Quantum manifestations of bifurcations of closed orbits in the photodetachment cross section of H{sup {minus}} in parallel fields
- Department of Chemistry, West Virginia University, Morgantown, West Virginia 23506 (United States)
- Colorado Northwest Community College, Craig, Colorado 81625 (United States)
- Hyperfine, Inc., 4946 N 63rd Street, Boulder, Colorado 80301-1843 (United States)
- Department of Physics and Chemistry, Kean College, Union, New Jersey 07083 (United States)
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187 (United States)
- JILA, University of Colorado, Boulder, Colorado 80309-0440 (United States)
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. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 531775
- Journal Information:
- Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 56; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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