Abstract
We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature (T) and density (ρ) with a low proton fraction (Yp ≤ 0.2), which is relevant to the inner crust and outer core of neutron stars. A strong-coupling theory developed for two-component atomic Fermi gases is generalized to the four-component case, and is applied to the system of spin-1/2 neutrons and protons. The phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to k = 2 fm−1 are described by multi-rank separable potentials. We show that the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}}= 1.68 MeV at {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.14}} with ρ0 = 0.17 fm−3. Also, the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} only above {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.70}}(0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{d}}} is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.
Highlights
The phase shifts of neutron-neutron, proton-proton and neutron-proton interactions up to k = 2 fm−1 are described by multi-rank separable potentials
Three of the present authors have recently shown[14] that a strong coupling theory, being based on the one developed by Nozières and Schmitt-Rink (NSR)[15] can provide a unified description of neutron matter and an ultracold Fermi gas in the unitary regime
We start from studied before note that since is numerically titdhnheeemdsciaufafnlpecdreuerilnnfaltgtui,lioedwnveepolhesfxaTotscfrneantthpwreoaiolntarhsteiietntiitcoShanEelmPsteo3mptionhpkitesFhrt,niaec =thauti r1igeo.h7nT3d.cn fFenmniigsn−uit1rpyewur3hree(geairno)eensTuhkctnorFn,woni n≳snvt m1ha.e3raio tfatmreberlt−yi(1cYdaopilf s=epaspu 0tpir)meewanarhteseuiscbthroeocfhnaTaucmsnsnbea. etWtteheneer phase shift at k = kF,n becomes zero there, by using the Padé approximation
Summary
It has been recognized that the dilute neutron matter and two-component ultracold atomic fermions near the unitarity have close similarity This is due to the strong pairing interactions associated with the large negative neutron-neutron scattering length as = −18.5 fm and relatively small effective range reff = 2.8 fm in the former In strongly interacting systems, such as neutron matter and the unitary Fermi gas, effects of pairing fluctuations near the superfluid phase transition are important. Three of the present authors have recently shown[14] that a strong coupling theory, being based on the one developed by Nozières and Schmitt-Rink (NSR)[15] can provide a unified description of neutron matter and an ultracold Fermi gas in the unitary regime This indicates that the latter atomic gas system can be used as a quantum simulator for neutron star interiors at subnuclear densities.
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