Shell Model Description of theC14DatingβDecay with Brown-Rho-ScaledNNInteraction

Abstract

We present shell model calculations for the β-decay of 14 C to the 14 N ground state, treating the states of the A = 14 multiplet as two 0p holes in an 16 O core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller (GT) 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 π , T ) = (1 + , 0) and (J π , T ) = (0 + , 1) states in 14 N is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of 14 C to the 14 N ground state are compatible with recent experiments.The beta decay of 14 C to the 14 N ground state has long been recognized as a unique problem in nuclear structure. Its connection to the radiocarbon dating method, which has had a significant impact across many areas of science, makes the decay of broad interest even beyond nuclear physics. But a priori one would not expect the beta decay of 14 C to be a good transition for radiocarbon dating over archaeological times, because the quantum numbers of the initial state (J π , T ) = (0 + , 1) and final state (J π , T ) = (1 + , 0) satisfy the selection rules for an allowed Gamow-Teller transition. The expected half-life would therefore be on the order of hours, far from the unusually long value of 5730 years [1] observed in nature. The corresponding nuclear transition matrix element is very small (≃ 2 × 10 −3 ) and is expected to result from an accidental cancellation among the different components contributing to the transition amplitude. This decay has therefore been used to investigate phenomena not normally considered in studies of allowed transitions, such as meson exchange currents [2,3], relativistic effects [4], and configuration mixing [5,6]. Of broader importance, however, is that this decay provides a very sensitive test for the in-medium nuclear interaction and in particular for the current efforts to extend the microscopic description of the nuclear force beyond that of a static two-body potential fit to the experimental data on two-nucleon systems. One such approach is to include hadronic medium modifications, in which the masses of mesons and nucleons are altered at finite density due to the partial restoration of chiral symmetry [7,8,9] or many-body interactions with either intermediate nucleon-antinucleon excitations [10] or resonance-hole excitations [11]. These effects are traditionally incorporated in models of the three-nucleon force (3NF), which have been well-tested in ab initio nuclear structure calculations of light nuclei [12,13].In this Letter we suggest that a large part of the observed 14 C beta decay suppression arises from inmedium modifications to the nuclear interaction. We study the problem from the perspective of Brown-Rho scaling (...

Origin of the Anomalous Long Lifetime ofC14

“…A chiral 3NF with coupling constants consistent with other works and within their natural range can provide the precise lifetime. This indicates that corrections to the lifetime that arise from increasing the basis space, from including additional many-body interactions and from corrections to the GT operator in ChPT [2] may be absorbed into an allowed choice of the 3NF.Our work features two major advances over recent alternative explanations [3,4]: (1) we treat all nucleons on the same dynamical footing with the no-core shell model (NCSM) [5], and (2) we include the 3NF of ChPT [6] as a full 3-nucleon interaction. This follows previous work detailing the structure and electroweak properties of selected A=10-13 nuclei [7] with the same chiral NN + 3NF.…”

“…Our work features two major advances over recent alternative explanations [3,4]: (1) we treat all nucleons on the same dynamical footing with the no-core shell model (NCSM) [5], and (2) we include the 3NF of ChPT [6] as a full 3-nucleon interaction. This follows previous work detailing the structure and electroweak properties of selected A=10-13 nuclei [7] with the same chiral NN + 3NF.…”

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths

“…This half life is anomalously long in the sense that it exceeds the half lives of neighboring β unstable nuclei by many orders of magnitude. Recently, several studies attributed the long half life of 14 C to 3NFs [28][29][30], while the experiment points to a complicated strength function [55]. What do 2BCs contribute to this picture?…”

“…For the states of the daughter nuclei, we generalize a coupled-cluster technique and compute them as isospin-breaking excitations of the mother nuclei. We present predictions and spin assignments for the exotic isotopes 22,24 F, and revisit the anomalously long half life of 14 C [28][29][30].…”

“…For the current we use the empirical value g A = 1.2695 (29). The 2BCs enter at NNLO and depend on the LECs c D , c 3 , c 4 of the chiral interaction [37,38].…”