Add massive neutrino support and improve CSV/CLI output
- Add neutrino mass parameter to SpectrumConfig and CLI interface - Update PhaseSpace component to handle neutrino mass effects properly - Update CSV headers to show basic endpoint and all transition types - Add --csv-verbosity option to CLI with 'full' and 'concise' options - Fix comparison plots to properly show linear scale variations - Add comprehensive tests for neutrino mass functionality
This commit is contained in:
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5202
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nuJ
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12
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]xe-lcun[
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1v44571.6052:viXra
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The measurement of the 99Tc β-decay spectrum and its implications for the effective
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value of weak axial coupling
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J. W. Song,1,2 M. Ramalho,3,4 M. K. Lee,1 G. B. Kim,5 I. Kim,5 H. L. Kim,6 Y. C.
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Lee,6,7 K. R. Woo,6 J. Kotila,8 J. Kostensalo,9 J. Suhonen,4,10,∗ and H. J. Kim2,†
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1Korea Research Institute of Standards and Science, Daejeon 34113, South Korea
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2Department of Physics, Kyungpook National University, Daegu 41566, South Korea
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3School of Physics, Engineering and Technology,
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University of York, Heslington, York YO10 5DD, United Kingdom
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4Department of Physics, University of Jyva¨skyla¨,
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P. O. Box 35 (YFL), FI-40014, Jyva¨skyl¨a, Finland
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5Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
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6Institute for Basic Science, Daejeon 34126, South Korea
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7Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
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8Finnish Institute for Educational Research, University of Jyva¨skyl¨a, Jyv¨askyla¨, Finland
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9Natural Resources Institute Finland, Yliopistokatu 6B, FI-80100 Joensuu, Finland
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10International Centre for Advanced Training and Research in Physics (CIFRA), 077125 Bucharest-Magurele, Romania
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(Dated: June 24, 2025)
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Measurements of β-spectral shapes is an important way to examine the effective value of the
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weakaxialcouplingg . Thesestudiesfocusspecificallyonforbiddennon-uniqueβ− transitions,as
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A
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only in these cases is the spectral shape directly sensitive to the ratio g /g . Here, the value of
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A V
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the weak vector coupling constant, g , is fixed at 1.0 according to the Conserved Vector Current
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V
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(CVC) hypothesis. In previous studies for the fourth-forbidden non-unique β− decays of 113Cd
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[J. Kostensalo et al., Phys. Lett. B 822, 136652 (2021)] and 115In [A. F. Leder et al., Phys.
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Rev. Lett. 129, 232502 (2022) and L. Pagnanini et al., Phys. Rev. Lett. 133, 122501 (2024)] a
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quenchedvaluewasdeterminedfortheratiog /g usingg =1.0. Anotableexceptionistherecent
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A V V
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measurementandanalysisofthesecond-forbiddennon-uniqueβ-decaytransitionin99Tc,performed
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byM.Paulsenet al.,Phys. Rev. C110,05503(2024). Whereanenhancedratiog /g =1.526(92)
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A V
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was suggested. To resolve this apparently contradictory situation with the effective value of g , we
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A
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haveperformedcalculationsbasedonthenuclearshellmodel(NSM)Hamiltoniansglekpn,jj45pnb,
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andtheMQPMapproachwithacarefulconsiderationofthesmallrelativisticvectornuclearmatrix
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element(sNME).Thetheoreticalspectrawerecomparedtothe99Tcβ-decayspectrumbyusingthe
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4πgoldabsorberwithaMetallicMagneticCalorimeter(MMC).Inallcases,wefoundthatthedata
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matches well with reduced g /g values of 1.0–1.2. Our result contradicts the previously reported
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A V
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measurementfor99Tcandinsteadsupportsaquenchedaxialcouplingasreportedforotherisotopes.
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Introduction.—Electrons and electron antineutrinos turebeyond-the-standard-modelexperiments;seethere-
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are emitted in β− decays as a result of a transmuta- views [1–3].
