  A class of exact solutions are obtained for the problem of N-anyons
interacting via the N-body potential $V (\vec x_1,\vec x_2,...,\vec x_N)$ =
$-{e^2\over\sqrt{{1\over N}\sum_{i<j} (\vec x_i-\vec x_j)^2}}$ Unlike the
oscillator case the resulting spectrum is not linear in the anyon parameter
$\alpha (0\leq \alpha\leq 1)$. However, a la oscillator case, cross-over
between the ground states is shown to occur for N-anyons $(N\geq 3)$
experiencing the above potential.
