Eur. Phys. J. D 3, 105-111 (1998)
https://doi.org/10.1007/s100530050153

On the continuity in energy of the free-bound one-photon cross-sections

¹ Faculty of Physics, University of Bucharest, P.O. Box 5211, Bucharest-Magurele, 76900, Romania
² Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

Corresponding author: ^a flor@barutu.fizica.unibuc.ro

Received: 13 February 1998
Accepted: 14 May 1998
Published online: 15 August 1998

Abstract

For a charged particle in a central field of force we discuss the continuity in energy of the cross-sections for the related processes of ground state photoeffect and radiative capture. This continuity follows from general arguments, while for a Coulomb potential, where exact analytic expressions are available, the continuity can also be traced explicitly through the calculation. Our analysis allows us to identify an error in papers on radiative muon capture in the ground state which claim the existence of a discontinuity in the cross-section, occurring in hydrogen for muon energies in the neighbourhood of 2.8 keV. As a discontinuity in radiative capture would imply a discontinuity in atomic photoeffect, we note that in the latter case there are extensive experimental results in good qualitative agreement with the usual continuous result (Stobbe formula) for the cross-section.