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 ¹⁴C to the ¹⁴N ground state, treating the states of the A=14 multiplet as two 0p holes in an ¹⁶O 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^π,T)=(1⁺,0) and (J^π,T)=(0⁺,1) states in ¹⁴N is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of ¹⁴C to the ¹⁴N ground state are compatible with recent experiments.