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- W4377029196 abstract "We present an alternative analysis of the $^{113}mathrm{Cd}phantom{rule{4pt}{0ex}}ensuremath{beta}$-decay electron energy spectrum in terms of spectral moments ${ensuremath{mu}}_{n}$, corresponding to the averaged values of $nmathrm{th}$ powers of the $ensuremath{beta}$ particle energy. The zeroth moment ${ensuremath{mu}}_{0}$ is related to the decay rate, while higher moments ${ensuremath{mu}}_{n}$ 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: $r={g}_{mathrm{A}}/{g}_{mathrm{V}}$ (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 ${g}_{mathrm{V}}=1$. 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 $(r,phantom{rule{0.16em}{0ex}}s)$ plane: An ellipse for $n=0$ and hyperbolas for $nensuremath{ge}1$, 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 ${ensuremath{mu}}_{n}$, identify the favored values of $(r,phantom{rule{0.16em}{0ex}}s)$ at a glance, without performing detailed fits. In particular, we find that values around $rensuremath{approx}1$ and $sensuremath{approx}1.6$ are consistently favored in each nuclear model, confirming the evidence for ${g}_{mathrm{A}}$ quenching in $^{113}mathrm{Cd}$, and shedding light on the role of the $s$-NME. We briefly discuss future applications of the SMM to other forbidden $ensuremath{beta}$-decay spectra sensitive to ${g}_{mathrm{A}}$." @default.
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- W4377029196 date "2023-05-18" @default.
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- W4377029196 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mmultiscripts><mml:mi>Cd</mml:mi><mml:mprescripts /><mml:none /><mml:mn>113</mml:mn></mml:mmultiscripts></mml:math> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>β</mml:mi></mml:math> -decay spectrum and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:math> quenching using spectral moments" @default.
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- W4377029196 doi "https://doi.org/10.1103/physrevc.107.055502" @default.
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