Effect of Woods-Saxon Wave Functions on the Calculation ofA=18, 206, 210Spectra with a Realistic Interaction

Abstract

The spectra of the nuclei ${\mathrm{O}}^{18}$, ${\mathrm{F}}^{18}$, ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{210}$ are calculated using realistic forces and a Woods-Saxon form for the shell-model average field. The substitution of Woods-Saxon for harmonic-oscillator single-particle wave functions leads to appreciable upward shifts in the calculated positions for many low-lying levels in the $A=18\mathrm{}$ nuclei. In particular the $T=0\mathrm{}$, $J=1^{+}$ and $T=1\mathrm{}$, $J=0^{+}$ binding energies are decreased by 0.6-1.7 MeV. In the heavier nuclei, one finds significant changes in observed energy levels perhaps only for the ground states. Nevertheless, the introduction of the more realistic single-particle average field in the Pb isotopes and in neighboring nuclei permits one to improve the conceptual basis upon which this field is erected.