Density-Dependent Nuclear Interactions and the Beta Decay of ¹⁴C: Chiral Three-Nucleon Forces and Brown-Rho Scaling

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 Λ_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.