One-electron capture in slow collisions of highly charged ions with atoms

Volume 66A, number 3

PHYSICS LETTERS

15 May 1978

ONE-ELECTRON CAPTURE IN SLOW COLLISIONS OF HIGHLY CHARGED IONS WITH ATOMS T.P. GROZDANOV and R.K. JANEV Institute of Physics, Belgrade, Yugoslavia Received 13 February 1978

Some characteristic features of the one-electron capture process in the low- and medium-energy collisions of highly charged ions with atoms are considered within the electron tunneling model. The theoretical results are compared with the experimental data of Salzborn’s group.

It has recently been recognized that the charge exchange process (1) Al- Bz+ A~+B~1~ ~ 1 .~

—~

plays an extremely important role in the radiative energy losses from thermonuclear fusion plasmas [1,21, and that this process can serve as an efficient pumping mechanism for creation of population inversion for the VUV and X-ray lasers [3,4]. Such a states of reaction (1) results from the fact that highly excited states of the B(z_1)+ product ion are preferentially produced in it. The systematic experimental investigation of reaction (1), performed during the last few years by the group of Salzborn [5—8],has revealed the following characteristic features of the reaction cross section ointheenergyrangebelow25keV/amuandforz~4: (a) a is very large (~~l0_15_10_14 cm2); (b) a depends weakly on the energy; (c) a depends strongly on the initial state electron binding energy; (d) a depends (strongly) on z, but not on the other characteristics of the ion Bz4. These features of a imply that reaction (1) predominantly takes place at large internuclear distances, has a quasi-resonant character and that the reaction dynamics is mostly governed by the strong Coulomb field of the Bz+ ion. In order to describe these properties of reaction (1) in an unified manner, a model has recently been proposed [9,10], which consists of considering the process as electron tunneling from the atomic potential well

into the “quasi-continuous” spectrum of the excited states of the ion B(z_l)+. It has been demonstrated in ref. [10] that this model successfully reproduces all the above mentioned properties of reaction (1). The aim of the present letter is to provide a more complete comparison of the theoretical results obtamed within the electron tunneling model with the experimental data, and to give an estimation of the final state energy level which is dominantly populated by reaction (1). Within the electron tunneling model the cross section of reaction (1) in the adiabatic energy region is given by [10] (in atomic units)

~

(

=

~ 0’

~

F(R)RdR = 0 28 ~J’R2_R2

2

0

where u is the relative collision velocity, R is the internuclear distance and [‘(R) is the electron transition probability (per unit time) given by [10]: [‘(R) =B(nA, 1, m)(4R2/zn~)2n1A_~_m X exp ——--~-f(a) p(a) —

(3)

,

ZflA

N2 In \2~A (21÷1)(l+m).

B(nA, l~m) ~ ‘~

L1

2

r

f(a) =

~—

a

1 _1n(v’f~&+v&)j Va(1 + a)

~

=

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I

I

30 keV

p515

I

~

z

Fig. 1. Cross sections versus initial ionic charge state z for 30 KeV Xe~and ArZ+ ions incident on Kr and He, respectively. The solid lines denote the theoretical results and the open circles and triangles are the experimental measurements taken from refs. [6,8].

~r— ~(a)= 2(2nA—l —m)

~

In the above formulae ~A= (21A)”2 (IA is the electron binding energy in atom A), 1 and m are the angular momentum and the magnetic quantum numbers of the electron in atom A, and NA is a “normalization” constant of the asymptotic atomic electron wavefunction. (The values ofNA are given elsewhere [10,11].) The adiabatic region where eqs. (2) are valid is defined by u ~ 3(z/nA)h/2 [10]. As calculated from eqs. (2) and (3) the reaction cross section a is function of the following variables:z, ~A(~A)~ m and NA. Note that NA itself is dependent on ~A and 1. The z- and u-dependences of a have been investigated in detail in ref. [10]. It was shown that within this model a behaves like: a zlnz and a —In v. Below are presented some calculations of a as a function of z, v and ‘A and the results are compared with the experimental data. Figs. 1 and 2 illustrate the z-dependence of a for the cases of He, Ne, Kr and Xe target atoms. The experimental points plotted in the figures are taken from ref. [6] (for Arz+~~~He), ref. [7] (for Arz+_Ne) and ref. [8] (for Ar~—Xeand Xe~~_Kr). The agreement ~

192

I

I

I

I

O~_Xe

13456

-~

I

30 keV

~14~O

-15

I

~

Ii

i3

I

I

£5678

9~

z

Fig. 2. Cross sections versus initial ionic charge state z for 30 KeV Ar~ions incident on Xe and Ne. The solid lines denote the theoretical resulst and the open circles and triangles represent the experimental measurements taken from refs. [7,8].

