Statistical distribution of bonding distances in a unidimensional solid

We study a Fermi-Pasta-Ulam-like chain with Lennard-Jones potentials to model a unidimensional solid in contact with heat baths at a given temperature. We formulate an explicit analytical expression for the probability density of bonding distances between neighboring particles, which depends on temperature similarly to the distribution of velocities. For a finite number of particles, its validity is verified with high accuracy through molecular dynamics simulations. We also provide a theoretical framework which is consistent with the numerical findings. We give an analytic expression of the mean bond distance and elastic constant in the case of the square-well and harmonic interparticle potentials: we outline the role played by the hard-core repulsion. We also calculate the same quantities in the case of series expansions of Lennard-Jones potential truncated at different, even series power.