Nuclear Spectroscopy With a Soft Core Potential

Abstract

Nuclear spectroscopic calculations with a potential of the type $v\left(r\right)=v_0\left[\right(r^n-\frac{c^n}{r^n}\left)\right]\exp (-\frac{r^2}{{r_0}^2})$ are made for the core radius $c=0.4\mathrm{}$ F and potential range $r_0=2.06\mathrm{}$ F. For simplicity of calculation, $n=2\mathrm{}$ is assumed. The calculations are made for $f$, $p$, and $g$-shell nuclei. It is shown that in the case of ${\mathrm{Zr}}^{90}$ the configuration dependence of the effective two-body interaction can be replaced by a singular potential. The configuration interaction in this nucleus is found to depress the ground state $0^{+}$ by ∼ 0.4 MeV and raise the excited $0^{+}$ level by the same amount. For the $f$ and $p$ shells, the level splittings in ${\mathrm{Ti}}^{50}$, ${\mathrm{Ni}}^{58}$, and ${\mathrm{Be}}^{10}$ are analyzed. The calculations show that the triplet forces are small for these configurations.