Density-dependent nuclear interactions and the beta decay of 14C: chiral three-nucleon forces and Brown-Rho scaling

TL;DR

This paper investigates how density-dependent nuclear interactions, derived from chiral effective field theory and Brown-Rho scaling, explain the unusually long beta decay lifetime of 14C by incorporating medium modifications into shell model calculations.

Contribution

It demonstrates that medium modifications of nuclear forces are crucial for accurately reproducing the long lifetime of 14C within a shell model framework.

Findings

Both three-nucleon forces and Brown-Rho scaling yield similar qualitative results.

Medium modifications significantly increase the 14C lifetime to archaeological timescales.

Effective interactions at low-momentum scales are essential for accurate decay predictions.

Abstract

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.