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Kirkwood-Monroe approximation for quantum solids

1978; American Physical Society; Volume: 18; Issue: 7 Linguagem: Inglês

10.1103/physrevb.18.3189

1095-3795

Michael David Miller, William J. Mullin, R. A. Guyer,

Material Dynamics and Properties

The energy of a Boltzmann quantum solid is calculated using the Kirkwood-Monroe liquid ansatz for the solid pair correlation function. Approximate liquid pair correlation functions generated from the Born-Bogoliubov-Green-Kirkwood-Yvon, Kirkwood-superposition-approximation (BBGKY-KSA) equation and from the hypernetted-chain (HNC) equation are used to calculate the energy of solids with $\frac{{\ensuremath{\hbar}}^{2}}{m\ensuremath{\epsilon}{\ensuremath{\sigma}}^{2}}=\ensuremath{\eta}$ of 0.1815 ($^{4}\mathrm{He}$) and 0.200. The calculations are done over the physical density range ($0.024<~\ensuremath{\rho}<~0.035$ part. /${\mathrm{\AA{}}}^{3}$). The energy of the liquid is also calculated. Results are obtained for solid and liquid energies which depend critically on the choice of liquid correlation function and on $\ensuremath{\eta}$. For $\ensuremath{\eta}=0.1815$ and the BBGKY-KSA pair correlation function the system has a liquid \ensuremath{\rightarrow} solid \ensuremath{\rightarrow} liquid phase transition, whereas for $\ensuremath{\eta}=0.1815$ and the HNC pair correlation function the system can exist as a zero-pressure solid.