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tion of a parent nucleus (Z,N) to a daughter nucleus
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In allowed β decays, such as Fermi and Gamow–Teller
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(Z +1,N −1), Z being the number of protons and N
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transitions, the emitted lepton pair (electron and an-
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the number of neutrons. Studies of β-electrons (elec-
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tineutrino)carrieszeroorbitalangularmomentum[4]. In
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trons emitted in β− decays) have become an important
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contrast,forbiddendecaysoccurwhentheemittedlepton
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subject of study, e.g., in connection with nuclear reac-
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pair carries nonzero orbital angular momentum [5]. The
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tors and the anomalies in their fluxes of antineutrinos,
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degreeofforbiddennesscanrangefromfirst-forbiddento
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and rare-events experiments searching for beyond-the-
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n:th-forbidden, with each additional level typically in-
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standard-modelphysics,likethosetryingtomeasurerare
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creasing the decay half-life by a factor of approximately
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β-decays and double beta decays. The β-electrons can 104. Forbidden β-transitions are generally classified into
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also be severe backgrounds in these experiments. In all
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two types: unique and non-unique. Unique transitions
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the aforementioned cases, measurements of the associ-
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are characterized by a single dominant nuclear matrix
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atedβ-spectralshapeisessential. Distortionsinβ-decay
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element (NME) and thus exhibit a universal β-spectral
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spectral shapes also provide important input for under-
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shapethatisindependentofnuclearstructure[4]. Incon-
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standing the weak axial coupling constant g , which
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A trast, non-uniquetransitionsinvolveacomplexinterplay
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is relevant for sensitivity estimates in current and fu-
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of several NMEs, making the β-decay spectrum highly
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sensitivetothenuclearwavefunctionsofboththeinitial
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and final states [5–7].
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∗ jouni.t.suhonen@jyu.fi The (partial) half-life of a forbidden non-unique β-
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† hongjoo@knu.ac.kr transitionsalsodependsonthevaluesoftheweakvector
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2
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and axial-vector couplings, g and g , respectively [5– plings by writing
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V A
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7]. The conserved vector current (CVC) hypothesis
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sets g V = 1.0 whereas the partially conserved axial- C(w e )=g V 2C V (w e )+g A 2C A (w e )+g V g A C VA (w e ) (2)
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vector current (PCAC) hypothesis leads to an effective
|
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where w is the total (rest-mass plus kinetic) energy of
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(quenched) value of geff in finite nuclei [8], its bare- e
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A the emitted electron. The shape of the β-electron spec-
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nucleon value g =1.27 resulting from the experimental
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A trum is sensitive to the value of g due to subtle in-
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studies of the decay of an isolated neutron. The quench- A
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terference effects among the vector C (w ), axial-vector
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ing of the effective value of g has recently been studied V e
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A C (w), and mixed vector–axial-vector C (w) contribu-
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extensively in [2, 8, 9], and in particular its effects on A VA
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tionstothetransitionmatrixelement[6]. Forsomenuclei
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the neutrinoless double beta decay have been addressed
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(veryfew,ascharteduptopresentdays[2,18,19,21,22])
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in [1, 3]. To quantify the quenched value of g , com-
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A this causes measurable changes in the β-spectra. Thus,
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binedexperimentalandtheoreticalanalysesofβ-spectral
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the effective value geff can be found by computing the-
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shapes of individual β− transitions have recently been A
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oretical β-spectra for a set of geff values and comparing
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performed for the fourth-forbidden non-unique β-decays A
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themwiththemeasuredone. Thismethod,coinedasthe
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of 113Cd [10–13] and 115In [14–16].
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spectrum-shape method (SSM), was originally proposed
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A recent measurement of the β-decay spectrum
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in [6].
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for the second-forbidden non-unique ground-state-to-
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Another factor influencing theoretical analyses of β-
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ground-state transition 99Tc(9/2+) → 99Ru(5/2+),
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spectral shapes and half-lives is the so-called small rela-
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which has a 100% branching ratio, was reported by
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tivistic vector nuclear matrix element (sNME) [5]. The
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Paulsen et al. [17]. The accompanying theoretical analy-
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sNME gathers contributions outside the valence major
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sisyieldedacontradictoryresult,suggestinganenhance-
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shell that contains the proton and neutron Fermi sur-
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ment of the axial coupling with a value of g /g =
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A V faces, which makes its calculation particularly hard for
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1.526(92) using g =1.0.
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V nuclear-theoryframeworksused,e.g.,inthepresentwork
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ThegA-EXPERimentandTheory(gA-EXPERT)col-
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and also in the work of Paulsen et al. [17]. Despite its
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laboration is an international effort dedicated to quan-
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smallness, the sNME can influence the β-spectral shapes
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tifying the effective axial-vector coupling constant, geff,
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A and half-lives quite strongly [11, 12, 19, 21].
