RELATION BETWEEN THE NEAREST-LEVEL-SPACING DISTRIBUTION P(S) NEAR S=OAND THE DISTRIBUTION OF SOME TRANSITION MATRIX-ELEMENTS

In this paper by making use of a method to study avoided level crossin gs with very small splitting magnitudes, a relation is found between t he nearest-level-spacing distribution P(s) near s=0 of a Hamiltonian H and the distribution of \[psi(i)(lambda(1))\V\psi(i+1)(lambda(1))]\ ( where V is a perturbation term and \psi(i)(lambda(1))] are eigen-funct ions of H(lambda(1))=H + lambda(1)V with small lambda(1). Then some of the features of P(0) can be qualitatively explained.