Random matrix structure of nuclear shell model Hamiltonian matrices and comparison with an atomic example |
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Authors: | Manan Vyas and V K B Kota |
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Institution: | 1.Physical Research Laboratory,Ahmedabad,India |
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Abstract: | We present a comprehensive analysis of the structure of Hamiltonian matrices based on visualization of the matrices in three
dimensions as well as in terms of measures for GOE, banded and two-body random matrix ensembles (TBRE). We have considered
two nuclear shell model examples, 22Na with Jp T = 2+0\ensuremath J^{\pi} T = 2^+0 and 24Mg with Jp T = 0+0\ensuremath J^{\pi} T = 0^+0 and, for comparison we have also considered the SmI atomic example. It is clearly established that the matrices are neither
GOE nor banded. For the TBRE structure we have examined the correlations between diagonal elements and eigenvalues, fluctuations
in the basis states variances and structure of the two-body part of the Hamiltonian in the eigenvalue basis. Unlike the atomic
example, nuclear examples show that the nuclear shell model Hamiltonians can be well represented by TBRE. |
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Keywords: | |
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