We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.

Some points about the search for analytical expressions for the equation of state of the hard-disk fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.

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It has recently been proposed that several anomalous features in Raman and neutron scattering experiments on superfluid helium can be explained by the formation of two-roton bound states. In the present paper we analyze in detail the structure in the superfluid helium excitation spectrum associated with bound roton pairs and propose further experiments to examine the nature of the bound states. The two-roton spectrum is calculated including roton-roton interactions over a wide momentum range, and exhibits structure due to bound states which is in remarkable agreement with experiment. Interaction of the two-roton bound state with the single-particle excitations results in a hybridization of these states and a consequent splitting of the single-particle spectrum into two branches; the calculated momentum dependence of these branches is consistent with the neutron data. Inclusion of a finite roton lifetime is shown to be essential to the interpretation of the experimentally observed excitation spectrum in the vicinity of the bound-state energy. Possible physical mechanisms for the roton-roton interaction are considered, and the angular momentum character of the bound states is briefly discussed.

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