Convenient formulae for some integrals in perturbation theory

• Видавець: Інститут фізики конденсованих систем НАН України
• Дата: 2010
• Автор: Henderson, D.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут фізики конденсованих систем НАН України 2010
• Назва видання: Condensed Matter Physics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/32040
• Цитувати: Convenient formulae for some integrals in perturbation theory / D. Henderson // Condensed Matter Physics. — 2010. — Т. 13, № 1. — С. 13002: 1-10. — Бібліогр.: 16 назв. — англ.

The free energy and pressure of a fluid, as given by perturbation theory, involve integrals of the hard sphere correlation functions and their density derivatives. In most applications a straightforward procedure would be to obtain these integrals, possibly numerically, using the formulae and computer codes for the hard sphere correlation functions, given previously [Mol. Phys., 2007, 106, 2; Condens. Matter Phys., 2009, 12, 127], followed by numerical differentiation with respect to the density and a possible compounding of errors. More sophisticated methods are given in this paper, which is the second in a planned trilogy, drawn from the author's lecture notes. Three representative model fluids are considered. They are the square-well fluid, the Yukawa fluid, and the Lennard-Jones fluid. Each model fluid is popular for theoretical and engineering calculations and can represent a simple fluid such as argon. With the methods presented here, numerical integration and differentiation are not necessary for the square-well and Yukawa fluids. Numerical integration cannot be easily avoided in the case of the Lennard-Jones fluid. However, numerical differentiation with respect to the density is not required.