Superfluid Phase Transitions and Effects of Thermal Pairing Fluctuations in Asymmetric Nuclear Matter

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 of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value = 1.68 MeV at with ρ0 = 0.17 fm−3. Also, the critical temperature of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over only above (0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.

Low-dimensional fluctuations and pseudogap in Gaudin-Yang Fermi gases

“…is the Fermi-Dirac distribution function. A similar approximation has been employed in nuclear physics with finite-range interactions [86][87][88][89]. On the basis of G H σ (p, iω n ), we incorporate pairing fluctuation effects described by the four-point vertex diagrammatically shown in Fig.…”

Cooper quartet correlations in infinite symmetric nuclear matter

“…Note that the contribution of the isovector pairing is ignored in the above equations as in the previous subsection. Nevertheless, this approximation is still valid for qualitative understanding of in-medium quartet correlations in infinite nuclear matter since the isovector pairing is much weaker than the isoscalar pairing [20].…”

“…Such a phenomenon is called BCS-BEC crossover, which has been realized in ultracold Fermi atomic gases [12][13][14] and in superconductors [15,16], and its connections to nuclear systems have also been studied extensively [17,18]. In asymmetric nuclear matter, both the isovector and isoscalar pairing states can appear and compete with each other [19][20][21]. While the isoscalar pairing interaction is stronger than the isovector one, the imbalance between neutron and proton Fermi levels suppresses the isoscalar neutron-proton pairing.…”

Low-Density Neutron Matter and the Unitary Limit

“…It is known from a general argument (see e.g., references [44][45][46]), which applies to any dilute fermionic system, that the pair correlations of fermions interacting with a large scattering length differ from what is considered in the conventional BCS theory. Corrections due to pair correlations in the normal phase of neutron matter have been considered by several authors [47][48][49][50][51][52] using the Nozières-Schmitt-Rink approach [46], which is the simplest one that interpolates correctly between the BCS and BCE limits. BCS-BEC crossover effects and the existence, above the critical temperature T c for the transition to the superfluid state, of a pseudo-gap in neutron matter have been also recently studied within the in-medium T-matrix formalism by Durel and Urban in reference [53].…”