Strong Linear Correlation Between Eigenvalues and Diagonal Matrix   Elements
  We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations. 
J. J. Shen, A. Arima, Y. M. Zhao, N. Yoshinaga