Summary

A new strategy of fitting the coupling constants of the nuclear energy density functional was recently proposed by our group [22]. It is based on a fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants directly to the $f_{5/2} - f_{7/2}$ SO splittings in $^{40}$Ca, $^{56}$Ni, and $^{48}$Ca. Our results show that drastic changes in the isoscalar SO strength and the tensor coupling constants are required as compared to the commonly used values.

This work briefly addresses the consequences of strong attractive tensor fields on binding energies. In particular, a contribution to the binding energy due to the tensor interaction is calculated. It shows a generic pattern closely resembling that of the shell-correction. The tensorial magic numbers are shifted up relatively to the standard magic numbers, toward $N(Z)$=14, 32, 56, or 90, which, in the extreme s.p. scenario at the spherical shape, correspond to the maximum spin-orbit asymmetry in the $1d_{5/2}$, $1f_{7/2}\oplus 2p_{3/2}$, $1g_{9/2}\oplus 2d_{5/2}$, and $1h_{11/2}\oplus 2f_{7/2}$ configurations, respectively. It is shown that these numbers are smeared out by the pairing effects and shifted in the case of proton tensorial magic numbers by changes in the sub-shell ordering. It is also shown that strong attractive tensor interaction may give rise to an increased stability of nuclear binding at the drip lines, in particular around $Z\approx 14, N\approx 32$, $Z\approx 28, N\approx 56$, and $Z\approx 50, N\approx 90$.

This work was supported in part by the Polish Ministry of Science under Contract No. N N202 328234, by the Academy of Finland and University of Jyväskylä within the FIDIPRO programme, and by the Swedish Research Council.