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arXiv:nucl-th/0307113 · Physical Review C

Spin polarized states in strongly asymmetric nuclear matter

A. A. Isayev, J. Yang

Published Feb 4, 2004• 59 citations
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Abstract

The possibility of appearance of spin polarized states in strongly asymmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with the Skyrme effective interaction. The zero temperature dependence of the neutron and proton spin polarization parameters as functions of density is found for $SLy4$ and $SLy5$ effective forces. It is shown that at some critical density strongly asymmetric nuclear matter undergoes a phase transition to the state with the oppositely directed spins of neutrons and protons while the state with the same direction of spins does not appear. In comparison with neutron matter, even small admixture of protons strongly decreases the threshold density of spin instability. It is clarified that protons become totally polarized within a very narrow density domain while the density profile of the neutron spin polarization parameter is characterized by the appearance of long tails near the transition density.

DOI
10.1103/physrevc.69.025801

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The possibility of appearance of spin polarized states in strongly asymmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with the Skyrme effective interaction. The zero temperature dependence of the neutron and proton spin polarization parameters as functions of density is found for SLy4SLy4SLy4 and SLy5SLy5SLy5 effective forces. It is shown that at some critical density strongly asymmetric nuclear matter undergoes a phase transition to the state with the oppositely directed spins of neutrons and protons while the state with the same direction of spins does not appear. In comparison with neutron matter, even small admixture of protons strongly decreases the threshold density of spin instability. It is clarified that protons become totally polarized within a very narrow density domain while the density profile of the neutron spin polarization parameter is characterized by the appearance of long tails near the transition density.
The possibility of appearance of spin polarized states in symmetric and strongly asymmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with the Skyrme effective interaction. The zero temperature dependence of the neutron and proton spin polarization parameters as functions of density is found for SkM∗^*∗, SGII (symmetric case) and SLy4, SLy5 (strongly asymmetric case) effective forces. By comparing free energy densities, it is shown that in symmetric nuclear matter ferromagnetic spin state (parallel orientation of neutron and proton spins) is more preferable than antiferromagnetic one (antiparallel orientation of spins). Strongly asymmetric nuclear matter undergoes at some critical density a phase transition to the state with the oppositely directed spins of neutrons and protons while the state with the same direction of spins does not appear. In comparison with neutron matter, even small admixture of protons strongly decreases the threshold density of spin instability. It is clarified that protons become totally polarized within a very narrow density domain while the density profile of the neutron spin polarization parameter is characterized by the appearance of long tails near the transition density.
Spin polarized states in nuclear matter with an effective nucleon-nucleon interaction are studied for a wide range of isospin asymmetries and densities. Based on a Fermi liquid theory, it is shown that there are a few possible scenarios of spin ordered phase transitions: (a) nuclear matter undergoes at some critical density a phase transition to a spin polarized state with the oppositely directed spins of neutrons and protons (Skyrme SLy4 and Gogny D1S interactions); (b) at some critical density, a spin polarized state with the like-directed neutron and proton spins appears (Skyrme SkI5 interaction); (c) nuclear matter under increasing density, at first, undergoes a phase transition to the state with the opposite directions of neutron and proton spins, which goes over at larger density to the state with the same direction of nucleon spins (Skyrme SkI3 interaction).
This paper presents the results of investigation of the superfluid states in a two-component Fermi liquid within the framework of the Fermi liquid approach. Particular attention is paid to the superfluid states in nuclear matter which are characterized by the superposition of singlet and triplet types of pairing in spin and isospin spaces. The fundamental principles of the Fermi liquid approach are formulated and further used in the study of superfluidity in nuclear matter with the superposition of singlet and triplet types of pairing. The system of self-consistency equations is derived and its solutions are presented. The conditions of existence of the considered states are determined. These conditions impose certain constraints on the interaction potential and particle density in the system. It is shown that the states with a complete set of nonzero order parameters are realized only in a narrow density range, the width and position of which on the density scale depend on the actual parametrization of the Skyrme potential employed. We considered 18 different parameterizations and indicated for which of them the studied types of superfluid states may appear. The problem of stability of the states with the superposition of singlet and triplet pairing is studied. It is shown that the lowest value of the thermodynamic potential corresponds to purely triplet states. Then, in the order of increasing, follow the thermodynamic potentials of purely singlet states and mixed singlet-triplet states. Separately, we consider the case of unitary states, for which the solutions of the self-consistency equations are also analyzed. It is shown that the density range in which such states can be realized is different from that corresponding to the nonunitary states. The problem of existence of the unitary superfluid states with the superposition of singlet and triplet superfluidity is considered in the case of asymmetrical nuclear matter. It is shown that the appearance of asymmetry in nuclear matter breaks the unitarity of superfluid states in nuclear matter with regard to isospin.
Low-density neutron matter has been studied extensively for many decades, with a view to better understanding the properties of neutron-star crusts and neutron-rich nuclei. Neutron matter is beyond experimental control, but in the past decade it has become possible to create systems of fermionic ultracold atomic gases in a regime close to low-density neutron matter. In both these contexts pairing is significant, making simple perturbative approaches impossible to apply and necessitating ab initio microscopic simulations. Atomic experiments have also probed polarized matter. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) arriving at the lowest-energy configuration to date. For small-to-intermediate relative fractions, the system turns out to be fully normal, while beyond a critical polarization we find phase coexistence between a partially polarized normal neutron gas and a balanced superfluid gas. As in cold atoms, a homogeneous polarized superfluid is close to stability but not stable with respect to phase separation. We also study the dependence of the critical polarization on the density.
The density, spin, and isospin correlation functions in nuclear matter with a neutron-proton condensate are calculated to study the possible signatures of the BEC-BCS crossover in the low-density region. It is shown that the criterion of the crossover (Phys. Rev. Lett. 95 , 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. The presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states can be used as an unambiguous signature of the BEC-BCS transition.
We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.