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by precisely measuring β-decays of various nuclei and
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ArealisticvalueofthesNMEcanbeestimatedfromits
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comparing the results with state-of-the-art nuclear the-
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CVC value [5], first used for spectral-shape calculations
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ory calculations. To address the tension raised by the
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in Ref. [18] and later by Paulsen et al. [17]. It should be
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enhanced value of geff = 1.526(92) reported in Ref. [17],
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A noted,though,thattheCVCvaluerepresentsan“ideal”,
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we performed a high-precision measurement of the 99Tc
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pertaining to a perfect many-body theory, which is not
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β-decay spectrum using metallic magnetic calorimeter
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the case for the nuclear-structure frameworks typically
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quantum sensors with a low-energy threshold of 10 keV.
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used for β-decay calculations of heavy open-shell nuclei,
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The measured spectrum was compared to predictions
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like the presently discussed 99Tc. To circumvent the use
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from three nuclear models, each based on distinct nu-
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of the CVC value, the experimental works [11, 13, 15]
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clear Hamiltonians. In this Letter, we present a quan-
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and theoretical works [12, 16] used sNME as a fitting
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titative comparison between data and modern nuclear
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parameter, together with geff. By this, it was possible to
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theory,providingnewconstraintsongeff anddemonstrat- A
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A reproduce both the measured β-spectral shape and the
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ing the sensitivity of precision β-spectroscopy to nuclear
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experimental (partial) half-life of the corresponding β-
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structure effects.
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transitionwithoutlosingtheCVCvalueg =1.0forthe
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Theory.—Tofirstorder,thehalf-lifeofaβ-decaytran- A
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vector coupling. This approach, termed the enhanced
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sition can be written as:
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spectrum-shape method (ESSM) in Ref. [19], is adopted
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κ in the present work.
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t = , (1)
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1/2 C˜ In this Letter, we present new theoretical calculations
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of the β spectrum of 99Tc (with Z = 43 and N = 56)
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where κ is a constant [18, 19] and C˜ is the integrated and compare them to the measured spectrum in order
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shapefunctionC,whichincorporatesvariousphase-space to extract the geff, using ESSM. To gain preliminary in-
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A
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factors and NMEs arising in the next-to-leading-order sightsintotheeffectiveaxialcouplinggeff intheβ-decay
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A
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expansion, as discussed in detail in Refs. [6, 7]. Our β- of 99Tc, we performed nuclear shell model (NSM) cal-
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spectral shape and half-life analyses employ screening, culations and compared the results with the measured
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radiative, and atomic-exchange corrections. For electron spectrum reported in Ref. [17]. As the β-decay rate
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energies below some tens of keV, the distortion in the β- has a quadratic dependence on the sNME, two solutions
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decay spectral shape is mostly dominated by the atomic werefoundforeachvalueofgeff,onecloserto[sNME(c)]
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A
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exchange correction, as originally studied for allowed β- and one further away from [sNME(f)] CVC value. In
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decays [20]. This correction is responsible for the sharp references [21, 23] the related two sets of theoretical β-
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upward trend of the spectral shape at low energies. spectra of 99Tc were introduced for two NSM Hamilto-
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The complexity of the shape function C can, however, nians, namely jj45pnb [24] and glekpn [25]; In that pre-
|
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be cast in a very simple dependence on the weak cou- liminary study, for the glekpn interaction we’ve used a
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3
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set of single particle energies fit to the A=94−98 mass below 1 Bq.
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region, however here we use the default single particle
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energies since it yields better experimental agreement
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for this isotope. Comparison with the measured spec-
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trum[17]indicatedthatbothsNMEvaluesusedwiththe
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jj45pnb Hamiltonian yielded good agreement, while the
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fit is somewhat poorer with sNME(c), and significantly
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worsewithsNME(f)whenusingtheglekpn Hamiltonian,
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further details of this preliminary study and its calcula-
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tions can be found in Refs [21, 23].
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In addition to the two NSM Hamiltonians described
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above, we also employ the nuclear many-body method
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known as the Microscopic Quasiparticle-Phonon Model
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(MQPM). A concise presentation of the essentials of
|
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NSM, and MQPM can be found in Ref. [2]. It should
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be pointed out here that Ref. [17] employed the NSM
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in their analysis, adopting the CVC value for the sNME
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withoutfittingittotheexperimentalhalf-lifeofβ-decay.
