Odd-even mass difference and isospin dependent pairing interaction

The neutron and proton odd-even mass differences are studied with Hartree-Fock $+$ BCS ($\mathrm{HF}+\mathrm{BCS}$) calculations with Skyrme interactions and an isospin dependent contact pairing interaction, which is recently derived from a microscopic nucleon-nucleon interaction. To this end, we perform $\mathrm{HF}+\mathrm{BCS}$ calculations for even and odd semi-magic tin and lead isotopes together with even and odd $Z$ isotones with $N=50$ and 82. The filling approximation is applied to the last unoccupied particle in odd nuclei. Comparisons with the experimental data show a clear manifestation of the isospin dependent pairing correlations in both proton and neutron pairing gaps.

Figure 1

Odd-even mass staggering ${\Delta }_n^{(3)}$ calculated by Eq. (4) for the semi-magic Sn and Pb isotopes: (a) for Sn isotopes and (b) for Pb isotopes. The SkP interaction is adopted together with the IS pairing (3) or the $\mathrm{IS}+\mathrm{IV}$ pairing (2) in the $\mathrm{HF}+\mathrm{BCS}$ model. The filling approximation is applied to the last unoccupied particle in odd nuclei. See the text for details.

Figure 2

Odd-even mass staggering ${\Delta }_p^{(3)}$ calculated by Eq. (4): (a) for the $N=50$ and (b) for $N=82$ isotones. The SkP interaction is adopted together with the IS pairing (3) or the $\mathrm{IS}+\mathrm{IV}$ pairing (2) in the $\mathrm{HF}+\mathrm{BCS}$ model. See the caption to Fig. 1 and the text for details.

Figure 3

Odd-even mass staggering ${\Delta }_p^{(3)}$ calculated by Eq. (4): (a) for the $N=50$ and (b) for $N=82$ isotones. The SLy4 interaction is adopted together with the IS pairing (3) or the $\mathrm{IS}+\mathrm{IV}$ pairing (2) in the $\mathrm{HF}+\mathrm{BCS}$ model. See the caption to Fig. 1 and the text for details.

Figure 4

Odd-even mass staggering ${\Delta }_p^{(3)}$ calculated by Eq. (4): (a) for the $N=50$ isotones and (b) for the $N=82$ isotones. The SLy4 interaction is adopted together with the IS pairing (3) or the $\mathrm{IS}+\mathrm{IV}$ pairing (2) in the $\mathrm{HF}+\mathrm{BCS}$ model. The different pairing strength $V_0^p=1462$ MeV fm${}^3$ is adopted in the proton channel for the dotted line with the $V_0^n=1300$ MeV fm${}^3$ for the neutron channel. See the caption to Fig. 1 and the text for details.