Independent-Particle-Model Energy-Level Formula

The Morse function is assumed to approximate a nonlocal or velocity-dependent nucleon-nuclear potential. Analytic neutron and proton wave functions and eigenvalue formulas are obtained for all states of all nuclei, using a modified version of an analytic perturbation method due to Pekeris. The eigenvalue formula is in approximate agreement with the following experimental data: (1) the last-particle binding energies of neutrons and protons, (2) the neutron and proton magic numbers, (3) the positions of the $S$-wave-size resonances in total-neutron-cross-section data, and (4) the recent experimental work on deeply bound inner particle states by Amaldi et al. The eigenvalue formula gives results that are consistent with recent Hartree-Fock calculations.