The exact computation of the nearest-neighbor spacing distribution P(s) is
performed for a rectangular billiard with point-like scatterer inside for
periodic and Dirichlet boundary conditions and it is demonstrated that for
large s this function decreases exponentially. Together with the results of
[Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral
statistics of such systems is of intermediate type characterized by level
repulsion at small distances and exponential fall-off of the nearest-neighbor
distribution at large distances. The calculation of the n-th nearest-neighbor
spacing distribution and its asymptotics is performed as well for any boundary
conditions.Comment: 38 pages, 10 figure