Approximate Energy Expression for Spin-Polarized Fermi Liquids

Abstract

An approximate energy expression is proposed for arbitrarily spin-polarized Fermi liquids with central two-body forces. It is explicitly expressed as a functional of spin-dependent radial distribution functions and can be used conveniently in the variational method. It includes the potential energies completely and the kinetic energies up to main parts of the three-body cluster terms. This approximation is similar to that used previously for spinunpolarized and fully polarized matter. A notable feature of this expression is that it guarantees the necessary conditions on arbitrarily spin-polarized structure functions automatically. The Euler-Lagrange equations are derived from this energy expression and are numerically solved for arbitrarily spin-polarized liquid 3 He. The results for liquid 3 He with the HFDHE2 potential are consistent with the nearly ferromagnetic property. §1. Introduction Studies of strongly correlated fermion systems, such as liquid 3 He and nuclear matter at 0 K, is a fundamental and important problem in quantum many-body physics. In particular, the variational method called the fermi hypernetted chain (FHNC) has been proving to be a useful approximation for calculating the energy per particle of the system. 1) The FHNC method is very sophisticated and powerful, but there is still some doubt as to whether the minimization of the energy expectation value is performed with sufficient accuracy in the numerical calculations. 2) As an alternative approach, two of the present authors (Takano and Yamada) have recently proposed a different type of variational method. 2)-4)One of the distinctive characteristics of this new method is the use of various pair distribution functions as argument functions (variational functions) of the variational method. In the conventional variational method, the correlation functions that describe the correlation between particles in the wave function are taken as the variational functions. On the other hand, the pair distribution functions (or, radial distribution functions) represent the probabilities of finding particle pairs in variously specified spin-isospin states as functions of the distance between particles. (When non-central forces are present, corresponding non-centrally correlated pair distribution functions are also used.) The pair distribution functions and the correlation functions are not independent of each other; the former can, in principle, be expanded into cluster series with terms expressed with the latter. Therefore, if we could treat the problem exactly, e.g., by calculating the whole cluster series of * ) Present address: NEC corporation, 5-7-1, Shiba, Minato-ku, Tokyo 108-8001, Japan.

Variational Study of Asymmetric Nuclear Matter and a New Term in the Mass Formula

“…7), and the other for spin-polarized liquid 3 He, which is presented in Ref. 8) and modified in the last section. The "spin polarization" in the latter procedure is replaced here by "isospin polarization".…”

“…17). Next, taking into account the exchange correction and introducing denominators, 8) we modify and improve Eq. (3 .…”

“…7) For liquid 3 He, we have an expression valid for arbitrary spin-polarized states. 8) In this paper, we extend the theory to treat asymmetric nuclear matter, utilizing the analogy between spin polarization and isospin polarization. Here, we should mention the guiding principle of these variational studies.…”

“…In §2, we make a modification of the previously derived energy expression for the spin-polarized fermion system, 8) because we encountered a difficulty in treating spin-polarized neutron matter, and because we use the analogy between isospin polarization and spin polarization. In §3, we construct the approximate energy expression to be used for asymmetric nuclear matter, and the results of numerical calculations are presented.…”