Cross Sections in the Quantum Theory of Scattering

Volker Enß, Barry Simon A

A.S. Davydov

K. Shigemura, M. Kitajima, M. Kurokawa +7 more

Absolute total cross sections for electron scattering from He and Ne are obtained in the energy range from 20 eV down to below 10 meV with a very narrow electron energy width of 6--8 meV using the threshold-photoelectron source. Total cross sections obtained in the present study generally agree well with those obtained in the previous experiments for both He and Ne above 100 meV, where several experimental works have been reported. Comparison of the present cross sections with the theoretical cross sections which have been regarded as the ``standard'' cross sections shows very good agreement even at very low energies below 10 meV, which confirms the validity of theoretical cross sections. The scattering lengths for electron scattering from He and Ne are also determined from the present total cross sections using the modified effective range theory. The resonant structures in the total cross sections due to Feshbach resonances of He and Ne are also observed. Analysis of the resonant structure was carried out based on the spin-dependent resonant scattering theory in order to determine the values of natural width of Feshbach resonance of Ne.

W. N. Mei, Glenn A. Sowell

Applying the commonly used partial wave method in the quantum theory of collisions, the scattering cross-sections of the two- and three-dimensional attractive and repulsive potentials are expressed as sums of phase shifts. With the help of the Maple software program, the phase shifts and cross-sections are plotted as functions of the kinetic energy and potential height, and it is demonstrated that the systematic convergence of the cross-sections as higher angular-momentum phase shifts are included in the summations. It is found that the cross-sections of the attractive potential oscillate with both the kinetic energy and the potential strength, even though the phase shifts are monotonic. It is also shown that in the case of the repulsive potential, both the phase shifts and cross-sections change profoundly when the kinetic energy of the incident particle is lower than the potential height.

Carl M. Penney

Quantum-mechanical expressions for nonresonance-dipole light-scattering cross sections are related to corresponding expressions for oscillator strengths and refractive indices. In particular, Rayleigh and Raman cross sections for atoms are expressed in terms of oscillator strengths and vector-coupling coefficients. Several of our results, including the relationship between Rayleigh scattering and refractive index, differ in general from the corresponding results of classical dispersion theory. We show that these differences arise from antisymmetric components Ckja = (Ckj − Cjk)/2 of the polarizability tensor, which have been neglected in the classical analyses. Calculated Rayleigh cross sections for cesium and aluminum atoms, and Raman cross sections for aluminum atoms are presented to illustrate our results. The antisymmetric contribution is found to be substantial in all of these cross sections; its most obvious effect is to cause the depolarization (for linearly polarized incident light) to exceed 34 over extended wavelength ranges away from resonance. On the other hand, for atoms initially in states of zero angular momentum, and molecules under conditions which allow the use of Placzek’s polarizability approximation, our results agree with those of classical dispersion theory.