Degeneracies when T=0 two body interaction matrix elements are set equal to zero: Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle - art. no. 057302

In a previous work [S.J.Q. Robinson and Larry Zamick, Phys. Rev. C 63, 0644 16 (2001)] we studied the effects of setting all two body T=0 matrix elemen ts to zero in shell model calculations for Ti-43 (Sc-43) and Ti-44. The res ults for Ti-44 were surprisingly good despite the severity of this approxim ation. In single-j shell calculations (f(7/2)(n)) degeneracies arose betwee n the T = 1/2 I = (1/2)(1)(-) and (13/2)(1)(-) states in Sc-43 as well as t he T = 1/2 I = (13/2)(2)(-), (17/2)(1)(-), and (19/2)(1)(-) in Sc-43. For T i-44 the T = 0 states 3(2)(+), 7(2)(+), 9(1)(+), and 10(1)(+) are degenerat e as are the 10(2)(+) and 12(1)(+) states. The degeneracies can be explaine d by certain 6j symbols and 9j symbols either vanishing or being equal as i ndeed they are. Previously we used Regge symmetries of 6j symbols to explai n the vanishing 6j and 9j symbols. In this work a simpler, more physical me thod is used. This is Talmi's method of calculating coefficients of fractio nal parentage (cfp) for identical particles to states which are forbidden b y the Pauli principle. This is done for both the one particle cfp to handle 6j symbols and the two particle cfp for the 9j symbols. From this we learn that the common thread for the angular momenta I for which the above degen eracies occur is that these angular momenta cannot exist in the calcium iso topes in the f(7/2) shell. There are no T = 3/2 f(7/2)(3) states with angul ar momenta 1/2, 13/2, 17/2, and 19/2. In the same vein there are no T = 2 f (7/2)(4) states with angular momenta 3, 7, 9, 10, or 12. For these angular momenta, all the states can be classified by the dual quantum numbers (J(pi ),J(v)).