Selection Rules for M1 and Gamow Teller transitions with a J=0 T=1 pairing interaction

We consider selection rules for M1 transtions in a single j shell with a J=0 T=1 pairing interaction. We use J=1$^{+}$ to J=2$^{+}$ in $^{46}$Ti as an example.The states are classified as (v,T,t)-seniority- isospin and reduced isospin. We obtain vanishing B(M1)'s for 3 reasons. a.$\Delta$T=2 b. $\Delta$v=4 or 6 c. The final state differs from the initial state in both v and t. The first case a. is obvious because the M1 operator is of rank 1 in isospin.For case b. we note that the M1 operator acting on a J=0 v=0 pair can only change v by 2 units. In c. the M1 operator cannot change both v and t at the same time. Examples af a. are (411) to $(231),$$(231)$. Examples of b. are (611) $to(221)$, (211) Examples of c. are (611) to (412), (422); (220) to (412), (411),$(422)$, (421). Transitons in which the seniority changes by 2 units and the reduced isospin does not change are allowed.These selection rules also apply to corresponding Gamow-Teller transiitons.