Document Type

Article

Department/Program

Physics

Journal Title

Physical Review A

Pub Date

7-1997

Publisher

American Physical Society

Volume

56

Issue

1

First Page

345

Abstract

In the preceding paper, we showed that the semiclassical approximation diverges at a bifurcation, and that this divergence coincides with the 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 to eliminate the divergences in the photodetachment cross section. To describe the focused cusp, we first discuss the wave function of an ordinary two-dimensional (nonfocused) cusp. This wave function is known as a Pearcey function, and it has been studied extensively. Then we show how the formulas that lead to the Pearcey function have to be modified to describe a cylindrically focused cusp. The resulting wave function turns out to be given by an integral of Fresnel type containing within it a cylindrical Bessel function. This wave function is used to derive a formula for the photodetachment cross section near a bifurcation. That formula is a simple closed-form expression containing a Fresnel integral. Comparison with exact quantum calculations shows that this corrected-semiclassical formula is quite accurate.

DOI

https://doi.org/10.1103/PhysRevA.56.345

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