  We present shell model calculations for the beta-decay of the 14C ground
state 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 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,T)=(1+,0) and (J,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.
