Phase diagrams of BCS-BEC crossover in asymmetric nuclear matter

TL;DR

This work addresses the BCS-BEC crossover in isospin-asymmetric nuclear matter with neutron-proton pairing in the $^3SD_1$ channel, focusing on the roles of angle-dependent gaps (ADG) and FFLO states. By constructing phase diagrams in the $T$-$\alpha$, $\alpha$-$\rho$, and $T$-$\rho$ planes for both angle-averaged and angle-dependent gaps, the study disentangles how ADG and finite-momentum pairing interact with normal–superfluid phase separation (PS). The key findings show the crossover is primarily density-driven, with isospin asymmetry suppressing homogeneous superfluidity in the BCS regime but mitigated by FFLO and ADG; at high density their combined effects nearly eliminate PS, while at low density the influence weakens as the $D$-wave fraction declines and the system evolves toward a conventional $S$-wave superfluid. In the BEC regime, FFLO and ADG vanish and PS persists, yielding a PS-BEC mixed phase with a deuteron condensate in the superfluid component. These results illuminate how angular-gap structure and finite-momentum pairing shape the phase structure of asymmetric nuclear matter across the BCS-BEC crossover, though they rely on a bare $NN$ potential and neglect medium effects and clustering, motivating further work to include screening, self-energies, and cluster formation.

Abstract

The phase structure of the BCS-BEC crossover for neutron-proton superfluid in asymmetric nuclear matter is systematically investigated, with particular focus on the roles of the angle-dependent gap (ADG) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. Phase diagrams in the T-alpha, alpha-rho, and T-rho planes are constructed using both angle-averaged and angle-dependent gap treatments, enabling a unified analysis of the interplay between the FFLO pairing, ADG, and normal-superfluid phase separation (PS). The results confirm that the crossover is primarily density-driven. In the weak-coupling BCS regime, isospin asymmetry suppresses the stability of the homogeneous superfluid phase and drives the system toward PS, while the FFLO and ADG mechanisms partially alleviate this suppression. Although the ADG itself does not extend the asymmetry window for superfluidity, in combination with the FFLO state it enlarges the asymmetry range over which superfluidity survives and significantly reduces PS. At high density, these combined effects can nearly eliminate PS. However, as density decreases, ADG-induced suppression of PS is progressively weakened, due to both the reduced destructive effect of isospin asymmetry and the decreasing D-wave fraction in the 3SD1 channel. In general, the system evolves smoothly from a D-wave-dominated superfluid at high density to an S-wave superfluid at low density, with a corresponding weakening of ADG effects. Furthermore, the ADG lifts the orientational degeneracy of the FFLO state, resulting in two distinct FFLO-ADG phases separated by a first-order transition. In contrast, in the BEC regime, the FFLO and ADG states vanish, while the PS persists, leading to an inhomogeneous mixed phase at low temperatures and large asymmetries, where the superfluid component forms a BEC of deuterons.

Figures (5)

• Figure 1: (Color online) Phase diagram of the ADG and the AAG states in the $T-\alpha$ plane. The thick solid and dashed lines indicate the phase boundaries separating the BCS and BEC superfluid phases from the normal phase, respectively. The thick dotted line marks the condition $\mu=0$, signaling the onset of the BCS-BEC crossover. The thin dash-dotted and dash-dot-dotted lines denote the stability condition against PS for the AAG and ADG states, respectively. The shaded region highlights the normal-superfluid PS domain of the ADG state. The black, purple, orange, red, and blue colors correspond to densities $\rho=\rho_0$, $\rho=\rho_0/2$, $\rho=\rho_0/10$, $\rho=\rho_0/100$, $\rho=\rho_0/1000$, respectively, where $\rho_0=0.17~\text{fm}^{-3}$ is the saturation density.
• Figure 2: (Color online) Phase diagram of the AAG (a), ADG (b), FFLO-AAG (c) and FFLO-ADG (d) states in the $\alpha-\rho$ plane. The thick solid lines denote the phase boundary corresponding to the superfluid-normal transition. The thick dashed lines mark the transition from the FFLO state to the conventional BCS state. The thick dotted lines identify the condition $\mu=0$. The yellow shaded region corresponds to the domain of PS, while the thin dash-dot-dotted lines indicate the stability condition against PS in the homogeneous superfluid state. For the AAG state, the thin dashed line represents the zero value of the superfluid density. For the ADG state, the thin dashed and short-dashed lines correspond to the zero values of the transverse ($\rho_T$) and longitudinal ($\rho_L$) components of the superfluid density, respectively. For the FFLO-ADG state, the thin dashed line represents the phase transition from FFLO-ADG-O state to FFLO-ADG-P state (O-P).
• Figure 3: (Color online) Normalized gaps $\Delta_0(k_F)/\Delta(k_F)$ and $\Delta_2(k_F)/\Delta(k_F)$ as a function of number density at $T = 0.1$ MeV for symmetric nuclear matter. The thick red solid and blue dashed lines represent the gaps for the $^3S_1$ and $^3D_1$ channel, respectively. The thick magenta dotted lines identify the condition $\mu=0$.
• Figure 4: (Color online) Phase diagram of the FFLO-AAG state in the $T-\rho$ plane. The thick solid lines represent the transition from the superfluid to the normal states, while the thick dashed lines mark the transition from the FFLO-AAG state to the conventional BCS state. The thick dotted lines identify the condition $\mu=0$. The shaded regions represent the normal-superfluid PS domain, with the stability boundaries $\lambda_-$ marked by thin dash-dot-dotted lines. The black, purple, orange, red, and blue colors correspond to isospin asymmetries $\alpha=0.1$, $\alpha=0.3$, $\alpha=0.5$, $\alpha=0.7$, $\alpha=0.9$, respectively.
• Figure 5: (Color online) Same as Fig. \ref{['fig:T-alpha-aag']}, but for the FFLO-ADG state. The FFLO-ADG state splits into the FFLO-ADG-O and FFLO-ADG-P states. The thin dashed, thick dashed, and thick short-dashed lines denote the transition from FFLO-ADG-O to FFLO-ADG-P (O-P), from FFLO-ADG-O to ADG (O-A), and from FFLO-ADG-P to ADG (P-A), respectively.