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Energy and structure of dilute hard- and soft-sphere gases
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The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.
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MAZZANTI CASTRILLEJO, Ferran, POLLS MARTÍ, Artur and FABROCINI, A. Energy and structure of dilute hard- and soft-sphere gases. Physical Review A. 2003. Vol. 67, num. 6, pags. 063615. ISSN 1050-2947. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/9573