Quantum-Mechanical Equation of State of a Hard-Sphere Gas at High Temperature. II
1969; American Institute of Physics; Volume: 184; Issue: 1 Linguagem: Inglês
10.1103/physrev.184.119
ISSN1536-6065
Autores Tópico(s)Quantum, superfluid, helium dynamics
ResumoAs the continuation of a preceding paper, an expansion for the quantum-mechanical free energy $F$ of a hard-sphere gas at high temperature is extended up to the second order in the thermal wavelength $\ensuremath{\lambda}={(\frac{2\ensuremath{\pi}{\ensuremath{\hbar}}^{2}}{\mathrm{mkT}})}^{\frac{1}{2}}$. To reach this order, one must study the three-body problem in a lowest-order approximation, in which adjacent sphere surfaces can be regarded as parallel planes. Coefficients of the $\ensuremath{\lambda}$ series for $F$ are given in terms of classical correlation functions. Using known density expansions for these correlation functions, one can obtain $\ensuremath{\lambda}$ expansions for the virial coefficients; the third virial coefficient is ${B}_{3}=(\frac{5{\ensuremath{\pi}}^{2}{a}^{6}}{18})[1+(\frac{3}{\sqrt{2}})(\frac{\ensuremath{\lambda}}{a})+1.707660{(\frac{\ensuremath{\lambda}}{a})}^{2}+\ensuremath{\cdots}]$, where $a$ is the hard-sphere diameter (only the last term is a new result).
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