Spacings of Nuclear Energy Levels

The ideas about the distribution law governing the spacings of adjacent energy levels. of the same spin and parity, of highly excited nuclei were studied by a numerical analysis. A set of 200 real symmetric matrices of order 20 was considered with matrix elements chosen at random from a symmetric uniform distribution. The results for the uniform distribution is shown in the form of a histogram. The calculations were repeated, with the matrix elements selected at random from a Gaussian distribution 10,01. Both sets of results confirm Wigner's conjectures that the distribution law for x (the value of a particular spacing divided by the mean value) does not depend sensitively on the precise distribution law for the matrix elements and that the correct p(x) is given approximately by p(x) = pi /2 x exp(- 1/4 pi x/sup 2/). (M.H.R.)