ar X iv : n uc l - th / 0 50 50 57 v 2 1 A ug 2 00 5 Degeneracies when only T = 1 two - body interactions are present

Abstract In the nuclear f7/2 shell, the nucleon–nucleon interaction can be represented by the eight values E(J) = 〈(f2 7/2) J |V |(f2 7/2) J〉, J = 0, 1, · · · , 7, where for even J the isospin is 1, and for odd J it is 0. If we set the T = 0 (odd J) two-body matrix elements to zero (or to a constant), we find several degeneracies which we attempt to explain in this work. We also give more detailed expressions than previously for the energies of the states in question. New methods are used to explain degeneracies that are found in Ti (I = 25/2− and 27/2−), V (I = 12 1 and 13 1 , as well as I = 13 2 and 15), and V (I = 29/2− and 31/2−).