Multistate curve-crossing model for scattering: Associative ionization and excitation transfer in helium

A model has been derived to treat the multistate curve-crossing problem which often arises in diabatic representations of scattering processes. Transitions between diabatic states are assumed to occur only in the vicinity of curve crossings and the probabilities are evaluated semiclassically. Otherwise the nuclear trajectories are treated classically except for tunneling through long-range potential barriers taken into account by the JWKB approximation. Closed channels are included on an equal footing with the scattering channels. The model is applied to the problems of symmetric associative (and dissociative) ionization and excitation transfer in collisions of excited helium with the ground-state atom, using the diabatic representation for the Rydberg states of ${\mathrm{He}}_2$ presented in the preceding paper. The electronic coupling of the repulsive diabatic states in the continuum yields much larger ionization cross sections than does direct vibronic coupling of low-lying adiabatic states to the continuum. The diabatic-states model is shown to be a valid interpretation of associative ionization in helium. Ionization has a significant effect on some excitation-transfer cross sections. Integrated cross sections are presented for ionization of helium in the $n{}_{}{}^3{}_{}{}^{}S$, $n{}_{}{}^3{}_{}{}^{}P$, and $n{}_{}{}^3{}_{}{}^{}D$ states, $n=3, 4$, and for excitation transfer from the $n=3\mathrm{}$ states to states with $2\le n\le 4$ for collision energies from thermal to 100 eV. The thermally averaged associative ionization cross sections, in units of ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, obtained at 300°K are as follows: ${\overline{Q}}_i\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)=0.06\mathrm{}$, ${\overline{Q}}_i\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)=2.0\mathrm{}$, ${\overline{Q}}_i\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)=2.9\mathrm{}$, ${\overline{Q}}_i\left(4\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)=0.6\mathrm{}$, ${\overline{Q}}_i\left(4\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)=1.7\mathrm{}$, and ${\overline{Q}}_i\left(4\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)=4.3\mathrm{}$. The results are in quite satisfactory agreement with recent experiments.