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A systematic comparison of various theoretical models
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with the measured spectrum offers a more robust frame-
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work for extracting the geff from high-precision spectral
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A
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data.
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Experiment.— Metallic magnetic calorimeters
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(MMCs) are some of the most advanced cryogenic FIG. 1. The detector setup used for the β-decay measure-
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ment. The gold sample containing the 99Tc source is ther-
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detectors for precision energy measurements. These
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mally coupled to the MMC sensor via gold wire bonds. A
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devices utilize paramagnetic ions embedded in metal-
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support washer with a Kapton tape on top for thermal insu-
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lic hosts—typically Au:Er or Ag:Er—as temperature
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lation was placed below the sample to align its height with
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sensors thermally coupled to metallic absorbers. The
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that of the MMC sensor.
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paramagnetic material is placed in a weak magnetic
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field (<10 mT) and operated at temperatures below The detector setup consists of an MMC and a Mag-
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100 mK. When an incident particle deposits energy nicon SQUID (Model X1) for signal readout (see Fig-
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E in the absorber, it induces a temperature rise ∆T ure 1). The detector was installed and operated in a
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in the paramagnetic bath. This temperature increase pulsed tube pre-cooled 3He/4He dilution refrigerator at
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leads to a decrease in the total magnetization of the Lawrence Livermore National Laboratory (LLNL). The
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paramagneticions,whichissensedbyasuperconducting signal was amplified using an additional array SQUID
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pickupcoil. Themagneticsignalisthentransmittedtoa (Model X16) installed at the 4 K stage.
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superconducting quantum interference device (SQUID) The output was low-pass filtered using a Stanford Re-
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for precise readout. In this work, we employed an search Systems SRS 560 amplifier [30] with a 30 kHz
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MMC fabricated at the Korea Research Institute of cutoff frequency. Data acquisition was performed over
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Standards and Science (KRISS), incorporating 420 ppm 34 hours at 15 mK in un-triggered continuous mode to
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of Ag:168Er as the sensor material Refs [26, 27]. capture the full information, with a sampling rate of
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Radionuclide sources were prepared in the form of 4π 200 kS/s. A software trigger was applied using a trape-
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solid-angle absorbers. A solution of 99Tc dissolved in ni- zoidal filter with a 1-ms shaping time.
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tric acid was dropped onto a gold foil (2 mm × 2 mm For energy calibration, an external 133Ba source was
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× 33 µm) and subsequently dried. The foil, containing used as a reference, while a 148Gd source was introduced
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approximately 10 Bq of 99Tc activity, was then folded inside the setup for internal calibration. Although the α
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androlledthreetimesinaprocessknownasthekneading signals from 148Gd were not observed due to slight mis-
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method[28,29]. Thistechniqueenhancestheuniformity alignment, characteristic X-rays from 148Gd interactions
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of 99Tc distribution within the absorber and improves weresuccessfullydetected. Thesimultaneousobservation
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energyresolution. Aportionofthekneadedfoilwascut, ofγraysfrom133BaandX-raysresultingfrom148Gdpro-
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encapsulated between two 25 µm thick gold foils, and videdmultiplereferencepointsforaccuratecalibrationof
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compressed using a rolling machine. The final encapsu- the energy scale.
