Realistic Nuclear Single-Particle Hamiltonians and the Proton Shell 114

A simple self-consistent single-particle equation is investigated and compared with similar attempts. The proposed model is designed to be particularly suitable for the calculation of (adiabatic) fission processes. The kernel of this integrodifferential equation has a structure that allows satisfactory reproduction, with one constant set of five physical parameters, of (1) charge density distributions, including isotope shifts, (2) $1s$ proton levels as measured in ($e,e^{\prime }p$) scattering, (3) total binding energies or nuclear mass defects, and (4) the shell-model spin assignments and mass structure throughout the periodic table. Hence, it seems that all future work in this direction has to confirm quantitatively the essential features determined here, particularly the nonlocality and rearrangement effects. Rearrangement energies appear explicitly, since the present model, like self-consistent fields of appropriate many-body formalisms, yields different eigenvalue spectra and mass defects for different occupation functions. The partial derivative $\frac{\partial E}{\partial Z}$ of the total binding energy (mass) changes considerably at the proton number $Z=114\mathrm{}$ when the present Hamiltonian is used for superheavy nuclei. This confirms an earlier suggestion made by this author on the basis of a gap in the proton eigenvalue spectrum at $Z=114\mathrm{}$. The present calculations show that this shell effect becomes insignificant for isotopes too far from the extrapolated $\beta$ stability line, in particular for $N\lesssim 172$.