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We theoretically investigate the fate of a neutron-alpha $p$-wave resonancein dilute neutron matter, which may be encountered in neutron stars andsupernova explosions. While $^5$He is known as a resonant state that decays toa neutron and an alpha particle in vacuum, this unstable state turns into astable bound state in the neutron Fermi sea because the decay process isforbidden by the Pauli-blocking effect of neutrons. Such a resonance-to-boundtransition assisted by the Pauli-blocking effect can be realized in cold atomicexperiments for a quantum mixture near the heteronuclear Feshbach resonance.

Resonance-to-bound transition of $^5$He in neutron matter and its analogy with heteronuclear Feshbach molecule