In this paper we investigate regular patterns of matrix elements of the
nuclear shell model Hamiltonian $H$, by sorting the diagonal matrix elements
from the smaller to larger values. By using simple plots of non-zero matrix
elements and lowest eigenvalues of artificially constructed "sub-matrices" $h$
of $H$, we propose a new and simple formula which predicts the lowest
eigenvalue with remarkable precisions.Comment: six pages, four figures, Physical Review C, in pres
In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonian. We find that nonzero off-diagonal elements exhibit a regular pattern, if one sorts the diagonal matrix elements from smaller to larger values. The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small. nuclear shell model, geometry property, linear correlation, randomize
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