Coupled-State Calculations of Proton-Helium Scattering

Using the impact-parameter method, calculations have been done on the excitation of helium by protons in the kinetic-energy region of 10-10 000 keV. The total wave function of the system is expanded in a set of helium eigenstates including the $n=1\mathrm{}$, $n=2\mathrm{}$, and $n=3\mathrm{}$ (except for $3{}_{}{}^1{}_{}{}^{}S$) states. The resulting linear differential equations (up to 18) have been solved numerically and compared with existing calculations and experiment. It is shown that for higher impact energies the many-state cross sections tend to the Born cross sections, but that for non-allowed transitions discrepancies exist up to very high energy. For allowed transitions, the agreement between theory and experiment is reasonable. Sublevel cross sections are shown to be very sensitive to the number of states retained in the expansion; only at the highest energies for which calculations have been done are they in agreement with Born sublevel cross sections. This fact is also shown by a comparison of calculated and measured polarization fractions of the emitted light induced by the excitations.