J=0 T=1 Pairing Interaction Selection Rules

Wave functions arising form a pairing Hamiltonian E(0) i,e, one in which the interaction is only between J=0^{+}T=1 pairs, lead to magnetic dipole and Gamow-Teller transition rates that are much larger than those from an interaction E(J_{max}) in which a proton and a neutron couple to J=2j. With realistic interactions the results are in between the 2 extremes. In the course of this study we found that certain M1 and GT matrix elements vanish with E(0) . These are connected to seniority and reduced isospin isospin selection rules. We find the surprising result that The M1 strength to the single j scissors is larger for a J=0 T=1 pairing interaction than it is for Q.Q