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Title: Pair distribution function for interacting bosons and the ground-state energy of solid helium-4
Authors: Khanna, K M
Ayodo, Y K
Sakwa, T W
Rotich, S K
Torongey, P K
Mbugua, W S
Keywords: Bosons
Solid helium-4
Ground-state energy
Issue Date: May-2009
Publisher: CSIR
Abstract: The pair distribution function <i>g</i>(<i>r</i>) 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 <i>E</i><sub>k </sub>and the fundamental definition relating the structure factor <i>S</i>(<i>k</i>) and <i>g</i>(<i>r</i>) . This has been used in obtaining the ground state energy of solid <sup>4</sup>He using the kinetic energy and potential energy expressions of Hansen and Levesque. The most stable ground state of solid <sup>4</sup>He corresponds to a potential width of <i>b</i>=3.8Ǻ ,but the corresponding <<i>E</i>>/<i>N</i> for the density, ρ, of solid <sup>4</sup>He is very large compared with the experimental value. However, for <i>b</i> =4.81Ǻ and ρ=2.8×10<sup>22</sup> particles/ cm<sup>3</sup>, <<i>E</i>>/<i>N</i> =-11.24 K= -93.4Joule/mol. and for <i>b</i>=4.82Ǻ and ρ=2.5×10<sup>22</sup> particles/cm<sup>3</sup>, <<i>E</i>>/<i>N</i> = -6.84 K=56.8 Joule/mol. The experimental value for the ground state energy of solid <sup>4</sup>He =-59.5J/mol.
Description: 325-331
ISSN: 0019-5596
Appears in Collections:IJPAP Vol.47(05) [May 2009]

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