Abstract
We present an alternative analysis of the -decay electron energy spectrum in terms of spectral moments , corresponding to the averaged values of powers of the particle energy. The zeroth moment is related to the decay rate, while higher moments are related to the spectrum shape. The here advocated spectral-moment method (SMM) allows for a complementary understanding of previous results, obtained using the so-called spectrum-shape method (SSM) and its revised version, in terms of two free parameters: (the ratio of axial-vector to vector couplings) and (the small vectorlike relativistic nuclear matrix element, -NME). We present numerical results for three different nuclear models with the conserved vector current hypothesis (CVC) assumption of . We show that most of the spectral information can be captured by the first few moments, which are simple quadratic forms (conic sections) in the plane: An ellipse for and hyperbolas for , all being nearly degenerate as a result of cancellations among nuclear matrix elements. The intersections of these curves, as obtained by equating theoretical and experimental values of , identify the favored values of at a glance, without performing detailed fits. In particular, we find that values around and are consistently favored in each nuclear model, confirming the evidence for quenching in , and shedding light on the role of the -NME. We briefly discuss future applications of the SMM to other forbidden -decay spectra sensitive to .
- Received 15 February 2023
- Revised 24 March 2023
- Accepted 9 May 2023
DOI:https://doi.org/10.1103/PhysRevC.107.055502
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