SPATIAL CORRELATIONS IN SPIN-POLARIZED 3He LIQUID

Variational Fermi HNC calculations are performed for spin-polarized 3 ~ e liquid at zero temperature. The trial wave function is optimized by solving an Euler-Lagrange equation in the Fermi HNC approximation. Results for liquid structure function and one-particle momentum distribution are compared with the corresponding quantities of the spin-saturated liquid. In this report we present results of a theoretical evaluation of liquid structure function and one-particle momentum distribution for spin-polarized and normal 3 ~ e liquids. The calculations are based on the variational method. The ground state many-body trial wave function is chosen to be of standard Jastrow form where 0 is the ideal gas wave function and the correlation factor f is a function of radial dependence only. The expectation value of the energy is determined by employing the Fermi hypernetted-chain (FHNC) method /1-4/ and the minimization of the energy is carried out by solving the EulerLagrange equation /5,6/ in which v is the usual Lennard-Jones potential and w is an induced potential due to dynarnical and exchange correlations. The induced potential is a functional of the radial distribution function g and it is calculated self-consistently as described in ref. /5/. The liquid structure function S(k) is related to g by a Fourier transformation ~ ( k ) = 1 + p Irg(r)-l] eikar IF ( 3 ) * -On leave from : Dept. of Theoretical Physics, University of Oulu, Finland. where p is the average density of the liquid. Once the distribution function g and the correlation factor f are known one can calculate the one-particle density matrix n(rl,r;) by a method similar to FHNC treatment of the radial distribution function /7,8/. The density matrix exhibits the following functional form where r = Irl-r;l I nc is a strength factor and % (kFr) is the inverse Fourier transform of the ideal gas momentum distribution function. The functions GDD and GWW represent infinite partial summations of the contributing diagrams : see ref./7/ for details. The one-particle momentum distribution function is obtained as a Fourier transform of the density matrix given by eq. ( 4 ) . The present method is an extension to Ferni systems of the variational method which we have recently applied for a calculation of ground state properties of the condensed spin-aligned atomic hydrogen /9/. In the Bose case the momentum distribution shows singular low momentum behavior ; n(k) % nc/k as k + 0, where nc is the Bose-Einstein condensate fraction. The calculated condensate fraction of Hf at T = 0 K varied from 95% to 29% as the density of hydrogen atoms was increased from 2x10~0 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980735