From pair correlations to pair interactions: An exact relation in one-dimensional systems

We demonstrate that the pair potential $V(r)$ in one-dimensional systems can be obtained analytically from the pair-distribution function in case of short-ranged interactions. We re-examine the exact statistical mechanics solution and propose a simple procedure for extracting the pair potential and the equation of state from experimentally measured pair-distribution functions. The method is applied to charge-stabilised colloids which are confined to a one-dimensional laser trap