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lated sample, measuring 1.2 mm × 1.3 mm × 50 µm, Two trapezoidal filters with different shaping parame-
|
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was thermally coupled to the MMC sensor. The total ters were applied to the raw pulses. The long trapezoid
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absorber mass was 1.75 mg, and the total heat capacity, was used to obtain information about the entire DC sig-
|
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includingthecontributionfromtheparamagneticionsin nal, while the short trapezoid was designed to capture
|
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the MMC sensor, was approximately 400 pJ in the 15- information corresponding only to the rise time of the
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50 mK temperature range. The final 99Tc activity was DC signal [31, 32]. All data were analyzed using custom
|
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4
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MATLAB○R
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scripts [33]. five most prominent γ peaks from 133Ba: 383.8 keV,
|
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Results.—Inthebackgrounddataset,atotalof130,001 356.0 keV, 302.8 keV, 276.4 keV, and 80.9 keV. The re-
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sultingcalibrationfunctionwasthenappliedtotheanal-
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| events | were | recorded. | Among | them, | 80,903 | events ex- | | | | | | | | |
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| ------ | ---- | --------- | ----- | ----- | ------ | ---------- | --- | --- | --- | --- | --- | --- | --- | --- |
|
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ceededtheenergythresholddefinedfortheanalysisas10 ysis dataset. The positions of the Gd X-ray peaks were
|
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keV. A pulse shape discrimination (PSD) cut was sub- compared between the calibration and analysis datasets,
|
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sequently applied to select events consistent with 99Tc andnosignificantdiscrepancieswereobserved. Thiscon-
|
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signal-like pulses. After that, 77,487 events remained for sistency validated the use of the same calibration func-
|
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further analysis. tion for both datasets. Specifically, the 42.3097 keV,
|
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Similarly, the calibration dataset obtained with an ex- 42.9968 keV, and 48.6957 keV peaks in the two datasets
|
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| | 133Ba | | | | | | differedby0.14(11)keV,0.093(18)keV,and0.38(5)keV, | | | | | | | |
|
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| ------ | ----- | ------ | --------- | ------ | ------- | ------ | ------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- |
|
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| ternal | | source | contained | 47,491 | events. | Out of | | | | | | | | |
|
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these, 35,821 events passed the energy threshold. Af- respectively—well within the corresponding uncertain-
|
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| ter applying | | the same | PSD | criteria, | 23,596 | events were | ties. | | | | | | | |
|
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| ------------ | --- | -------- | --- | --------- | ------ | ----------- | ----- | --- | --- | --- | --- | --- | --- | --- |
|
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retained.
|
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FIG.2. 99Tcspectrumwithexternal133Bacalibrationsource.
|
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| Details | of the | X-ray peaks | are | provided | in Table | I. | | | | | | | | |
|
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| ------- | ---------- | ----------- | -------- | -------- | -------- | ---- | -------- | -------- | ---- | ----------- | ----- | ----------- | ----- | ------- |
|
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| | | | | | | | FIG. 3. | Spectrum | of | calibrated | 99Tc, | plotted | with | a 1 keV |
|
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| Figure | 2 presents | | the 99Tc | spectrum | measured | with | | | | | | | | |
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| | | | | | | | binning, | compared | with | theoretical | | predictions | based | on the |
|
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the external 133Ba source in place. Characteristic X-ray farCVC variants of the glekpn, jj45pnb, and MQPM models.
|
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peaksfromGdandPtfluorescence,aswellasγlinesfrom Themodelswerefittedusingaχ2 method. Theresidualgraph
|
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ν
|
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133Ba, are clearly visible [34]. These peaks, along with below was calculated over the energy range from 0–280 keV,
|
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| | | 133Ba | | | | | corresponding | | to the | χ2 fitting | range. | | | |
|
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| -------- | ----------- | ----- | --------------- | ------------ | ----------- | ---------- | ------------- | ---- | ------ | ---------- | ------ | --------- | --- | --------- |
|
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| the γ | lines from | | and | escape peaks | due | to partial | | | | ν | | | | |
|
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| energy | deposition, | were | used | for energy | calibration | [35]. | | | | | | | | |
|
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| The peak | positions | | were determined | | by Gaussian | fitting | | | | | | | | |
|
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| | | | | | | | In our | ESSM | theory | framework, | | templates | | of the β- |
|
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withalinearbackgroundmodel,andtheresultsaresum- spectra were generated for a set of g values (with
|
||||
A
|
||||
marized in Table I. g = 1.0), adjusting simultaneously the sNME value(s)
|
||||
V
|
||||
Mostpeaksexhibitexcellentagreementwithliterature to correctly reproduce the decay half-life. Then, reduced
|
||||
values,with∆E typicallybelow0.3keVandenergyreso- chi-square (χ2) fitting was performed using the provided
|
||||
ν
|
||||
lutionsbetterthan1keVinthe66–383keVenergyrange. models,applyingsimpleshapecomparisonsandcalculat-
|
||||
TheentriesinTableIlabeledas“Notdistinguished,”in- ingresidualstoidentifytheenergyregionswiththemost
|
||||
| cluding | K and | K | transitions | from | Gd X-ray | and Au | | | | | | | | |
|
||||
| ------- | ----- | --- | ----------- | ---- | -------- | ------ | ----------- | ----------- | --- | --- | --- | -------- | ---- | -------- |
|
||||
| | β3 | β1 | | | | | significant | deviations. | | The | bin | size for | each | spectrum |
|
||||
escape lines, correspond to peaks with low relative in- was set to 1 keV.
