Origin of the Anomalous Long Lifetime ofC14

Abstract

We report the microscopic origins of the anomalously suppressed beta decay of 14 C to 14 N using the ab initio no-core shell model (NCSM) with the Hamiltonian from chiral effective field theory (EFT) including three-nucleon force (3NF) terms. The 3NF induces unexpectedly large cancellations within the p-shell between contributions to beta decay, which reduce the traditionally large contributions from the NN interactions by an order of magnitude, leading to the long lifetime of 14 C. The measured lifetime of 14 C, 5730±30 years, is a valuable chronometer for many practical applications ranging from archeology to physiology. It is anomalously long compared to lifetimes of other light nuclei undergoing the same decay process, allowed Gamow-Teller (GT) betadecay, and it poses a major challenge to theory since traditional realistic nucleon-nucleon (NN) interactions alone appear insufficient to produce the effect [1]. Since the transition operator, in leading approximation, depends on the nucleon spin and isospin but not the spatial coordinate, this decay provides a precision tool to inspect selected features of the initial and final states. To convincingly explain this strongly inhibited transition, we need a microscopic description that introduces all physicallyrelevant 14-nucleon configurations in the initial and final states and a realistic Hamiltonian that governs the configuration mixing.We report the first no-core solutions of 14 C and 14 N using a Hamiltonian with firm ties to the underlying theory of the strong interaction, Quantum Chromodynamics (QCD), which allows us to isolate the key canceling contributions involved in this beta decay. We find that the three-nucleon force (3NF) of chiral perturbation theory (ChPT) plays a major role in producing a transition rate that is near zero, needed for the anomalous long lifetime. 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. We also establish a foundation for future work on the GT transitions to excited A=14 states [8].ChPT provides a theoretical framework for internucleon interactions based on the underlying symmetries of QCD. Beginning with pionic or the nucleon-pion system [9] one works consistently with systems of increasing nucleon number [10][11][12]. One makes use of the explicit and spontaneous breaking of chiral symmetry to expand the strong interactio...

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].…”

“…However, the Hamiltonians employed in these works are not consistent with the currents (and they contain no 3NFs), and/or the 2BCs are approximated by averaging the second nucleon over the Fermi sea of symmetric nuclear matter. The recent studies [27,28] of electroweak transitions in light nuclei employ 3NFs but lack 2BCs. This gives urgency for a calculation of weak decays that employs 3NFs and consistent 2BCs.…”

Evolved chiralNN+3NHamiltonians forab initionuclear structure calculations

“…Ref. [8,32,42]. We propose to use JT -coupled three-body matrix elements for a more efficient storage and retrieval combined with an on-the-fly decoupling during the many-body calculation [33], in complete analogy to the standard procedure for two-body matrix elements.…”

“…In many NCSM applications including chiral 3N interactions [8,30,42], the complete set of m-scheme matrix elements (16) was computed and stored before the actual many-body calculation. As mentioned earlier, the sheer number of three-body mscheme matrix elements sets a severe limit to the model-space sizes that are accessible with this approach.…”