Role of proton pairing in a semimicroscopic treatment of the inner crust of neutron stars

The TETFSI (temperature-dependent extended Thomas-Fermi plus Strutinsky integral) method for calculating the properties of the inner crust of neutron stars is here extended in the zero-temperature limit to include proton pairing. The main effect is to smooth out the proton shell effects, although the energetically favored value of $Z$, the number of protons per Wigner-Seitz cell, remains at, or close to, 40.

Figure 1

Variation of TETFSI energy $e$ per nucleon as a function of $Z$, the number of protons in the Wigner-Seitz cell, for functional BSk21 with and without proton pairing at temperature $T=0$ and for two different mean densities: $\overline{n}=2.6\times {10}^{-4}$ nucleons ${\mathrm{fm}}^{-3}$ (a) and $\overline{n}=5.5\times {10}^{-2}$ nucleons ${\mathrm{fm}}^{-3}$ (b). The number of neutrons in the WS cell is optimized for each value of $Z$.

Figure 2

Optimal value of nucleon number $A$ in the WS cell as a function of density $\overline{n}$ at $T$ = 0 for functional BSk21.