113Cdβ-decay spectrum and gA quenching using spectral moments

We present an alternative analysis of the 113Cdβ-decay electron energy spectrum in terms of spectral moments μn, corresponding to the averaged values of nth powers of the β particle energy. The zeroth moment μ0 is related to the decay rate, while higher moments μn 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: r=gA/gV (the ratio of axial-vector to vector couplings) and s (the small vectorlike relativistic nuclear matrix element, s-NME). We present numerical results for three different nuclear models with the conserved vector current hypothesis (CVC) assumption of gV=1. 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 (r,s) plane: An ellipse for n=0 and hyperbolas for n≥1, 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 μn, identify the favored values of (r,s) at a glance, without performing detailed fits. In particular, we find that values around r≈1 and s≈1.6 are consistently favored in each nuclear model, confirming the evidence for gA quenching in 113Cd, and shedding light on the role of the s-NME. We briefly discuss future applications of the SMM to other forbidden β-decay spectra sensitive to gA.