Comparison of realistic and symmetry-determinedSandDpairs forGd156

Underlying symmetries of realistic interactions and the nuclear many-body problem

“…Hence the pure two-body W (2) matrix elements (6), and consequently the correlation coefficients involving H sp (4) , are independent of the C (and E 0 ) parameter(s) in the (isospin-)scalar case.…”

“…The latter are expressed through the parameters of the model interaction for isospin rank 0 and 2 of H sp (4) and {r ≤ (s, t); t ≤ u} orbits as follows,…”

“…For the purposes of this paper, we will use only the isoscalar part of our model Hamiltonian (4) and set all the orbits equal to j = 7/2 (r = s = t = u) because we choose to focus on a study of nuclei in the single 1f 7/2 level. In addition, these matrix elements correspond to the pure nuclear interaction and do not include Coulomb repulsion because its effect is corrected in the experimental energies themselves by applying an empirical formula deduced in [41].…”

“…In comparison, each of them has a correlation with the Sp(4) symmetric interaction of order of 0.6-0.8, which is typically regarded as a good one [13]. This implies that the realistic interactions possess around 40-60% of the dynamical symplectic symmetry of H sp (4) [(ζ H sp(4) ,HR ) 2 ] and hence 0.4-0.6 portion of H R is dynamically symmetric under Sp(4) transformations. Equivalently, the H sp(4) model interaction contains 40-60% of the realistic interactions under consideration.…”

“…For instance, in the same environment two very similar interactions are expected to yield similar patterns of their matrix elements (see, for example, [1,2,3]), as well to yield large overlaps of corresponding eigenstates (e.g., [4,5]) and close energy spectra (e.g., [6,7]). On the other hand, a complementary comparison that is based on the theory of spectral distributions [8,9] that invokes overall correlations of two interactions offers a broader view on their global behavior and universal properties [10,11,12,13,14].…”