Nearest-neighbour spacing distribution of energy levels in the region between integrability and chaos

We derive an expression for the level spacing distribution for a quantal system displaying both regular and chaotic classical motion, assuming that the level-repulsion function for the mixed system is obtained by averaging the corresponding functions for the regular and chaotic regimes with weights given by their fractional phase-space volumes. The Liouville measures of the regular region obtained from comparing this expression with the level spacing distributions of a hydrogen atom in a uniform magnetic field agree with the corresponding values obtained in the classical-mechanical analysis of this system. (author)