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Proceedings of the National Academy of Sciences

On the Quantum Theory of the Ramsauer Effect

J. Robert Oppenheimer

Published Mar 1, 1928• 2 citations
Publisher

Abstract

The Ramsauer effect does not correspond to the decrease in optical scattering by a particle when the wave-length of the light is increased. For one may compute the cross-section for elastic collision of an electron with an atom, without making the approximations used by Born. If one does this, and neglects the resonance of the colliding electron with the atomic electrons one finds that, for atoms with no dipole moment in the normal state, the cross-section approaches a finite limit when the electronic velocity is decreased. The only general result of this calculation is that the distribution of scattered electrons tends, in this limit, to become uniform over all angles.

DOI
10.1073/pnas.14.3.261

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The Ramsauer effect does not correspond to the decrease in optical scattering by a particle when the wave-length of the light is increased. For one may compute the cross-section for elastic collision of an electron with an atom, without making the approximations used by Born. If one does this, and neglects the resonance of the colliding electron with the atomic electrons one finds that, for atoms with no dipole moment in the normal state, the cross-section approaches a finite limit when the electronic velocity is decreased. The only general result of this calculation is that the distribution of scattered electrons tends, in this limit, to become uniform over all angles.
Abstract An outstanding defect of the old quantum theory was its inability to treat the phenomena occurring in the collision of electrons with atoms, and Born’s theory showed how the new quantum mechanics was capable of removing this defect. The original theory of Born was a method of successive approximations to the solution of the wave equation representing the colliding systems, and could be applied to both elastic and inelastic collisions. In its actual applications, which could be worked out to the first approximation, the theory fell far short of expectations. The Ramsauer effect, the most interesting phenomenon exhibited in the elastic scattering of electrons, could not be explained, and in the field of inelastic collisions, it failed to provide a means of explaining the excitation of levels of a term system which does not combine with the ground state system, e. g., the excitation of the triplet lines of helium. These failures are, of course, failures of the theory in its first approximation. The first approximation in Born’s method of successive approximations neglected the disturbance of the electron waves by the field of the scatterer, and also the possibility of exchange of electrons between the atoms and the colliding beam. The neglect of both these effects becomes important for low velocity impacts, and it was clear that the Ramsauer effect, which is only observed for low velocity electrons, could only be explained by more accurate theory. The question was whether both effects, the distortion of the electron waves by the atomic field, and the exchange of electrons was important, or only one of them.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, Fd{F}_{d}Fd​ and Fx{F}_{x}Fx​. All cross sections must be expressible in terms of ∣Fd∣|{F}_{d}|∣Fd​∣ and ∣Fx∣|{F}_{x}|∣Fx​∣, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.
A theory of inelastic n,l-changing and quasielastic l-mixing collisions of Rydberg atoms with the heavy rare-gas atoms is developed. It is based on the semiclassical impact-parameter approach combined with the normalized perturbation theory. Semiclassical formulas for scaled transition probabilities and cross sections as functions of the inelasticity parameter and the collision strength are analyzed. This approach gives a general description of collisional nl\ensuremath{\rightarrow}${\mathit{n}}^{\ensuremath{'}}$ transitions independently of the specific values of the principal quantum number, the relative velocity, and the type of colliding atoms. The energy and angular dependence of the electron-atom scattering amplitude is included in the theory by incorporating the impulse-approximation results in the weak-coupling limit. The Ramsauer-Townsend effect affects significantly the values of the cross sections, especially for the inelastic transitions with large energy transfer. The results obtained are used in calculations of the quenching cross sections for the Rb(nS,nD,nF) atoms in collisions with Ar, Kr, and Xe. Comparison of theory and experiment is made in a wide range of the principal quantum numbers and transition energy defects. \textcopyright{} 1996 The American Physical Society.