed elsewhere. We restrict the discussion to the A ~ + ( ~ P ~ / ~ ) electron peak, which corresponds to the single ionic channel v+(~II~/~). The corresponding curve has a well depth of 50 meV at : R - ^{5.1 a , .} The relevant difference potentials v ~ ( R ) -

v+('IIl 2) exhibit relative minima and maxima, which lead to singularities in classi- cal caiculations of cross sections. Quantum mechanical calculations of the separate R-spectra yield peaks with electron energy shifts A(R)=EP~~(Q)-E~ (relative to the 'p1 2 nominal energy) of about A(o)=+~o meV, A(l )=+l0 meV, A(2)=-4 meV and

~(3$=-14 meV. The experimental peak occurs at A-+l8 meV with a shoulder around A-+45 meV. The shoulder can be without doubt associated with ionization due to R=o.

The dominant contribution to the experimental peak appears to be due to R=l with minor admixtures from R=2 (and possibly R=3). The rise of both the R=o and R=1 frac- tion when changing from n ~ t o all is compatible qualitatively with calculated effec- tive R-populations. In order to explain the relative intensities of the different R-contributions, as distinguishable from the observed peak shape, one needs a pro- pensity in the autoionization in favour of R=o,l, which is again compatible with the dominance of the amplitude U , , . A more detailed discussion of the polarization effects will be given elsewhere.

6. Conclusions

Ionizing collisions of laser-excited Ne(3p) atoms with Ar and K r have been studied by electron and ion spectrometry. The measured strong state-dependence of the total ionization cross section has been recovered in a calculation based on theoretical potential curves and a single autoionization width common to all channels. The ob- served behaviour mainly reflects the amount of admixture of the attractive 3p8- and repulsive 3po-orbitals, resulting in large differences of the respective (aver- age) distance of closest approach. Significant polarization effects have been obser- vedinthe total and partial ion cross sections as well as in the shapes and fine- structure populations of the electron spectra, especially for ~ e ( 3 ~ 3 ~ 3 ) + ~ r . The polarization effects can only be understood with more refined models, requiring R-dependent autoionization probabilities such that the dominant (but not the only) amplitude is due to o

o electron transfer.

This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 91).

We thank R.J. Allan for his collaboration, D. Hausamann for useful correspondence, and R. Diiren for providing the numerical data of their alkali-rare gas potentials.

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