Numerical evaluation for classical one-dimensional gas of hard rods with an interaction of finite range

In a recent formulation of the theory of the classical one-dimensional gas of hard rods with an interaction of finite range, the Gibbs potential and distribution functions are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of the homogeneous linear integral equation. The description is given of a practical numerical procedure for obtaining those eigenvalue and eigenfunction. As an illustration, the procedure is applied to the system with the square-well potential, for the cases where the range of the interaction is three times and four times, respectively, the hard-core diameter. The equation of state and the pair distribution function are then calculated for this system.