|
||||
tensities [36]. Given the limited event statistics, these Areducedchi-squared(χ2)fittingprocedurewasthen
|
||||
ν
|
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| peaks | could | not be | individually | resolved | in | the spectral | | | | | | | | |
|
||||
| ----- | ----- | ------ | ------------ | -------- | --- | ------------ | --- | --- | --- | --- | --- | --- | --- | --- |
|
||||
appliedtocomparethetheoreticalmodelswiththemea-
|
||||
fit. Theuncertaintiesreportedforeachvaluereflectonly suredspectrum. Thebinsizeforeachspectrumwassetto
|
||||
thestatisticalerrorsderivedfromtheGaussianfits,with- 1keV.Thefitswereperformedbyminimizingχ2 overthe
|
||||
ν
|
||||
out accounting for potential systematic contributions. energy ranges 10–41 keV and 50–280 keV, excluding the
|
||||
148Gd
|
||||
The Gd X-ray peaks from the internal source GdX-rayregion. Simpleshapecomparisonsandresidual
|
||||
and the 133Ba γ lines were used as primary reference analyseswereusedtoidentifyenergyregionswithsignifi-
|
||||
points for the calibration. Additional fluorescence lines cantdeviations. Figure3visuallydemonstrateshowwell
|
||||
| fromPtareattributedtomaterialsinthedetectorsetup | | | | | | | | | | | 99Tc | | | |
|
||||
| ------------------------------------------------ | --- | --- | --- | --- | --- | --- | ---------- | ------ | ---- | --- | ---- | ----- | --- | --- |
|
||||
| | | | | | | | each model | aligns | with | the | | data. | | |
|
||||
and collimator. Several low-energy escape peaks (below We performed the fitting using geff with both the
|
||||
A
|
||||
20keV)showbroaderFWHManddegradedrelativereso- closeCVC[sNME(c)]andfarCVC[sNME(f)]models,and
|
||||
lutionduetoincreasednoiseandlimitedeventstatistics. the results are summarized in Table II. For the farCVC
|
||||
modelatgeff
|
||||
A linear energy calibration was performed using the cases,theglekpn =1.2yieldsthebestagree-
|
||||
A
|
||||
|
||||
5
|
||||
TABLE I. Measured X-ray and gamma-ray lines, including their tabulated and measured energies.
|
||||
Tabulated Measured FWHM
|
||||
Origin Radiation type ∆E [keV]
|
||||
energy [keV] [34, 35] energy [keV] resolution [keV]
|
||||
X-rayK 42.3097(13) 42.30(10) 0.9(4) 0.01(10)
|
||||
α2
|
||||
Gdfluorescence X-rayK 42.9968(12) 42.9427(31) 0.686(10) 0.0541(33)
|
||||
α1
|
||||
frominternalsource X-rayK 48.5505(21)
|
||||
β3 48.29(5)a 1.05(22) 0.41(5)
|
||||
X-rayK 48.6957(21)
|
||||
β1
|
||||
Ptfluorescence X-rayK 65.1226(21) 65.005(22) 0.96(6) 0.118(22)
|
||||
α2
|
||||
fromcollimator X-rayK 66.8311(20) 66.78(5) 0.65(15) 0.06(5)
|
||||
α1
|
||||
γ 80.9979(11) 80.881(24) 0.77(8) 0.117(25)
|
||||
γ 276.3989(12) 276.12(5) 0.57(13) 0.28(5)
|
||||
133Bacalibrationlines γ 302.8508(5) 302.764(21) 0.60(5) 0.087(21)
|
||||
γ 356.0129(7) 355.926(9) 0.653(21) 0.087(9)
|
||||
γ 383.8485(12) 383.69(6) 0.82(14) 0.16(6)
|
||||
Absorbed Escaping
|
||||
133Ba γ line [keV] Au X-ray [keV]
|
||||
66.993(23)[K ] 316.8555(26) 316.817(18) 0.37(5) 0.038(18)
|
||||
383.8485 α2
|
||||
68.8069(22)[K ] 315.0416(25) 315.09(4) 0.72(9) 0.05(4)
|
