Ferromagnetic instabilities in neutron matter at finite temperature with the Gogny interaction

Abstract

The properties of spin-polarized neutron matter are studied both at zero and finite temperature using the D1 and the D1P parametrizations of the Gogny interaction. The results show two different behaviors: whereas the D1P force exhibits a ferromagnetic transition at a density of ρ c ∼ 1.31 fm −3 whose onset increases with temperature, no sign of such a transition is found for D1 at any density and temperature, in agreement with recent microscopic calculations. The possible existence of a phase transition of neutron matter to a ferromagnetic state has motivated many investigations of the equation of state (EOS) of spin-polarized neutron matter. In addition to the interest that such a transition could have in the context of neutron stars [1], this problem has gained interest in itself and has been addressed in the framework of very different theoretical approaches [2][3][4][5][6][7][8][9][10][11]. Whereas some of these calculations, like for instance those based on Skyrme-like interactions, predict a transition at densities in the range (1 − 4)ρ 0 (with ρ 0 = 0.16 fm −3 the saturation density of symmetric nuclear matter), others, like recent Monte Carlo [7] or Brueckner-Hartree-Fock (BHF) calculations [9,10] using modern two-and three-body realistic interactions, exclude such a transition at least up to densities around five times ρ 0 . In spite of this discrepancy, it is interesting to study how temperature influences the ferromagnetic transition [12,13]. In Ref. DOI[12] an analysis of the temperature effects in the framework of a Hartree-Fock calculation with Skyrme interactions was performed. In the present Brief Report, we study the influence of the finite-range terms of the interaction on the ferromagnetic transition. To this end, we consider the Gogny interaction. This is an effective nucleon-nucleon force with both zero-and finite-range terms and a simple spin-isospin structure. In addition to the original D1 parametrization [14], several other parametrizations of this force are available. The D1S force, for instance, was introduced to improve the pairing properties and surface effects of finite nuclei [15], whereas more recently the D1P [16] interaction has been introduced with the aim of reproducing the EOS of pure neutron matter given by a variational microscopic calculation with realistic interactions [17].The properties of nuclear matter deduced from Gogny interactions have already been treated in the literature [18]. Indeed, several instabilities produced by these forces at zero temperature have been studied in previous works [19]. The isospin instability, for instance, is a common feature to all the existing Gogny parametrizations as well as of most Skyrme forces. This instability is signaled by the fact that, above a certain critical density, the energy per particle of nuclear matter becomes more repulsive than that of neutron matter. For the D1P force, this instability takes place at ρ I ∼ 7ρ 0 , whereas for D1 it occurs at ρ I ∼ 3ρ 0 . Furthermore, D1 and D1S also exhibit a spinodal instability in...

Spin instabilities of infinite nuclear matter and effective tensor interactions

“…(38) shows that the inclusion of the tensor interaction results always in a smaller value for the critical density than the one without tensor terms, and consequently the spontaneous magnetization would appear at densities closer to ρ 0 . In the next subsection we shall show that neither finite-range effective interactions [25] nor realistic calculations [26] predict such a spontaneous magnetization in neutron matter, which therefore should be considered as an artifact of the Skyrme interaction.…”

Effective interaction dependence of the liquid–gas phase transition in symmetric nuclear matter

“…The Gogny mean-field cannot be separated cleanly into an effective mass and a momentum independent term. This separation might eventually be performed as an additional approximation and, on the whole, should provide reasonable results [52]. However, full mean-field calculations are preferable for accurate calculations of liquid-gas coexistence curves.…”

Spin-polarized states in neutron matter in a strong magnetic field

“…[9] the consideration also has been done for the Gogny effective NN interaction (D1S, D1P parametrizations) up to densities 4̺ 0 . Since for the D1S parametrization there is no spontaneous ferromagnetic transition in neutron matter for all relevant densities, and for the D1P parametrization this transition occurs at the density larger than 7̺ 0 [23], no sign of a ferromagnetic transition at a strong magnetic field was found in Ref. [9] up to densities 4̺ 0 for these Gogny forces.…”

“…On the one hand, the models with the Skyrme effective nucleonnucleon (NN) interaction predict the occurrence of spontaneous spin instability in nuclear matter at densities in the range from ̺ 0 to 4̺ 0 for different parametrizations of the NN potential [10]- [22] (̺ 0 = 0.16 fm −3 is the nuclear saturation density). For the Gogny effective interaction, a ferromagnetic transition in neutron matter occurs at densities larger than 7̺ 0 for the D1P parametrization and is not allowed for D1, D1S parametrizations [23]. However, for the D1S Gogny force an antiferromagnetic phase transition happens in symmetric nuclear matter at the density 3.8̺ 0 [24].…”