The effect of three-body interactions on the elastic properties of hexagonal close packed solid ⁴He is investigated using variational path integral (VPI) Monte Carlo simulations. The solid’s nonzero elastic constants are calculated, at T = 0 K and for a range of molar volumes from 7.88 cm³/mol to 20.78 cm³/mol, from the bulk modulus and the three pure shear constants C₀, C₆₆, and C₄₄. Three-body interactions are accounted for using our recently reported perturbative treatment based on the nonadditive three-body potential of Cencek et al. Previous studies have attempted to account for the effect of three-body interactions on the elastic properties of solid ⁴He; however, these calculations have treated zero point motions using either the Einstein or Debye approximations, which are insufficient in the molar volume range where solid ⁴He is characterized as a quantum solid. Our VPI calculations allow for a more accurate treatment of the zero point motions which include atomic correlation. From these calculations, we find that agreement with the experimental bulk modulus is significantly improved when three-body interactions are considered. In addition, three-body interactions result in non-negligible differences in the calculated pure shear constants and nonzero elastic constants, particularly at higher densities, where differences of up to 26.5% are observed when three-body interactions are included. We compare to the available experimental data and find that our results are generally in as good or better agreement with experiment as previous theoretical investigations.

中文翻译：

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hcp固体⁴ He的三体相互作用和弹性常数

使用变路径积分（VPI）蒙特卡洛模拟研究了三体相互作用对六方密堆积固体⁴ He弹性特性的影响。根据体积模量和三个纯剪切常数C ₀，C ₆₆和T，分别在T = 0 K和7.88 cm ³ / mol至20.78 cm ³ / mol的摩尔体积范围内计算固体的非零弹性常数。C ₄₄。基于Cencek等人的非加性三体潜力，使用最近报道的微扰治疗可解释三体相互作用。。先前的研究试图解释三体相互作用对固体⁴ He弹性性质的影响。但是，这些计算使用爱因斯坦或德拜近似值来处理零点运动，这在固体⁴的摩尔体积范围内是不够的他的特征是量子固体。我们的VPI计算可对包括原子相关性在内的零点运动进行更精确的处理。从这些计算中，我们发现当考虑三体相互作用时，与实验体积模量的一致性得到了显着改善。此外，三体相互作用导致计算的纯剪切常数和非零弹性常数的差异不可忽略，特别是在较高密度下，当包含三体相互作用时，观察到的差异高达26.5％。我们与可用的实验数据进行了比较，发现我们的结果与先前的理论研究在总体上与实验具有相同或更好的一致性。