Analytical solution to a nonseparable interaction model for a one-dimensional fluid of anisotropic molecules near a hard wall

We introduce a one-dimensional fluid model of anisotropic molecules near a hard wall having a nonseparable interaction and yet being analytically solv able. We compute radial and angular profiles of the particles as well as th e equation of state of the system. The model is worked out for two differen t hard core potentials and the results are compared to a Monte Carlo simula tion. We find that the model provides a very accurate description of the sy stem except in the limit of low pressure and large particle anisotropy wher e the fluctuation of the particle orientations become too large. In particu lar, the nonseparable character of the particle interaction potential leads to a coupling of the radial and angular parts of the one-body distribution that allows for a study of the correlation between the alignment of the pa rticles and their distance to the hard wall. This feature constitutes a rem arkable qualitative improvement with respect to any separable interaction m odel in which the radial and angular variables are necessarily decoupled.