QUANTUM MANIFESTATIONS OF BIFURCATIONS OF CLOSED ORBITS IN THE PHOTODETACHMENT CROSS-SECTION OF H- IN PARALLEL FIELDS

In the preceding paper, we showed that the semiclassical approximation diverges at a bifurcation, and that this divergence coincides with th e passage of a focused cusp through the origin. Here we obtain a wave function in the vicinity of this cusp, and we use that wave function t o eliminate the divergences in the photodetachment cross section. To d escribe the focused cusp, we first discuss the wave function of an ord inary two-dimensional (nonfocused) cusp. This wave function is known a s a Pearcey function, and it has been studied extensively. Then we sho w how the formulas that lead to the Pearcey function have to be modifi ed to describe a cylindrically focused cusp. The resulting wave functi on turns out to be given by an integral of Fresnel type containing wit hin it a cylindrical Bessel function. This wave function is used to de rive a formula for the photodetachment cross section near a bifurcatio n. That formula is a simple closed-form expression containing a Fresne l integral. Comparison with exact quantum calculations shows that this corrected-semiclassical formula is quite accurate.