Distribution of the eigenvalues of the energy operator of a continuous system in quantum statistical mechanics

It is shown that the distribution of the eigenvalues of the energy operator of a system of $N$ particles in a region A that interact by means of a two-body potential $\Lambda$ satisfies under certain conditions a Gaussian law in the limit $\Lambda\to\infty$, $|\Lambda|^{-1}N\to\delta$ and small $\delta$.