Relations between Gamow-Teller and magnetic dipole transitions.

Abstract

The Gamow-Teller transitions ${J}_{i}$${=0}^{+}$ ${T}_{i}$=${T}_{z}$=1/2(N-Z)\ensuremath{\rightarrow}${J}_{f}$${=1}^{+}$ ${T}_{f}$=${T}_{z}$=[1/2(N-Z)]-1are compared with analogous M1 transitions in which the final states are the same but the initial states have ${T}_{\mathrm{zi}}$=[1/2(N-Z)]-1. In the single j shell model for the even calcium isotopes, the summed strengths for the analogous M1's (in Sc) are independent of A, but the corresponding summed Gamow-Teller strength is proportional to (N-Z) and accounts for (j+1)/(3j), i.e., (3/7 of the total ``3(N-Z)'' sum rule strength. Isospin considerations are exploited as much as possible. It is noted that configuration mixing, e.g., admixtures of j'=l-1/2, lead an enhancement of the low lying strength for the two-particle system ${(}^{42}$Ca), but to a retardation of the low lying strength in the higher A system ${(}^{48}$Ca). An analytic expression is obtained in perturbation theory with a delta residual interaction, to explain this interesting behavior. A brief survey of the experimental situation is made.