Finite-range simple effective interaction including tensor terms

An existing parametrization of the simple effective interaction (SEI) that is able to reproduce the experimentally known crossing between the $2p_{3/2}$ and $1f_{5/2}$ single-particle (s.p.) proton levels in neutron-rich Ni isotopes has been generalized. We have added a short-range tensor force in order to describe the observed gaps between the $1h_{11/2}$ and $1g_{7/2}\mathrm{s}.\mathrm{p}.$ proton levels in the Sn isotopic chain and between the $1i_{13/2}$ and $1h_{9/2}\mathrm{s}.\mathrm{p}.$ neutron levels in $N=82$ isotones without compromising the good agreement with the splittings in the Ni isotopes. Different scenarios where tensor effects are relevant are considered with the new interaction and its predictions are compared with results from other mean-field models and experimental data where available.

Figure 1

Proton single-particle levels around the Fermi level for Ni isotopes from $A=68$ to $A=78$ computed with the SEI for the four EoSs.

Figure 2

Neutron single-particle levels around the Fermi level for Ni isotopes from $A=68$ to $A=78$ computed with the SEI for the four EoSs.

Figure 3

Nuclear charge radii $R_{\mathrm{ch}}$ of Ni isotopes using SEI-G ($\gamma =0.42$) compared with the experimental data [48].

Figure 4

Isotopic shift $\delta \langle R_{\mathrm{ch}}^2\rangle$, with respect to ${}^{60}\mathrm{Ni}$, of Ni isotopes using SEI-G ($\gamma =0.42$) compared with the experimental data [48].

Figure 5

Comparison of experimental [47] and SEI-G $(\gamma =0.42$) spins of 298 odd-nuclei in different spin states.

Figure 6

Energy differences between $1h_{11/2}$ and $1g_{7/2}$ proton s.p.levels in Sn isotopes with and without the tensor interaction. The experimental data are taken from Ref. [12]. For details see the text.

Figure 7

Energy differences between $1i_{13/2}$ and $1h_{9/2}$ neutron s.p. levels in $N=82$ computed with and without tensor interaction. The experimental data are taken from Ref. [12]. For details see the text.

Figure 8

Neutron levels of Sn isotopes in the $N=50$ to $N=82$ major shell. Solid (dashed) lines correspond to the s.p. energies computed with (without) the tensor force.

Figure 9

Occupation probability of the neutron levels of the Sn isotopes in the $N=50$ to $N=82$ major shell. Solid (dashed) lines correspond to the occupations computed with (without) the tensor force.

Figure 10

Proton levels of the $N=82$ isotones in the $Z=50$ to $Z=72$ major shell. Solid (dashed) lines correspond to the s.p. energies computed with (without) the tensor force.

Figure 11

Occupation probability of the proton levels of the $N=82$ isotones in the $Z=50$ to $Z=72$ major shell. Solid (dashed) lines correspond to the occupations computed with (without) the tensor force.

Figure 12

Neutron s.p. levels in $N=51$ isotones relative to the $2d_{5/2}$ level with and without tensor interaction.