  We completely solve the problem of classifying all one-dimensional quantum
potentials with nearest- and next-to-nearest-neighbors interactions whose
ground state is Jastrow-like, i.e., of Jastrow type but depending only on
differences of consecutive particles. In particular, we show that these models
must necessarily contain a three-body interaction term, as was the case with
all previously known examples. We discuss several particular instances of the
general solution, including a new hyperbolic potential and a model with
elliptic interactions which reduces to the known rational and trigonometric
ones in appropriate limits.
