Density-Dependent Nuclear Interactions and the Beta Decay of 14 C : Chiral Three-Nucleon Forces and Brown-Rho Scaling
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2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. 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 fromthe perspective of chiral effective field theory, in which genuine three-body forces generate an effective density-dependent twobody 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 amodel 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 mediummodifications 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 observedthat at a low-momentum scale of lowk= 2.1 fm1, medium-modifications of the nuclear forc play an essential role in increasing the lifetime of 14C from a few minutes to an archaeologically long one of 5730 years.
