  We study the role of density-dependent low-momentum nucleon-nucleon
interactions in describing the anomalously long beta decay lifetime of 14C. We
approach this problem both from the perspective of chiral effective field
theory, in which genuine three-body forces generate an effective
density-dependent two-body interaction, as well as from the perspective of
Brown-Rho scaling, in which the masses and form factor cutoffs in
one-boson-exchange interactions are modified in a dense nuclear medium due to
the partial restoration of chiral symmetry. The beta decay transition of 14C to
the ground state of 14N is calculated within the shell model using a model
space consisting of two 0p-shell holes within a closed 16O core. The effective
0p-shell interaction is calculated up to second order in perturbation theory
with single-particle energies extracted from experiment. We find that both
three-nucleon forces and Brown-Rho scaling medium modifications give
qualitatively similar results not only for the ground state to ground state
Gamow-Teller transition but also for Gamow-Teller transitions from excited
states of 14C to the ground state of 14N. In this way, it is observed that at a
low-momentum scale of V_(low-k) = 2.1 fm-1, medium-modifications of the nuclear
force play an essential role in increasing the lifetime of 14C from a few
minutes to an archaeologically long one of 5730 years.
