Uniform stationary-phase methods for energy spectra resulting from collisions in a complex potential: Penning and associative ionization of He*(23S)+He*(23S)

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Abstract
Heavy-particle collisions involving strong electronic coupling can be conveniently described by using a complex (optical) potential in the entrance channel. Uniform JWKB stationary-phase techniques are used to evaluate T-matrix elements for transitions where an electron is ejected. The semi-analytic expressions for the resulting electron energy spectra are no more difficult to implement than corresponding ones for totally real potentials. Numerical results are reported for Penning and associative ionization from subthermal He*(23S)+He*(23S) collisions. These are in excellent agreement with fully quantal, complex-potential computations. The stationary-phase expressions for T-matrix elements and differential cross sections are employed to elucidate the rapid and slow rainbow interference oscillations in the spectra, including the significant effects of turning points and the imaginary width of the entrance-channel potential.