Binary kernel and pair distribution functions of a system with coulomb interactions

• Published in: Physica 1974-03, Vol.72 (2), p.319-331
• Main Author: Trivedi, P.C.
• Format: Article
• Language: English
• ISSN: 0031-8914
• DOI: 10.1016/0031-8914(74)90032-9

The first- and second-order terms in the expansion of the binary kernel are calculated for a system with Coulomb interactions by a method developed recently. The pair distribution function for an electron gas, in the high-temperature limit, is calculated. The result agrees with that of Fujita, Isihara and Montroll. The pair distribution function for a charged boson system, in the low-temperature limit, is also calculated. Its correctness is demonstrated by calculating the structure factor and the energy of an elementary exciton. The former result agrees with that of Lee and Feenberg. The first- and second-order terms of the binary kernel are also calculated for a system with hard-sphere interactions. Some articles, which are concerned with the pair distribution functions at such physically meaningless distances as the zero-separation distance between the particles or the distances less than the diameter of the hard-spheres, are critically examined. In our opinion the elimination of the 1/ r term from the pair distribution functions of a hard-sphere Bose system and the removal of the divergence from its ground-state energy in the calculations of Isihara and Yee are not correct.