Jastrow wave function and correlations of the Lennard-Jones Bose fluid

The Temperature Dependence of the Static Structure Factor for Liquid4He BelowTλ

“…This is the main deviation between theory and experi-persion spectrum Ek(7') are in good agreement with neutron scattering measurement of Sears et al [7, 101 and X-ray scattering results of Robkoff and Hallock [8, 111. Near T A rotons are no longer good elementary excitations and one should take into account the fact that the lifetimes of the roton states become finite in order to explain the reversion to the normal behaviour of S ( k , 7') above TA. Gaglione et al [4] did this using a Lorentzian distribution for energy of rotons wih a width 6k(7') taken from experiments and found a qualitative agreement with neutron scattering measurements also above TA.…”

“…In Fig. 3 we compare the height and the position of the main peak as calculated both from HFDHE2 and W-potentials with experiments as well as with perturbation calculations done by Gaglione et al [4] where also the finite line widths of the roton states were taken into account semiempirically. Our results for k,,,…”

“…In this report we calculate S ( k , T ) also from the Penrose density matrix with the help of the HNC-equation in whole wavevector range (both in phonon and roton regions). Only the latter was studied by Gaglione et al [4] whereas the former was studied by Feenberg [6] within the random phase approximation. Also we want to compare the S(k, T ) determined microscopically from the Jastrow-wavefunction (incorporating threebody correlations in the ground state as zero-point motion of rotons) with experiments and with the perturbation theoretic calculations of Reatto's group.…”

Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

“…These functions satisfy Eqs. (14), (31), (32). Modified pair equations are solved up to a cutoff distance L c ≤ L b , like in the previous case.…”

“…The simplest variational ansatz for helium consists of the parametrized leading-term solution proposed by McMillan and by Schiff and Verlet 25,26 , or similar solutions 27,28 . The improvements beyond the leading order for helium can be seen as falling into the following categories: (a) addition to the leading term (12) of various explicit short-and long-range corrections derived from known general properties of the system [29][30][31][32] , (b) parametrization of the mid-range behavior of u 2 focused primarily on improving the variational energy or structural properties [32][33][34][35] , and (c) extracting the solution to the pair equation ( 8) beyond the leading order, or using such solutions as a basis set [36][37][38] . These approaches are considered in some detail below.…”