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On the effect of the electron bound state structure on ionization cross sections in atomic collisions
Volume 31A. number 10
PHYSICS
LETTERS
ON THE EFFECT OF THE ELECTRON ON IONIZATION CROSS SECTIONS
18 May 1970
BOUND STATE STRUCTURE IN ATOMIC COLLISIONS
V. S.SENASHENKO, V. S.NIKOLAEV and V.Yu. SHAFER of Nuclear Physics, Moscow State University . Moscow. USSR
Institute
Received 11 March 1970
The cross sections for Is- and %-electron loss by various hydrogen-like ions colliding with H and He have been calculated and compared. An exact expression is given for the square of the matrix element of the 2s-electron transition to the continuum states.
In order to determine the theoretical dependence of ionization cross sections on the structure of the electron initial state, we have calculated the cross sections for 2s-electron loss by various hydrogenlike ions colliding with hydrogen and helium atoms and compared them with the previously computed [l] cross sections for Is-electron loss. Calculations were performed in a non-relativistic Born approximation with Coulomb wave functions for the initial and final states of the electron [l]. An exact analytical expression was obtained for the square of the matrix element I&f12 corresponding to the transition of a 2s-electron to the continuum state with momentum Kin collisions with transfer of momentum Q to the ion. Integrating this expression over the angular variables RK of the momentum space K yields:
/
k”f 2K2dKdnK
= ~2(q>k)dk =
s1K
~{2~l~-(llk~
+32)q*+
14k4+72$+82)q6-(6k6+40k4+62k2-20)q4
+
(1)
-(kB+8k6+!$k4-$)q2+(k10+8k8+22k6+28k4+17k2+4)}dk, where q = Q/po(Z/n), k =li/po(Z/n), p. = pe2/fi, Ze is the ion nucleus charge, and n the principal quantum number of the electron bound state. Expression (1) coincides with the expression obtained earlier by Burhop [4] and differs from the expression used by Khandelwal and Merzbacher [2]. The latter gives erroneous results at q?Z, in consequence of which the magnitude of the integral j,“c2(q,k)dk at i>> Z becomes close to i rather than t&e on the correct asymptotic value equal to unity. It follows from our calculations that an appreciable difference between the cross sections for electron loss from different states at an equal binding energy takes place only in the case of slow collisions when 21= V/(Z/n)v, 50( V/v)2eV a much greater difference between the Is- and Zs-electron loss cross sections may be anticipated.
565
Volume
31A, number 10
PHYSICS
LETTERS
18 May 1970
Fig. 1. Values of (Z/n)4a for loss of Is- and 2s-electrons by hydrogen-like ions in atomic hydrogen as a function of V/t*,(Z/n). The solid curve represents the cross section for 2s-electron loss and the dashed curve, for ls-electron loss. The numbers near the curves denote values of Z/n. The momentum distribution for the Is- and Ss-electrons is also shown in the figure.
References 1. 2. 3. 4.
I. S. Dmitriyev, Ya. M. Zhlleikin and V. S. Nikolayev, Zh. Eksp. i Teor. G. S. Khandelwal and E. Merzbacher, Phys. Rev. 151 (1966) 12. V. S. Nikolayev, Uspekhi Fiz. Nauk 85 (1965) 639. E. H. S. Burhop, Proc. Cambr. Phyl. Sot. 36 (1940) 43.
*****
566
Fiz. 49 (1965) 500.
PHYSICS
LETTERS
ON THE EFFECT OF THE ELECTRON ON IONIZATION CROSS SECTIONS
18 May 1970
BOUND STATE STRUCTURE IN ATOMIC COLLISIONS
V. S.SENASHENKO, V. S.NIKOLAEV and V.Yu. SHAFER of Nuclear Physics, Moscow State University . Moscow. USSR
Institute
Received 11 March 1970
The cross sections for Is- and %-electron loss by various hydrogen-like ions colliding with H and He have been calculated and compared. An exact expression is given for the square of the matrix element of the 2s-electron transition to the continuum states.
In order to determine the theoretical dependence of ionization cross sections on the structure of the electron initial state, we have calculated the cross sections for 2s-electron loss by various hydrogenlike ions colliding with hydrogen and helium atoms and compared them with the previously computed [l] cross sections for Is-electron loss. Calculations were performed in a non-relativistic Born approximation with Coulomb wave functions for the initial and final states of the electron [l]. An exact analytical expression was obtained for the square of the matrix element I&f12 corresponding to the transition of a 2s-electron to the continuum state with momentum Kin collisions with transfer of momentum Q to the ion. Integrating this expression over the angular variables RK of the momentum space K yields:
/
k”f 2K2dKdnK
= ~2(q>k)dk =
s1K
~{2~l~-(llk~
+32)q*+
14k4+72$+82)q6-(6k6+40k4+62k2-20)q4
+
(1)
-(kB+8k6+!$k4-$)q2+(k10+8k8+22k6+28k4+17k2+4)}dk, where q = Q/po(Z/n), k =li/po(Z/n), p. = pe2/fi, Ze is the ion nucleus charge, and n the principal quantum number of the electron bound state. Expression (1) coincides with the expression obtained earlier by Burhop [4] and differs from the expression used by Khandelwal and Merzbacher [2]. The latter gives erroneous results at q?Z, in consequence of which the magnitude of the integral j,“c2(q,k)dk at i>> Z becomes close to i rather than t&e on the correct asymptotic value equal to unity. It follows from our calculations that an appreciable difference between the cross sections for electron loss from different states at an equal binding energy takes place only in the case of slow collisions when 21= V/(Z/n)v,
565
Volume
31A, number 10
PHYSICS
LETTERS
18 May 1970
Fig. 1. Values of (Z/n)4a for loss of Is- and 2s-electrons by hydrogen-like ions in atomic hydrogen as a function of V/t*,(Z/n). The solid curve represents the cross section for 2s-electron loss and the dashed curve, for ls-electron loss. The numbers near the curves denote values of Z/n. The momentum distribution for the Is- and Ss-electrons is also shown in the figure.
References 1. 2. 3. 4.
I. S. Dmitriyev, Ya. M. Zhlleikin and V. S. Nikolayev, Zh. Eksp. i Teor. G. S. Khandelwal and E. Merzbacher, Phys. Rev. 151 (1966) 12. V. S. Nikolayev, Uspekhi Fiz. Nauk 85 (1965) 639. E. H. S. Burhop, Proc. Cambr. Phyl. Sot. 36 (1940) 43.
*****
566
Fiz. 49 (1965) 500.