Bound states of a uniform spherical charge distribution - revisited!

In this note, we revisit modeling the nucleus as a uniformly charged sphere : in order to examine finite nuclear size effects on atomic binding energie s. We use nonrelativistic quantum mechanics to extract binding energies of a negatively charged lepton bound by a uniform-sphere potential. Energies a re determined by using MATHEMATICA to match interior and exterior solutions at the nuclear radius. Muonic lead and tin binding energies are found, as are their fine-structure transition energies, and compared with experimenta l data. In the course of our reinvestigation of this problem, we came upon several subtle features of using infinite (especially asymptotic) series fo r numerical evaluation. Effective handling of these features is made practi cal both by using certain analytic transformations and the powerful compute r programs currently available. We believe that these technical observation s are of value to a wider class of problems beyond the ones considered in d etail in this paper. (C) 2000 American Association of Physics Teachers.