Tomchenko M. Wave functions of the ground and excited states of helium-II: inclusion of the three-particle and four-particle correlations

The N-particle wave functions of the ground (Psi-0) and excited one-phonon (Psi-k) states of helium-II are determined numerically by the collective-variable method for higher-order approximations compared with those investigated earlier: the four-particle correlations are taken into account for Psi-0, and the three-particle ones for Psi-k. The quasiparticle spectrum, the ground-state energy and the structure factor of He-II, calculated from Psi-0 and Psi-k, are in agreement with the experimental values. The amount of single-, two- and s-particle condensates are derived for T = 0 in the approximation which includes the three-particle correlations; without free parameters, we have obtained, accordingly, N1=0.06N, N2=0.16N, Ns=0 (s>=3). We also found thermodynamic formulas for an ensemble of noninteracting vortex rings in He-II and proposed an experiment for determining whether the vortex rings substantially influence the value of T-lambda.