Pair distribution function for interacting bosons and the ground-state energy of solid helium-4

• Published in: Indian journal of pure & applied physics Vol. 47; no. 5; pp. 325 - 331
• Main Authors: Khanna, K M, Ayodo, Y K, Sakwa, T W, Rotich, S K, Torongey, P K, Mbugua, W S
• Format: Journal Article
• Language: English
• Published: 01.05.2009
• ISSN: 0019-5596

The pair distribution function @@ig(r@) for a system of bosons interacting through a two-body potential composed of a hard core followed by a square well has been obtained using the reaction matrix formalism for the energy excitation spectrum @iEK and the fundamental definition relating the structure factor @@iS(k@) and @@ig(r@). This has been used in obtaining the ground state energy of solid @u4He using the kinetic energy and potential energy expressions of Hansen and Levesque. The most stable ground state of solid @u4He corresponds to a potential width of @ib=3.8Aa, but the corresponding (@@iE)/N@ for the density, r, of solid @u4He is very large compared with the experimental value. However, for @ib =4.81 Aa and r=2.8 x 10@@u22@ particles/ cm@u3, (@@iE)/N@ =-11.24 K= -93.4Joule/mol. and for @ib=4.82Aa and r=2.5 x 10@@u22@ particles/cm@u3, (@@iE)/N@ = -6.84 K=56.8 Joule/mol. The experimental value for the ground state energy of solid @u4He --59.5J/mol.