of theoretical and experimental data is within a factor of less than two for z ~4 where the model is applicable. The case of a Ne target is an exception. We note that the experimental data for this case violate the general trend of increasing a with decreasing ‘A (see fig. 4 below). We would like to point out that by analyzing 107 experimental cross section values Muller and Salzborn [8] found that a(z) z’~7~°~°9, which is in fair agreement with the z In z dependence of a predicted by the electron tunneling model. In fig. 3 is presented the velocity dependence of a for Ar~+ Ar (z = 6,7) and ArZ+ + He (z = 6). The experimental data are taken from refs. [5,7] (for Ar2~—Ar)and ref. [6] (for Ar~_He).Again, the agreement is within a factor of less than two. Fig. 4 gives the dependence of a on the ionization potential ‘A at v = 3.79 X 10~cm/s and z = 10. The curve is plotted according to the empirical law found by MUller and Salzbom [8]: a ~h76~ The points represent our calculated values for a number of target atoms. The agreement can be considered as satisfactory if we have in mind that the extrapolation of Muller and Saizbom’s curve towards lower ‘A (region of alkalis) might be somewhat arbitrary. —~

Volume 66A, number 3

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PHYSICS LETTERS

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E Cs

z~7 z:6

-

-

~zr7

~

x

X

x He

~0000~Z~6 °

10~

I

I

I

I

I

o

z=6

I

I

I

12345678

7~) v(O Fig. 3. Cross sections versus relative impact velocity for ArZ4 ions incident on Ar and He. The solid lines denote the theoretical results and the open triangles, crosses (Ar-target case) and the open circles (He-target case) represent the experimental measurements taken from refs. [5,6,7].

Let us now estimate the principal quantum number ~B of the dominantly populated level of ion ~ in reaction (1). Due to the strong dependence of[’(R) on the internuclear distance, the electron transfer process predominantly takes place at a given distance I

I

¶ vr3.79xl07-~~—

Kr

~ I 5

I

)3

I

15

4).

nB—znA[l+2znA/RO]1/2 (4) the n 6+_H potential 8 values calculations obtained and from the the numerical extensive solution molecular of the [12]corresponding and O8~—H[13] closecharge coupled exchange equations problem. for 0

•Ar

-

R0 determined by condition (2). At this distance the shifted atomic level e~= ‘A + z/R0 + O(z/R~)[101 falls with onecondition of the ionic levels, 2/(2in quasi-resonance This quasi-resonance determines z the energy level which is preferentially populated in reaction (1). Thus, nB is given by

0 determined from eq. (2). Fig. 5 shows the z-dependence for hydrogen, lithium and targets at u = 5ofXn13 10~ cm/s. The open circles oncesium the H-curve at z = 6 (~B= 4) and z = 8 (nB = 5) represents

iô

ii”

Fig. Principal quantum number level5.versus initial charge state in Aof + mostly populated ionic 8Z+ —* A~+ B(51 )+ charge exchange collisions (A = H, Li, Cs). The open circles denote the theoretical results taken from refs. [12,13].

withR

13 K

0

I

20

I

25

3J

I~(eV) Fig. 4. Cross section versus target atom ionisation energy for z = 10 and at relative impact velocity v 3.79 X iO’~cm/s. The solid circles denote the theoretical results and the solid line represents the empirical dependence taken from ref. [8].

This work is part of the research program partially supported by the International Atomic Energy Agency, Vienna, Austria, under the Contract No. 2043/RB. References [1] Summary Report INDC (NDS)-82/GB of the IAEA Advisory Group Meeting on Atomic and molecular data

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Volume 66A, number 3

[2]

[3] [4] [5] [6] [7]

PHYSICS LETTERS

for fusion (Culham, 1976), ed. A. Lorentz, IAEA Nuclear Data Section (Vienna). M.N. Panov, Proc. VILIth Intern. Summer School on The physics of ionized gases (Dubrovnik, 1976), ed. B. Navinkk (J. Stefan Institute, Univ. of Ljubljana, Yugoslavia) p. 165. A.V. Vinogradov and 1.1. Sobel’man, Soy. Phys. JETP 36 (1973) 1115. R.W. Waynant and R.C. Elton, Proc. IEEE 64 (1976) 1059. H. Klinger, A. Muller and E. Salzborn, J. Phys. B8 (1975) 230. A. MUller and E. Salzborn, Phys. Lett. 59A (1977) 19. E. Salzborn, IEEE Trans. Nuel. Sci. NS-23 (1976) 947.

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[8] A. MUller and E. Salzborn, Phys. Lett. 62A (9177) 391. [91 M.I. Chibisov, Zh. Eksp. Teor. Fiz. Pis’ma 24 (1976) 56 (in russian). [101 T.P. Grozdanov and R.K. Janev, Phys. Rev. A (1978), to be published. (111 B.M. Smirnov, Asymptotical methods in the theory of atomic collisions (Atomizdat, Moscow, 1973) (in russian). [12] A. Salop, R.E. Olson and A. Salin, Proc. Xth Intern. Conf. Phys. electron. Atomic coil. (Paris, 1977), ed. Commissariat a l’energie atomique (Paris, France) p. 534. [13] C. Harel and A. Salin, Proc. Xth Intern. Conf. Phys. Electron. Atomic Coil. (Paris, 1977), ed. Commissariat 1 l’energie atomique (Paris, France) p. 536.