Marvin H. Mittleman

Effects of the Pauli principle on the scattering of high-energy electrons by atoms☆

Abstract Some consequences of the Pauli principle for the elastic scattering of electrons by atoms are studied. The contributions both from the exchange integrals and from the Hartree-Fock condition that the scattered wave be orthogonal to the bound-state wave functions are expressed in a simple approximate form. For high-energy electrons these corrections are very small.

Coupled equations for rearrangement collisions. II

Abstract A projection operator which projects out direct and rearranged scattering from the total wave function is derived. It is much simpler than one previously presented; however, this new method has certain limitations, the most important one being that the recoil of the target must be neglected.

The scattering of electrons by atomic hydrogen

Abstract A method is presented which reduces the problem to the scattering of a single electron in an equivalent potential. The complexities of the electron-electron interaction are embodied in this potential. An exact expression is given for the potential, and various approximation methods are discussed. The adiabatic approxmation is investigated and the imaginary part of the potential is examined.

Electron capture by helium ions in neutral helium

Two distinct calculations are described in this paper. The first describes He+ + He by a two-atomic-state approximation. It modifies a previous calculation in order to include properly the Pauli principle. It is found that multiple electron exchange which this introduces is not important for the total cross section but is for angular distribution. The second calculation describes He2+ + He by a three-atomic-state approximation, allowing for both single and double exchange. It is found that ignorance of He exact wave functions causes conceptual difficulties in the calculation.

Scattering of H+ by H

Abstract An attempt is made to describe the H + on H collision in the intermediate energy range where neither the high energy nor the low energy theories are expected to work. A wave function that gives good results at both high and low energies is used in a variational expression to obtain intermediate energy results. This problem is considered as a prototype of ion-parent atom collisions where in general molecular wave functions are not available. Hence only atomic wave functions are used throughout. Results are presented for exchange to the ground state, total exchange, total ionization, and total nonexchange excitation. An attempt is also made to describe Everharts experiment. A “damping” of the resonances is obtained with some improvement over previous results.

Calculation of thep+H2→H−+2pReaction Cross Section

A method recently presented for calculation of double-charge transfer cross sections is applied to this reaction. The method neglects correlation between the two transferred particles. The amplitude for two-particle exchange is then obtained as the square of the amplitude for single-particle exchange. The one-particle exchange amplitude is calculated in Born approximation, and in a modified Born approximation (modified to correct for nonorthogonality), and the two-particle exchange cross section is obtained from these. Neither calculation should be good at the energies at which the cross section was measured, but the two calculations straddle the measured values. The corrected one appears to give a good agreement at the higher measured energies.

Calculation of the p + H 2 → H − + 2 p Reaction Cross Section

A method recently presented for calculation of double-charge transfer cross sections is applied to this reaction. The method neglects correlation between the two transferred particles. The amplitude for two-particle exchange is then obtained as the square of the amplitude for single-particle exchange. The one-particle exchange amplitude is calculated in Born approximation, and in a modified Born approximation (modified to correct for nonorthogonality), and the two-particle exchange cross section is obtained from these. Neither calculation should be good at the energies at which the cross section was measured, but the two calculations straddle the measured values. The corrected one appears to give a good agreement at the higher measured energies.