A new semiempirical shell correction to the droplet model: Gross theory of nuclear magics

Abstract

A new semiempirical atomic mass formula is presented. Special emphasis has been put on a theoretical basis for the microscopic (shell-correction) part, which is added to the macroscopic droplet-model expression. The latter includes the response to the surface diffuseness. The shell function, which is simple and analytic, is derived by bunching the average single-particle spectrum of nuclei with correct size according to the magic numbers. Shell effects from the inner shells are taken care of. In addition, ideas of changing magicities along neutron (proton) magic isotone (isotope) chains, and of damping of the off-Fermi-energy-shell contributions are introduced. These may be important for reliable extrapolations to very neutron-rich (or neutron-deficient) regions of the nuclear chart. The final mass formula is a fairly simple analytic expression. In the preliminary fit with 50 free parameters, presented here, 1312 experimentally known atomic masses are reproduced with a rms error, [ ∑ 1312 (M exp−M cal) 2 (1312−50 ] 1 2 of 670 keV. Comparisons with experimental data are presented in figures for the isobaric mass parabolas, masses, radii, and quadrupole moments. Atomic mass predictions for some 8000 nuclei with Z = 3 to 114 and N = 3 to 184, with S n (or S 2 n ) > 0 and with S p > −2 MeV are presented in the main table of this issue. The simple FORTRAN-IV program (mass excess in MeV as a function of Z and A) is available from the authors on request.