Polaronic neutron in dilute alpha matter: A $p$-wave Bose polaron

We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant $p$-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the $p$-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Moreover, two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of $^1S_0$ neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result would be useful for understanding many-body physics in astrophysical environments as well as the formation of multi-nucleon clusters in neutron-halo nuclei.