||||
α1
|
||||
66.993(23)[K ] 289.0199(24) 288.943(21) 0.51(5) 0.077(21)
|
||||
α2
|
||||
68.8069(22)[K ] 287.206(23) 287.051(26) 0.59(6) 0.155(26)
|
||||
356.0129 α1
|
||||
77.5773(35)[K ] 278.4356(36)
|
||||
β3 277.911(31)a 0.88(8) 0.122(31)
|
||||
77.983(37)[K ] 278.0329(38)
|
||||
Escapelines β1
|
||||
66.993(23)[K ] 235.8578(24) 235.659(23) 0.47(6) 0.199(23)
|
||||
302.8508 α2
|
||||
68.8069(22)[K ] 234.0439(23) 233.99(4) 0.63(11) 0.05(4)
|
||||
α1
|
||||
66.993(23)[K ] 209.4059(26) 209.137(12) 0.72(4) 0.269(12)
|
||||
276.3989 α2
|
||||
68.8069(22)[K ] 207.592(25) 207.36(5) 0.62(13) 0.24(5)
|
||||
α1
|
||||
66.993(23)[K ] 14.0049(25) 13.87(5) 1.49(21) 0.13(5)
|
||||
80.9979 α2
|
||||
68.8069(22)[K ] 12.191(25) 12.144(17) 0.97(6) 0.046(17)
|
||||
α1
|
||||
a Notdistinguished
|
||||
considered, glekpn slightly outperforms the others, but
|
||||
TABLE II. Results for the three considered nuclear models
|
||||
allthreesuggestthataquenchedaxial-vectorcouplingof
|
||||
ontheparametersofinterestg . Thereducedchi-squareand
|
||||
A geff =1.0–1.2providesthebestagreementwiththedata.
|
||||
p-value are also reported as an estimator of the goodness of A
|
||||
Our result shows a clear deviation from that reported in
|
||||
fit.
|
||||
Ref. [17], and instead exhibits better consistency with a
|
||||
Model geff sNME[fm3] χ2 p-value
|
||||
A ν quenched g value comparable to those extracted from
|
||||
CloseCVC A
|
||||
glekpn 1.1 0.0674 1.1057 0.12 other nuclei.
|
||||
jj45pnb 1.0 0.0681 1.2436 0.004 Conclusions.—In this work, we performed a high-
|
||||
MQPM 1.0 0.0651 1.6437 <0.0001 resolutionmeasurementofthe β-decay spectrum of99Tc
|
||||
usingmetallicmagneticcalorimeterquantumsensorsand
|
||||
FarCVC(Bestfit)
|
||||
glekpn 1.2 -0.0698 1.0664 0.22 compared the results with predictions from multiple nu-
|
||||
jj45pnb 1.0 -0.0669 1.0966 0.14 clear models. The extracted value of the effective axial-
|
||||
MQPM 1.0 -0.0683 1.0951 0.14 vector coupling, geff, deviates from the enhanced value
|
||||
A
|
||||
reported in Ref. [17] and is more consistent with values
|
||||
observed in other nuclei. We attribute this discrepancy
|
||||
ment with the experimental spectrum, with a reduced primarilytothedifferenttreatmentofthesNMEadopted
|
||||
chi-squared value of χ2 = 1.0664 and a corresponding in Ref. [17]. By applying the ESSM, which simultane-
|
||||
ν
|
||||
p-value of 0.22. The jj45pnb model at geff = 1.0 also ously fits the measured β-spectrum and reproduces the
|
||||
A
|
||||
provides a good match with χ2 = 1.0966 and p-value of partialhalf-life,weplacedmorerobustconstraintsongeff
|
||||
ν A
|
||||
0.14. Similarly, the MQPM model at geff = 1.0 gives χ2 based on three nuclear theory approaches.
|
||||
A ν
|
||||
= 1.0951 and p-value of 0.14. All fits were performed Our results for the second-forbidden non-unique β−
|
||||
with ν = 261 degrees of freedom. decay of 99Tc provide valuable insight into the effective
|
||||
The reduced chi-squared values close to unity and p- axial-vector coupling strength geff in the mass region.
