Exploring $^3P_0$ Superfluid in Dilute Spin-Polarized Neutron Matter

We explore the theoretical possibility of $^3P_0$ neutron superfluid in dilute spin-polarized neutron matter, which may be relevant to the crust region of a magnetized neutron star. In such a dilute regime where the neutron Fermi energy is less than 1 MeV, the $^1S_0$ neutron superfluid can be suppressed by a strong magnetic field of the compact star. In the low-energy limit relevant for dilute neutron matter, the $^3P_0$ interaction is stronger than the $^3P_2$ one which is believed to induce the triplet superfluid in the core. We present the ground-state phase diagram of dilute neutron matter with respect to the magnetic field and numerically estimate the critical temperature of the $^3P_0$ neutron superfluid, which is found to exceed $10^7$ K.