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Physical Review A

Ionization collisions between two excited atoms: Application of the Glauber amplitude in the framework of the impulse approximation

Toshizo Shirai, Yohta Nakai, Hiroki Nakamura

Published Oct 1, 1984• 5 citations
Publisher

Abstract

The cross-section formula of Flannery [Phys. Rev. A 22, 2408 (1980)] in the semiquantal approximation for the processes referred to in the title is rewritten so as to make it more useful in practice. The formula is shown to be further simplified by taking an average over the azimuthal quantum number of a highly excited hydrogenic atom to be ionized. Numerical applications with use of the Glauber amplitude for the electron-atom inelastic scattering are made to the ionization collisions between two excited hydrogen atoms with simultaneous excitation and deexcitation of one of the atoms. The results are compared with those obtained by using the Born amplitude, and are analyzed in terms of the Glauber generalized oscillator strengths.

DOI
10.1103/physreva.30.1672

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The cross-section formula of Flannery [Phys. Rev. A 22, 2408 (1980)] in the semiquantal approximation for the processes referred to in the title is rewritten so as to make it more useful in practice. The formula is shown to be further simplified by taking an average over the azimuthal quantum number of a highly excited hydrogenic atom to be ionized. Numerical applications with use of the Glauber amplitude for the electron-atom inelastic scattering are made to the ionization collisions between two excited hydrogen atoms with simultaneous excitation and deexcitation of one of the atoms. The results are compared with those obtained by using the Born amplitude, and are analyzed in terms of the Glauber generalized oscillator strengths.
The title process with simultaneous rotational deexcitation of molecules was investigated theoretically by using the semiquantal approximation. The dipole Born and dipole Glauber differential cross sections were employed for the electron-molecule rotational deexcitation process. Numerical applications were made to the following systems: Xe+CO, HCl, HF, and LiF. A comparative study of the two approximations was carried out concerning the dependences of the cross sections on the following various quantities: n (principal quantum number), J (initial rotational quantum number), \ensuremath{\Delta}J (rotational quantum number change), D (dipole moment), V (relative collision velocity). As the molecular dipole moment becomes larger, there appears a prominent difference in the n dependence of the cross section. The Glauber approximation brings about a decrease in the cross section and yields a sawlike n dependence in contrast to a steplike n dependence in the case of the Born approximation. In the collisions involving lowly excited Rydberg atoms, ionization with simultaneous dipole-forbidden transition of a molecule becomes dominant compared to the ionization with simultaneous dipole-allowed transition. The cross section was found to be inversely proportional to the relative collision velocity; thus the ionization rate becomes independent of temperature. A comparison was also made between the experiment for the ionization rate at 300 K for Xe(27f)+HF and Xe(31f)+HCl.
For pt.I see ibid., vol.14, p.985 (1981). A general theory of the Rydberg atom inelastic scattering by perturber atoms has been developed previously, in which the leading term is the simple impulse amplitude, followed by the various correction terms. Theoretical estimates of these correction terms are presented in this paper, resulting in a general scaling formula. The non-impulse correction to the impulse approximation varies as n -2 at large principal quantum number n and depends on the signature of the electron-perturber scattering length. The distortion correction due to the interaction between the perturber and the Rydberg atomic core is large for the intermediate values of n<or approximately=20 behaves as n -4 , and depends on the perturber-core total cross section. The scaling formula derived here has been tested for the scattering systems consisting of Na and Rb targets and inert gas perturbers.
Excitation transfer process between atoms is investigated theoretically in the framework of the two-state approximation. Two methods are proposed with regard to the treatment of the non-local potential which results from the projection-operator formalism. One is a local potential approximation and the other is an extension of the method of Chadan. A new expression for the cross section is found. This formula is more accurate than the usual distorted wave one. The matrix elements of a coupling potential with respect to the wave functions of the relative motion are estimated by making use of the JWKB approximation. The new cross section formula obtained will be useful for a wide class of collision processes in which initial and final states are mutually orthogonal.
This paper contains a generalization of results described in previous work. A general formula is given for the total cross section for two-photon ionization of a hydrogenic state. An implicit method for evaluating the second-order radial matrix elements that occur in this expression is described in detail. Numerical results were obtained for the states with principal quantum numbers n = 1 through 5. It is concluded that, when both one-photon and two-photon ionization are energetically possible, the effect of the latter may be expressed as an intensity-dependent correction to the Gaunt factor which may therefore be written as G = g1 + ζIλ3g2. Here g1 is the usual Gaunt factor, I is the intensity of the light in W cm−2, λ is the wavelength in cm, g2 is a dimensionless factor of order unity, and ζ is a constant given by ζ = 0.1504 W−1 cm−1. Graphs of g2 are given as a function of electron energy. These results do not include the effect of three-photon processes, which can also contribute to the first-order intensity-dependent correction to the Gaunt factor as a result of interference between the first- and third-order amplitudes.
A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where AAA is an excited atom of an alkali metal and BBB is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.