New analysis ofO14β decay: Branching ratios and conserved vector current consistency

Abstract

The ground-state Gamow-Teller transition in the decay of 14 O is strongly hindered and the electron spectrum shape deviates markedly from the allowed shape. A reanalysis of the only available data on this spectrum changes the branching ratio assigned to this transition by seven standard deviations: Our new result is (0.54 ± 0.02)%. The Kurie plot data from two earlier publications are also examined, and a revision to their published branching ratios is recommended. The required nuclear matrix elements are calculated with the shell model, and, for the first time, consistency is obtained between the M1 matrix element deduced from the analog γ transition in 14 N and that deduced from the slope in the shape-correction function in the β transition, a requirement of the conserved-vector current hypothesis. This consistency is obtained, however, only if renormalized rather than free-nucleon operators are used in the shell-model calculations. In the mirror decay of 14 C, a similar situation occurs. Consistency among the 14 C lifetime, the slope of the shape-correction function, and the M1 matrix element from γ decay can be achieved only with renormalized operators in the shell-model calculation.

Shell Model Description of theC14DatingβDecay with Brown-Rho-ScaledNNInteraction

“…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.…”

Measurement of the branching ratio for theβdecay ofO14

“…As seen previously in Ref. [6], the fit to the SG data is not very good. In our reanalysis the total χ 2 is 76 for 11 data points.…”

“…(3), to determine the constant k in Eq. (6). Effectively, what this does is to fix the n(p) curve at p = 2.729 MeV/c to the value 0.0962.…”

“…A reanalysis of the SG measurements that includes the effects of the various correction factors appearing in Eq. (5) has been carried out by Towner and Hardy [6]. They use β-decay shape factors derived from theoretical calculations that have been optimized to fit the SG data, and obtain R = (5.4 ± 0.2) × 10 −3 .…”

“…Most recently, in 1966, Sidhu and Gerhart [5] obtained the result R = (0.61 ± 0.01)%. All three measurements have been discussed and reanalyzed by Towner and Hardy [6], and based on that reanalysis HT have adopted the value R = (0.571±0.068)% for use in the analysis of the superallowed 0 + → 0 + transitions. We will comment further on the previous determinations of R in Sect.…”