|
||||
A
|
||||
values well above 0.05 indicate that all three farCVC Theextractedquenchingpatternisconsistentwiththose
|
||||
models are statistically compatible with the measured observed in heavier nuclei, such as 113Cd [10–13] and
|
||||
spectrum. This consistency supports the reliability of 115In [14–16], suggesting that the quenching of g may
|
||||
A
|
||||
the farCVC scenario, where the sNME is adjusted to re- follow a systematic trend across mass regions. This im-
|
||||
produce the experimental half-life. Among the models pliesthatthesamelevelofquenchingcouldbeappliedto
|
||||
|
||||
6
|
||||
bothallowedandforbiddenvirtualtransitionscontribut- istryofResearch,InnovationandDigitization(theNEP-
|
||||
ing to 0νββ NMEs, thereby simplifying the theoretical TUN project). M. Ramalho acknowledges support by
|
||||
evaluation of NMEs. theOskarHuttunenFoundation. Weacknowledgegrants
|
||||
In particular, our findings can inform the modeling of of computer capacity from the Finnish Grid and Cloud
|
||||
100Mo, Infrastructure (persistent identifier urn:nbn: fi:research-
|
||||
| 0νββ decay | in | | which | lies | in the | same | mass re- | | | | | | | |
|
||||
| ---------- | ----- | ------ | -------- | --------- | ------ | -------- | -------- | ------------------ | --- | --- | ----------- | --- | ------ | ---- |
|
||||
| | | | | | | | | infras-2016072533) | | and | the support | by | CSC–IT | Cen- |
|
||||
| gion as | 99Tc. | If the | observed | quenching | | behavior | per- | | | | | | | |
|
||||
sists across neighboring nuclei, it could facilitate a more ter for Science, Finland, for generous computational re-
|
||||
| | | | | | | | | sources. | G. B. | Kim | and I. Kim | acknowledge | | support |
|
||||
| ----------- | ------------ | --------- | ------- | ------------ | ---- | ------- | ------ | -------- | --------------- | --- | ---------- | ----------- | --- | ------- |
|
||||
| unified and | robust | framework | | for | 0νββ | nuclear | matrix | | | | | | | |
|
||||
| | | | | | | | | from the | U.S. Department | | of Energy, | performed | | under |
|
||||
| element | calculations | | in this | mass region. | | | | | | | | | | |
|
||||
theauspicesofLawrenceLivermoreNationalLaboratory
|
||||
| These | results | demonstrate | | the sensitivity | | of | precision | | | | | | | |
|
||||
| -------------- | ------- | ----------- | --- | --------------- | ------- | --- | --------- | -------------- | -------------- | ------------------ | -------- | -------- | --------- | ------ |
|
||||
| | | | | | | | | under Contract | | DE-AC52-07NA27344. | | | This work | was |
|
||||
| β-spectroscopy | | to nuclear | | structure | effects | and | provide | | | | | | | |
|
||||
| | | | | | | | | funded by | the Laboratory | | Directed | Research | and | Devel- |
|
||||
valuable benchmarks for the development and validation opment program of Lawrence Livermore National Labo-
|
||||
| of nuclear | theory—an | | effort | central | to the | mission | of the | | | | | | | |
|
||||
| ---------- | --------- | --- | ------ | ------- | ------ | ------- | ------ | --- | --- | --- | --- | --- | --- | --- |
|
||||
ratory (23-LW-043).
|
||||
| gA-EXPERT | | collaboration. | | | | | | | | | | | | |
|
||||
| --------- | --- | -------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|
||||
ThisworkwascarriedoutwithinthegA-EXPERiment
|
||||
Acknowledgments.— H. J. Kim acknowledges support and Theory (gA-EXPERT) collaboration—an interna-
|
||||
by the National Research Foundation of Korea (NRF) tional effort involving Kyungpook National University
|
||||
grant, funded by the Korean government (MSIT), Con- (KNU), the Institute for Basic Science (IBS), the Korea
|
||||
tract No. RS-2024-00348317. J. W. Song acknowledges Research Institute of Standards and Science (KRISS),
|
||||
support by the National Research Foundation of Korea the University of Jyv¨askyl¨a, and the Finnish Institute
|
||||
(NRF)grant,fundedbytheMinistryofEducation,Con- of Natural Resources (Luke)—dedicated to determining
|
||||
tract No. RS-2023-00274589. J. Kotila and J. Suhonen theeffectiveaxial-vectorcouplingconstant, geff, through
|
||||
A
|
||||
acknowledge support from project PNRR-I8/C9-CF264, precision β-decay measurements and state-of-the-art nu-
|
||||
Contract No. 760100/23.05.2023 of the Romanian Min- clear theory comparisons.
|
||||
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