Use of Electron Scattering Data to Obtain Accurate Born Cross Sections for Atom-Atom and Other Heavy-Particle Collisions. II. Breakup of FastH2+upon Collision with He

Abstract

In an earlier paper it was suggested that, in Born calculations of total cross sections for heavy-particle collisions, it might be more practical, if accuracies of the order of 10% are acceptable, to obtain the necessary matrix elements by measuring differential electron-atom and electron-molecule cross sections than it would be to calculate the matrix elements from the wave functions of the initial and final atomic or molecular states. In this paper the foregoing idea is explored for ${\mathrm{H}}_{2}^{+}$-He collisions. Experimental electron cross sections are used only for He, theoretical ones being used for ${\mathrm{H}}_{2}^{+}$. Since Lassettre's electron-He measurements do not extend to large enough momentum transfers to allow calculation of the ${\mathrm{H}}_{2}^{+}$-He total cross sections for all transitions of interest, theory is introduced to provide quantitative extrapolations of the experimental data to larger momentum transfers. By this means the extent to which the ${\mathrm{H}}_{2}^{+}$-He total cross sections are determined by the unextrapolated electron-He measurements is examined. At the same time, ranges of momentum transfer are determined, over which the electron-He cross sections need to be measured if they are to be adequate for ${\mathrm{H}}_{2}^{+}$-He total cross-section calculations, without the use of quantitative extrapolation. By a generalization of the ${\mathrm{H}}_{2}^{+}$-He results, analogous ranges are determined for the electron scattering measurements relevant to most heavy-particle collisions of practical interest. The general results show that the most extensive of Lassettre's electron excitation measurements are adequate for heavy-particle collisions in which both collision partners undergo transitions to discrete excited states. Measurements of electron cross sections out to larger momentum transfers than this are required, however, for other combinations of the possible final states of the colliding particles. A table of the upper limits of the required ranges of momentum transfers is given in the hope that it may stimulate additional experimental work. Of particular importance is the measurement of differential electron ionization cross sections out to large values of momentum transfer and energy loss. From the ${\mathrm{H}}_{2}^{+}$-He cross sections, theoretical cross sections are obtained for the breakup of ${\mathrm{H}}_{2}^{+}$ via electronic excitation during collisions with He. These are compared with experiment.