Shell model description of the 14C dating β decay with brown-rho-scaled NN interactions

We present shell model calculations for the beta decay of C-14 to the N-14 ground state, treating the states of the A=14 multiplet as two 0p holes in an O-16 core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller (GT) matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find that the splitting between the (J(pi),T)=(1(+),0) and (J(pi),T)=(0(+),1) states in N-14 is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of C-14 to the N-14 ground state are compatible with recent experiments.