A general formula for the calculation of atomic photo-ionization cross-sections
Abstract
The general formula is derived by considering the model of a single electron moving in a central field. Approximate bound-state radial functions, accurate for large radial distances, may be obtained once the effective quantum numbers v( = n *) are known. Bates and Damgaard have shown that such functions may be used to obtain good estimates for bound-bound transition integrals. For bound-free transitions use is made of approximate free-state radial functions having exact asy1nptotic forms, their phases being given by 5= where M is the extrapolated quantum defect ( =n - v). The results of extensive numerical calculations are summarized in tables which permit the rapid calculation of transition integrals once the energy levels are known. Both bound-free and bound-bound transition integrals may be obtained. For bound-bound transitions ' good agreement is obtained with the Bates and Damgaard tables for v - V' > . Comparisons are made with other results for bound-free transitions, as obtained both from theory and from experiment. in nearly all cases the general formula gives results at least as accurate as those obtained in the best alternative methods of calculation.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- 1960
- DOI:
- 10.1093/mnras/120.2.121
- Bibcode:
- 1960MNRAS.120..121B