We show the functional dependence of eigenvalues in terms of sorted diagonal elements of a Hamiltonian matrix in the nuclear shell model (NSM), a matrix with uniform distribution and that with normal distribution. For a realistic two-body interaction, its relation is approximately expressed by a linear function, especially for the most elements in the intermediate region. We also derive their functional dependences for the uniform distribution and the normal distribution analytically. As a special case, the functional relation for the normal distribution turns out to be approximated by a hyperbolic-tangent function.

• Received 19 September 2008

DOI:https://doi.org/10.1103/PhysRevC.79.017301