Three-body force effect on ${}^3\mathit{P}$ ${\mathit{F}}_2$ neutron superfluidity in neutron matter, neutron star matter, and neutron stars

We investigate the effect of microscopic three-body forces on the ${}^3\mathit{P}$ ${\mathit{F}}_2$ neutron superfluidity in neutron matter, β-stable neutron star matter, and neutron stars by using the BCS theory and the Brueckner-Hartree-Fock approach. We adopt the Argonne V18 potential supplemented with a microscopic three-body force as the realistic nucleon-nucleon interaction. We have concentrated on studying the three-body force effect on the ${}^3\mathit{P}$ ${\mathit{F}}_2$ neutron pairing gap. It is found that the three-body force effect considerably enhances the ${}^3\mathit{P}$ ${\mathit{F}}_2$ neutron superfluidity in neutron star matter and neutron stars.

Figure 1

Neutron ${}^3\mathit{P}$ ${\mathit{F}}_2$ energy gap vs Fermi momentum in pure neutron matter predicted in the two cases of including and not including the TBF. The free-space energy spectrum approximation is adopted in the gap equation.

Figure 2

Neutron ${}^3\mathit{P}$ ${\mathit{F}}_2$ energy gap vs Fermi momentum in pure neutron matter predicted in the two cases of including and not including the TBF. The BHF energy spectrum is adopted in the gap equation.

Figure 3

The ${{}^3\mathrm{S}}_2$ and ${{}^3\mathrm{F}}_2$ components of the tensor force $V_T(\mathrm{TBF})$ expressed in a form of effective two-nucleon interaction, as a function of the distance $r$ between the two interacting neutrons in pure neutron matter at various densities.

Figure 4

Strength of the ${}^3\mathit{P}$ ${\mathit{F}}_2$ tensor force $V_T(\mathrm{TBF})$ expressed in a form of effective two-nucleon interaction, as a function of the distance $r$ between the two interacting neutrons in neutron matter.

Figure 5

Neutron ${}^3\mathit{P}$ ${\mathit{F}}_2$ energy gap as a function of density in β-stable neutron star matter predicted in the two cases of including and not including the TBF.

Figure 6

Proton fraction predicted in the two cases of including (solid curve) and not including (dashed curve) the TBF.

Figure 7

The ${{}^3\mathrm{S}}_2$ and ${{}^3\mathrm{F}}_2$ components of the tensor force $V_T(\mathrm{TBF})$ expressed in a form of effective two-nucleon interaction in neutron star matter (the solid and dashed curves) and those in pure neutron matter (the filled and empty squares) at several densities.

Figure 8

Distribution of neutron ${}^3\mathit{P}$ ${\mathit{F}}_2$ pairing gap in a typical neutron star.

Figure 9

The neutron effective mass $m_n^{*}$ as a function of density in pure neutron matter (left panel) and neutron star matter (right panel) in both cases of including and not including the microscopic TBF.