Superfluidity in nuclear systems and neutron stars

Abstract

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P -F -wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors. PACS. 97.60.Jd Neutron stars -21.65.+f Nuclear matter -47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids -67.85.+d Ultracold gases, trapped gases -74.25.Dw Superconductivity phase diagrams Contents arXiv:1802.00017v4 [nucl-th] 26 Sep 2019 emerge in the interaction part of the Hamiltonian when evaluating Eq. (5) in terms of Bogolyubov operators vanish. Such terms would account for fluctuations in the system, but are beyond the scope of the present mean-field treatment. 4 Note that the variation δ(E − µN )/δn p,↑ , with up and vp held constant, yields the quantity Ep, confirming its interpretation. Armen Sedrakian, John W. Clark: Superfluidity in nuclear systems and neutron stars 5

Neutron pairing with medium polarization beyond the Landau approximation

“…where the minus sign comes from the closed fermion loop, 3 is a short-hand notation for σ3σ 3 d 3 p 3 /(2π) 3 , and…”

“…This system of equations has actually two decoupled blocks corresponding to the indices 1, 2, 6, 8, 10, 13, 16, 18, which have products of two time-even operators, and to the indices 3,4,5,7,9,11,12,14,15,17, which have products of two time-odd operators.…”

Vector-boson condensates, spin-triplet superfluidity of paired neutral and charged fermions, and 3P2 pairing of nucleons

“…Therefore, in the neutron star interiors neutrons are supposed to be paired in the 1S 0 state at a low baryon density n ≤ (0.7 − 0.8)n 0 , where n 0 is the nuclear saturation density, and in 3P 2 state for (3 − 4)n 0 ≥ n ≥ 0.8n 0 , cf. [29] and recent works [30,31]. However the value of the 3P 2 nn gap in the neutron matter is poorly known and varies in various calculations from tiny values < ∼ 10 KeV up to values of the order of several MeV and may be more, see Refs.…”

“…With increasing density the 3D 2 channel becomes most attractive, cf. [31]. One of the hypothesis for the explanation of the level structure of super-deformed (rotated) nuclei is the spin-triplet pairing [62][63][64].…”

Evolution of Quasiperiodic Structures in a Non-Ideal Hydrodynamic Description of Phase Transitions

“…Formation of the pasta non-uniform phases is one of the possibilities [31,35,36]. Add here possibilities of the phase transitions between various superfluid [37,38] and ferromagnetic-superfluid [39] phases in the cold neutron stars and in the color-superconducting hybrid compact stars [40], as well as numerous possibilities of the phase transitions in the condensed matter physics at terrestrial conditions, like liquid-gas, liquid-glass, glass-metal transitions, etc.…”