Hartree-Fock calculations with two-body forces are presented in several nuclei, taken as spherical, from ${\mathrm{He}}^4$ to ${\mathrm{Pb}}^{208}$. We first present the results obtained with the best (SP1 and SP2) of the recent smooth semirealistic interactions of Saunier and Pearson. These yield good binding energies and radii except in the vicinity of ${\mathrm{Ni}}^{56}$. However, the spectra in nuclei with spin-unsaturated shells are poor: The spin-orbit splittings in such nuclei are very small (if not negative), and, in particular, in ${\mathrm{Pb}}^{208}$ the level ordering near the top of the Fermi sea is incorrect. This feature does not allow meaningful extrapolation to the superheavy region with these potentials.

In an attempt to find a two-body interaction allowing such an extrapolation, we modify SP1 and find that with a very strong positive triplet-even phenomenological tensor force the ${\mathrm{Pb}}^{208}$ spectrum is very much improved, and the level ordering and density of uppermost occupied states are comparable to the experimental ones. As a result, ${\mathrm{Pb}}^{208}$ is now found doubly magic, together with a good binding energy and radius. The magic nature of ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Ni}}^{56}$, and ${\mathrm{Zr}}^{90}$ is also reproduced by the modified SP1. Consequently this interaction provides new possibilities for valuable extrapolation to the superheavy region with a two-body force.

• Received 4 October 1971

DOI:https://doi.org/10.1103/PhysRevC.5.1223