Ferromagnetism of dense neutron matter

Abstract

The possibility of a ferromagnetic transition in dense neutron matter is investigated using a simplified model of a pure hard core gas, with core radius c. Previous estimates of the density at which the ferromagnetic transition would occur are shown to be incorrect. The inclusion of terms cubic in kFc, in particular the P state interaction, leads to the conclusion that neutron matter in the liquid phase should not exhibit ferromagnetism. NUCLEAR STRUCTURE Ferromagnetism of dense hard-core neutron and nuclear matter.b, &0.(2) Now, both E(0) and E(1) may be expanded in x =k~c with the known result (see, e.g. , Ref. 6):There have been suggestions that neutron matter at a density pz, comparable to densities expected in neutron stars, may become ferromagnetic. '"'The estimates'" of p& were performed for a simplified model of a pure hard core neutron gas. A, possible ferromagnetic transition in a hard core fermion system has been suggested" for a long time and is important in the theory of magnetism in metals. 'In the present paper, we want to show that the previous estimates of p& were incorrect, and that it appears to be unlikely that neutron matter would exhibit ferromagnetism in the liquid phase. Our conclusion agrees with existing calculations of magnetic susceptibility of neutron matter, performed with realistic forces (see, e.g. , Ref. 7).We adopt the model of a pure hard core interaction of radius c for neutron matter for two reasons: (i) At high densities the short range repulsion is the decisive part of the interaction; (ii) the attraction between neutrons with a reasonable spin dependence is expected to increase the stability of the spin unpolarized state. We employ nonrelativistic quantum mechanics, and restrict ourselves to zero temperature. The energy per neutron E(a)/N depends on the spin excess parameter a =(N& -N&)/N and on the density p=kz'/3v'. kz is the Fermi momentum of spin unpolarized neutron matter. If we denote d = E(1)/N -E(0)/N, then the condition for the occurrence of ferromagnetism is, +-' , v 'x+ , ',n'(-ll -2 ln2)x'The factor 2' ' in (4) represents the increase in kinetic energy in the transition from the normal 0, =0 to the ferromagnetic a =1 state. Terms linear and quadratic in x and the part of the cubic term with the coefficient 0.0377 arise from interaction in the S state and do not appear in E(1), due to the Pauli principle. This is in accordance with the usual argument in favor of ferromagnetism: Although in the ferromagnetic transition the kinetic energy of the system increases, at high density this is more than balanced by the disappearance of the repulsive interaction. What has been overlooked in this argument is the interaction in the P state, which contributes the part of the cubic terms with the coefficients in the curly brackets. Now, by the same argument, the P state interaction acts in the opposite direction and, in fact, makes the ferromagnetic state less favorable. The function b(x) calculated with the help of expressions (3) and (4) is shown in Fig. 1. The curve curves ...

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

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