Ground State Energy of Bose System with Lennard-Jones Potential

L. Liu

Johannes Egger, E. Krotscheck, Robert E. Zillich

Ryuzo Abe

The perturbation theoretic procedure is developed for a system of strongly interacting particles, by replacing the singular potential with an equivalent operator. As an application of the method, an expression for the ground state energy of a Bose system, which corresponds to Lenz's formula for the hard-sphere system, is obtained for the Lennard-Jones potential. The cohesive energy of liquid He4 is calculated and is shown to be about twice as large as the experimentally observed one. Some difficulties arising from the negative value of the scattering length are discussed, and it is suggested that the assumption, usually taken for Bose system, that nearly all the particles are in the single particle state with momentum 0 should be altered for the actual liquid He4.

龍蔵 阿部

Élliott H. Lieb, Jakob Yngvason

M. A. Sol̆s, Valdir C. Aguilera-Navarro, MANUEL DE LLANO +1 more

The thermodynamic perturbation scheme so successful for classical-liquid equations of state is applied to the ground-state energy of a many-boson system interacting pairwise via the Lennard-Jones intermolecular potential. The ensuing density and attractive-coupling double expansion for the energy is series analyzed with Pad\'e techniques, as well as generalizations thereof. Results through sixth order compare with Green's-function Monte Carlo simulations at the 1% level of accuracy.