  We consider a Sinai billiard where the usual hard disk scatterer is replaced
by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the
origin. Using periodic orbit theory and numerical evidence we show that its
spectral statistics tends to Poisson statistics for large energies when
$\alpha<2$ and to Wigner-Dyson statistics when $\alpha>2$, while for $\alpha=2$
it is independent of energy, but depends on $\lambda$. We apply the approach of
Altshuler and Levitov [Phys. Rep. {\bf 288}, 487 (1997)] to show that the
transition in the spectral statistics is accompanied by a dynamical
localization-delocalization transition. This behaviour is reminiscent of a
metal-insulator transition in disordered electronic systems.
