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arXiv:2207.13907 · Physical Review C

Resonance-to-bound transition of He5 in neutron matter and its analogy with heteronuclear Feshbach molecules

Hiroyuki Tajima, Hajime Moriya, W. Horiuchi, Kei Iida, Eiji Nakano

Published Oct 28, 2022• 3 citations
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Abstract

We theoretically investigate the fate of a neutron-alpha $p$-wave resonance in dilute neutron matter, which may be encountered in neutron stars and supernova explosions. While $^{5}\mathrm{He}$ is known as a resonant state that decays to a neutron and an alpha particle in vacuum, this unstable state turns into a stable bound state in the neutron Fermi sea because the decay process is forbidden by the Pauli-blocking effect of neutrons. Such a resonance-to-bound transition assisted by the Pauli-blocking effect can be realized in cold atomic experiments for a quantum mixture near the heteronuclear Feshbach resonance.

DOI
10.1103/physrevc.106.045807

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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 ppp-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 ppp-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 1S0^{1}S_{0}1S0​ neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result is useful for understanding many-body physics in astrophysical environments as well as the formation of multinucleon clusters in neutron-halo nuclei.
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We consider a dense ultracold Fermi gas in the presence of a Feshbach resonance. We investigate how the threshold for bound state formation, which is just at the Feshbach resonance for a dilute gas, is modified due to the presence of the Fermi sea. We make use of a preceding framework of handling this many-body problem. We restrict ourselves to the simple case where the chemical potential μ is negative, which allows us to cover in particular the classical limit where the effect is seen to disappear. We show that, within a simple approach where basically only the effect of Pauli exclusion is included, the Fermi sea produces a large shift of the threshold, which is of the order of the width of the Feshbach resonance. This is in agreement with very recent experimental findings.
In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment (due to Pauli-blocking effects), while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (BCS) regime of Cooper Fermi pairs) to a small and positive value (corresponding to the regime of the Bose-Einstein condensate (BEC) of molecular dimers), crossing the unitarity regime where the scattering length diverges. In the case of bulk neutron matter the s-wave scattering length of neutron-neutron potential is negative but fixed, and the condensate fraction of neutron-neutron pairs is studied as a function of the total neutron density. Our results clearly show a BCS-quasiunitary-BCS crossover by increasing the neutron density. Finally, in the case of neutron stars, where again the neutron-neutron scattering length is negative and fixed, we determine the condensate fraction as a function of the distance from the center of the neutron star, finding that the maximum condensate fraction appears in the crust of the neutron star.
We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.