Vanishing Gamow-Teller Transition Rate for A = 14 and the Nucleon-Nucleon Interaction in the Medium

The problem of the near vanishing of the Gamow-Teller transition (GT ) in the A = 14 system between the lowest J = 0+ T = 1 and J = 1+ T = 0 states is revisited. The model space is extended from the valence space (p−2) to the valence space plus all 2h̄ω excitations. The question is addressed as to what features of the effective nucleon-nucleon interaction in the medium are required to obtain the vanishing GT strength in this extended space. It turns out that a combination of a realistic strength of the tensor force combined with a spin-orbit interaction which is enhanced as compared to the free interaction yields a vanishing GT strength. Such an interaction can be derived from a microscopic meson exchange potential if the enhancement of the small component of the Dirac spinors for the nucleons is taken into account. In this work, we reconsider the old problem of the near-vanishing of the Gamow-Teller transition matrix element B(GT ) in the A = 14 system between the J = 0 T = 1 ground state of O or C and the J = 1 T = 0 ground state of N . This is an allowed transition, but somehow the configurations of the initial and final states conspire to make this matrix element nearly vanish. Therefore the calculation of this transition strength can serve as a very sensitive test for the nucleon-nucleon (NN) interaction in the nuclear medium. The simplest shell model configuration consists of two holes in the p shell for both the initial and final states. Using an LS representation, the wavefunctions can be written as :