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Journal of the Physical Society of Japan

Theory of Excitation Transfer between Atoms by Collision

Hiroki Nakamura

Published Jun 15, 1968• 19 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.24.1353

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Journal of the Physical Society of Japan•Dec 1, 1965•26 citations
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.
Formulas are derived for the differential and integral cross sections associated with laser-induced excitation transfer. The theory is patterned closely after our recent treatment of laser-induced chemi-ionization. It is found that cross sections specific to single-photon absorption are proportional to the square of the cosine of the angle between the laser polarization and the initial relative velocity of the two colliding atoms. The distortion by a laser of the cross section for an elastic scattering event also is treated. Finally, a cross-section formula is derived for a collision-induced two-photon absorption, mediated by a single intermediate electronic state.
The excitation transfers through collision between hydrogen atoms and between other simple identical atoms are considered theoretically by an impact parameter method. A rotating atom approximation and a fixed atom approximation (concerned with the direction of electronic polarization) are applied to the problem. The cross-section for the transfer of the excitation (2 p 2 P ) of a hydrogen atom with thermal velocity (kinetic energy of 0.025 ev) to the other hydrogen atom in the ground state is estimated to be 3065 Å 2 with the rotating atom approximation and 680 Å 2 with the fixed atom approximation. In the case of helium atoms, the cross-section for the transfer of the excitation (2 p 1 P ) is also estimated to be 606.7 Å 2 with thermal velocity.
A two-level model of an atomic system is investigated in order to study the cross section for certain inelastic collision processes. An impact-parameter method is employed. The time-dependent Schr\"odinger equation has been integrated numerically for some simple interaction potentials. Cross sections for excitation have been determined and are presented as functions of the parameters describing the model. The results are compared with those obtained by certain approximate methods. The effects of inclusion of diagonal matrix elements in the interaction Hamiltonian are found to be large. For a fixed form of the interaction potential, two cross sections, which may differ quite substantially, are obtained, depending on the algebraic sign of the coupling parameters or the energy difference between the states.
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 cross sections for the excitation transfer between unlike atoms are calculated by the impact parameter method. Approximate formulas for discrete-continuum and discrete-discrete transition probabilities are obtained. The cross section can be obtained by integrating this probability over the impact parameter. The approximate formula is applied to the case of Deuterium-Hydrogen excitation transfer as one of practical examples. Comparisons are made with two other formulas, i. e. Rosen-Zener (R-Z) and Vanishtein-Presnyakov-Sobelman (V-P-S) formulas. The dependence of the cross section on the resonance defect in the discrete-discrete case is also investigated. The agreements among these three formulas are found not very good.