Improved first-principles calculation of the third virial coefficient of helium

Abstract

We employ state-of-the-art pair and three-body potentials with path-integral Monte Carlo (PIMC) methods to calculate the third density virial coefficient C(T) for helium. The uncertainties are much smaller than those of the best experimental results, and approximately one-fourth the uncertainty of our previous work. We have extended our results in temperature down to 2.6 K, incorporating the effect of spin statistics that become important below approximately 7 K. Results are given for both the 3He and 4He isotopes. We have also performed PIMC calculations of the third acoustic virial coefficient γa; our calculated values compare well with the limited experimental data available. A correlating equation for C(T) of 4He is presented; differentiation of this equation provides a reliable and simpler way of calculating γa.

A determination of the molar gas constantRby acoustic thermometry in helium

“…where from theory [32]. The opportunity of the latter assumption relies on the observation that when A 2 is left as a free parameter in fitting (18), it is found to be not significantly different from zero: is based on the analysis of a significantly restricted dataset which excludes several modes and all the low-pressure data below 170 kPa.…”

Quantum Virial Coefficients via Path Integral Monte Carlo with Semi-classical Beads

“…Semi-classical virial coefficients up to fifth order have been computed for helium-4 by Shaul et al [15], and showed that first-principles properties could be evaluated with precision and accuracy that exceeds experiment. Garberoglio and Harvey [9,16,17] reported fully quantum second and third virial coefficients for helium-3 and helium-4 including exchange effects where needed, for temperatures as low as 2.6 K. Shaul et al [18] reported fully quantum virial coefficients of helium-4 (but without exchange) up to fourth order for temperatures of T = 2.6-1000 K.…”

“…(15) to a quantity that is dependent on both P and h as in Eq. (17). The inter-molecular potential experienced by the beads of the ring changes from being classical to semi-classical (dependent on P and h).…”

О Статистической Теории Разреженного Газа В Кулоновской Модели Вещества. Адиабатическое Приближение И Исходные Атомы

“…Среди имеющихся способов расчета в настоящее время наиболее перспективным представляется использование интегралов по траек-ториям Фейнмана и метода Монте-Карло (см. [48] и цитированную там литературу). Не менее важным является также развитие методов вычисления эффективного по-тенциала взаимодействия исходных атомов (15), где, на наш взгляд, наибольший интерес представляет ТФМП [29]- [31].…”