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Journal of the Physical Society of Japan

Collisional Excitation Transfer between Atoms in the Resonant Process

Masatake Mori, Tsutomu Watanabe, Kanji Katsuura

Published Mar 1, 1964• 20 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.19.380

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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.
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.
Resonant energy transfer collisions, those in which one atom or molecule transfers only internal energy, as oppposed to translational energy, to its collision partner require a precise match of the energy intervals in the two collision partners. Because of this energy specificity, resonant collisional energy transfer plays an important role in many laser applications, the He–Ne and CO 2 lasers being perhaps the best known examples. It is interesting to imagine an experiment in which we can tune the energy of the excited state of atom B through the energy of the excited state of atom A, as shown in Fig. 14.1. At resonance we would expect the cross section for collisionally transferring the energy from an excited A atom to a ground state B atom to increase sharply as shown in Fig. 14.1. In general, atomic and molecular energy levels are fixed, and the situation of Fig. 14.1 is impossible to realize. Nonetheless systematic studies of resonant energy transfer have been carried out by altering the collision partner, showing the importance of resonance in collisional energy transfer. The use of atomic Rydberg states, which have series of closely spaced levels, presents a natural opportunity for the study of resonant collisional energy transfer. One of the earliest experiments was the observation of resonant rotational to electronic energy transfer from NH 3 to Xe Rydberg atoms by Smith et al .
The collision of a proton with a hydrogen atom in the presence of electromagnetic radiation which is nearly resonant with the atomic levels is investigated theoretically. The non-perturbative quasi energy method is used to describe the laser-atom interaction and the proton-dressed atom collision is solved using a diagonalization technique. We have calculated the transition probabilities and the total cross-section for various transitions. We discuss the influence of various laser and collision parameters on the excitation process.
The absolute cross section for the energy transfer between the nP Rydberg atom (n=35--60) and the ground-state (5S) atom of rubidium is measured to be 4.8\ifmmode\times\else\texttimes\fi{}102{10}^{2}102 A˚2{\r{}}^{2}˚2 for thermal collisions at 420 K. This value of the cross section is in agreement with the calculated value for resonant charge transfer at the relevant collision energy. It is concluded that the energy transfer process is essentially charge transfer between the Rydberg ion core and the ground-state atom, where the Rydberg electron stays as a spectator.
Energy transfer and coherence transfer between two atoms of different species are studied theoretically. The electric dipole-dipole interaction is the mechanism considered for the excitation transfer. A generalized perturbation method for a damping system is used. A general formula is derived for the polarization of the sensitized fluorescence resulting from the excitation transfer. This polarization is shown to be dependent on the angular momenta of the two atoms, and to be independent of their relative velocity as well as of their difference in the energy of excitation. The polarizations are found to be nonzero in many cases which demonstrate the transfer of coherence through collision processes. A general and compact formula is also derived for the polarization of pure fluorescence where excitation exchange has not taken place. The polarization of the sensitized fluorescence is in general smaller than that of the pure fluorescence. This means that the coherence is transferred only partially. Finally, the magnetic field effect has been included. This field depolarization depends on the gj{g}_{j}gj​ values and the lifetimes of the excited states of both atoms. The general feature of the field dependence also differs considerably from that of the Hanle effect for resonance fluorescence.