Garberoglio Giovanni, Harvey Allan H
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT), Trento I-38123, Italy.
Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
J Chem Phys. 2021 Mar 14;154(10):104107. doi: 10.1063/5.0043446.
We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients D(T) of He and He as functions of temperature from 2.6 K to 2000 K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for He at the temperatures considered, but for He, they are necessary for quantitative accuracy below about 4 K. Our results are consistent with previous theoretical work (also with some of the limited and scattered experimental data) for He; for He, there are no experimental values, and this work provides the first values of D(T) calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures, the uncertainties related to the three-body potential and omitted higher-order contributions become dominant.
我们使用路径积分蒙特卡罗（PIMC）方法以及最先进的两体和三体势来计算氦气（He）的第四维里系数D(T)，它是温度从2.6 K到2000 K的函数。我们推导了由于氦同位素的玻色子或费米子性质而产生的交换效应的贡献表达式；这些效应在先前的计算中被忽略了。在所考虑的温度下，交换效应对于He相对不显著，但对于He，在约4 K以下的温度范围内，它们对于定量精度是必要的。我们的结果与先前关于He的理论工作（也与一些有限且分散的实验数据）一致；对于He，没有实验值, 这项工作提供了在此水平下计算得到的D(T)的首个值。结果的不确定性取决于PIMC计算的统计不确定性、势能中忽略四体项的估计效应以及由势的不确定性传播而来的不确定性贡献。在低温下，不确定性主要由PIMC计算的统计不确定性主导，而在高温下，与三体势和忽略的高阶贡献相关的不确定性变得主导。
