5202 nuJ 12 ]xe-lcun[ 1v44571.6052:viXra The measurement of the 99Tc β-decay spectrum and its implications for the effective value of weak axial coupling 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. Lee,6,7 K. R. Woo,6 J. Kotila,8 J. Kostensalo,9 J. Suhonen,4,10,∗ and H. J. Kim2,† 1Korea Research Institute of Standards and Science, Daejeon 34113, South Korea 2Department of Physics, Kyungpook National University, Daegu 41566, South Korea 3School of Physics, Engineering and Technology, University of York, Heslington, York YO10 5DD, United Kingdom 4Department of Physics, University of Jyva¨skyla¨, P. O. Box 35 (YFL), FI-40014, Jyva¨skyl¨a, Finland 5Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 6Institute for Basic Science, Daejeon 34126, South Korea 7Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea 8Finnish Institute for Educational Research, University of Jyva¨skyl¨a, Jyv¨askyla¨, Finland 9Natural Resources Institute Finland, Yliopistokatu 6B, FI-80100 Joensuu, Finland 10International Centre for Advanced Training and Research in Physics (CIFRA), 077125 Bucharest-Magurele, Romania (Dated: June 24, 2025) Measurements of β-spectral shapes is an important way to examine the effective value of the weakaxialcouplingg . Thesestudiesfocusspecificallyonforbiddennon-uniqueβ− transitions,as A only in these cases is the spectral shape directly sensitive to the ratio g /g . Here, the value of A V the weak vector coupling constant, g , is fixed at 1.0 according to the Conserved Vector Current V (CVC) hypothesis. In previous studies for the fourth-forbidden non-unique β− decays of 113Cd [J. Kostensalo et al., Phys. Lett. B 822, 136652 (2021)] and 115In [A. F. Leder et al., Phys. Rev. Lett. 129, 232502 (2022) and L. Pagnanini et al., Phys. Rev. Lett. 133, 122501 (2024)] a quenchedvaluewasdeterminedfortheratiog /g usingg =1.0. Anotableexceptionistherecent A V V measurementandanalysisofthesecond-forbiddennon-uniqueβ-decaytransitionin99Tc,performed byM.Paulsenet al.,Phys. Rev. C110,05503(2024). Whereanenhancedratiog /g =1.526(92) A V was suggested. To resolve this apparently contradictory situation with the effective value of g , we A haveperformedcalculationsbasedonthenuclearshellmodel(NSM)Hamiltoniansglekpn,jj45pnb, andtheMQPMapproachwithacarefulconsiderationofthesmallrelativisticvectornuclearmatrix element(sNME).Thetheoreticalspectrawerecomparedtothe99Tcβ-decayspectrumbyusingthe 4πgoldabsorberwithaMetallicMagneticCalorimeter(MMC).Inallcases,wefoundthatthedata matches well with reduced g /g values of 1.0–1.2. Our result contradicts the previously reported A V measurementfor99Tcandinsteadsupportsaquenchedaxialcouplingasreportedforotherisotopes. Introduction.—Electrons and electron antineutrinos turebeyond-the-standard-modelexperiments;seethere- are emitted in β− decays as a result of a transmuta- views [1–3]. tion of a parent nucleus (Z,N) to a daughter nucleus In allowed β decays, such as Fermi and Gamow–Teller (Z +1,N −1), Z being the number of protons and N transitions, the emitted lepton pair (electron and an- the number of neutrons. Studies of β-electrons (elec- tineutrino)carrieszeroorbitalangularmomentum[4]. In trons emitted in β− decays) have become an important contrast,forbiddendecaysoccurwhentheemittedlepton subject of study, e.g., in connection with nuclear reac- pair carries nonzero orbital angular momentum [5]. The tors and the anomalies in their fluxes of antineutrinos, degreeofforbiddennesscanrangefromfirst-forbiddento and rare-events experiments searching for beyond-the- n:th-forbidden, with each additional level typically in- standard-modelphysics,likethosetryingtomeasurerare creasing the decay half-life by a factor of approximately β-decays and double beta decays. The β-electrons can 104. Forbidden β-transitions are generally classified into also be severe backgrounds in these experiments. In all two types: unique and non-unique. Unique transitions the aforementioned cases, measurements of the associ- are characterized by a single dominant nuclear matrix atedβ-spectralshapeisessential. Distortionsinβ-decay element (NME) and thus exhibit a universal β-spectral spectral shapes also provide important input for under- shapethatisindependentofnuclearstructure[4]. Incon- standing the weak axial coupling constant g , which A trast, non-uniquetransitionsinvolveacomplexinterplay is relevant for sensitivity estimates in current and fu- of several NMEs, making the β-decay spectrum highly sensitivetothenuclearwavefunctionsofboththeinitial and final states [5–7]. ∗ jouni.t.suhonen@jyu.fi The (partial) half-life of a forbidden non-unique β- † hongjoo@knu.ac.kr transitionsalsodependsonthevaluesoftheweakvector 2 and axial-vector couplings, g and g , respectively [5– plings by writing V A 7]. The conserved vector current (CVC) hypothesis 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) vector current (PCAC) hypothesis leads to an effective where w is the total (rest-mass plus kinetic) energy of (quenched) value of geff in finite nuclei [8], its bare- e A the emitted electron. The shape of the β-electron spec- nucleon value g =1.27 resulting from the experimental A trum is sensitive to the value of g due to subtle in- studies of the decay of an isolated neutron. The quench- A terference effects among the vector C (w ), axial-vector ing of the effective value of g has recently been studied V e A C (w), and mixed vector–axial-vector C (w) contribu- extensively in [2, 8, 9], and in particular its effects on A VA tionstothetransitionmatrixelement[6]. Forsomenuclei the neutrinoless double beta decay have been addressed (veryfew,ascharteduptopresentdays[2,18,19,21,22]) in [1, 3]. To quantify the quenched value of g , com- A this causes measurable changes in the β-spectra. Thus, binedexperimentalandtheoreticalanalysesofβ-spectral the effective value geff can be found by computing the- shapes of individual β− transitions have recently been A oretical β-spectra for a set of geff values and comparing performed for the fourth-forbidden non-unique β-decays A themwiththemeasuredone. Thismethod,coinedasthe of 113Cd [10–13] and 115In [14–16]. spectrum-shape method (SSM), was originally proposed A recent measurement of the β-decay spectrum in [6]. for the second-forbidden non-unique ground-state-to- Another factor influencing theoretical analyses of β- ground-state transition 99Tc(9/2+) → 99Ru(5/2+), spectral shapes and half-lives is the so-called small rela- which has a 100% branching ratio, was reported by tivistic vector nuclear matrix element (sNME) [5]. The Paulsen et al. [17]. The accompanying theoretical analy- sNME gathers contributions outside the valence major sisyieldedacontradictoryresult,suggestinganenhance- shell that contains the proton and neutron Fermi sur- ment of the axial coupling with a value of g /g = A V faces, which makes its calculation particularly hard for 1.526(92) using g =1.0. V nuclear-theoryframeworksused,e.g.,inthepresentwork ThegA-EXPERimentandTheory(gA-EXPERT)col- and also in the work of Paulsen et al. [17]. Despite its laboration is an international effort dedicated to quan- smallness, the sNME can influence the β-spectral shapes tifying the effective axial-vector coupling constant, geff, A and half-lives quite strongly [11, 12, 19, 21]. by precisely measuring β-decays of various nuclei and ArealisticvalueofthesNMEcanbeestimatedfromits comparing the results with state-of-the-art nuclear the- CVC value [5], first used for spectral-shape calculations ory calculations. To address the tension raised by the in Ref. [18] and later by Paulsen et al. [17]. It should be enhanced value of geff = 1.526(92) reported in Ref. [17], A noted,though,thattheCVCvaluerepresentsan“ideal”, we performed a high-precision measurement of the 99Tc pertaining to a perfect many-body theory, which is not β-decay spectrum using metallic magnetic calorimeter the case for the nuclear-structure frameworks typically quantum sensors with a low-energy threshold of 10 keV. used for β-decay calculations of heavy open-shell nuclei, The measured spectrum was compared to predictions like the presently discussed 99Tc. To circumvent the use from three nuclear models, each based on distinct nu- of the CVC value, the experimental works [11, 13, 15] clear Hamiltonians. In this Letter, we present a quan- and theoretical works [12, 16] used sNME as a fitting titative comparison between data and modern nuclear parameter, together with geff. By this, it was possible to theory,providingnewconstraintsongeff anddemonstrat- A A reproduce both the measured β-spectral shape and the ing the sensitivity of precision β-spectroscopy to nuclear experimental (partial) half-life of the corresponding β- structure effects. transitionwithoutlosingtheCVCvalueg =1.0forthe Theory.—Tofirstorder,thehalf-lifeofaβ-decaytran- A vector coupling. This approach, termed the enhanced sition can be written as: spectrum-shape method (ESSM) in Ref. [19], is adopted κ in the present work. t = , (1) 1/2 C˜ In this Letter, we present new theoretical calculations of the β spectrum of 99Tc (with Z = 43 and N = 56) where κ is a constant [18, 19] and C˜ is the integrated and compare them to the measured spectrum in order shapefunctionC,whichincorporatesvariousphase-space to extract the geff, using ESSM. To gain preliminary in- A factors and NMEs arising in the next-to-leading-order sightsintotheeffectiveaxialcouplinggeff intheβ-decay A expansion, as discussed in detail in Refs. [6, 7]. Our β- of 99Tc, we performed nuclear shell model (NSM) cal- spectral shape and half-life analyses employ screening, culations and compared the results with the measured radiative, and atomic-exchange corrections. For electron spectrum reported in Ref. [17]. As the β-decay rate energies below some tens of keV, the distortion in the β- has a quadratic dependence on the sNME, two solutions decay spectral shape is mostly dominated by the atomic werefoundforeachvalueofgeff,onecloserto[sNME(c)] A exchange correction, as originally studied for allowed β- and one further away from [sNME(f)] CVC value. In decays [20]. This correction is responsible for the sharp references [21, 23] the related two sets of theoretical β- upward trend of the spectral shape at low energies. spectra of 99Tc were introduced for two NSM Hamilto- The complexity of the shape function C can, however, nians, namely jj45pnb [24] and glekpn [25]; In that pre- be cast in a very simple dependence on the weak cou- liminary study, for the glekpn interaction we’ve used a 3 set of single particle energies fit to the A=94−98 mass below 1 Bq. region, however here we use the default single particle energies since it yields better experimental agreement for this isotope. Comparison with the measured spec- trum[17]indicatedthatbothsNMEvaluesusedwiththe jj45pnb Hamiltonian yielded good agreement, while the fit is somewhat poorer with sNME(c), and significantly worsewithsNME(f)whenusingtheglekpn Hamiltonian, further details of this preliminary study and its calcula- tions can be found in Refs [21, 23]. In addition to the two NSM Hamiltonians described above, we also employ the nuclear many-body method known as the Microscopic Quasiparticle-Phonon Model (MQPM). A concise presentation of the essentials of NSM, and MQPM can be found in Ref. [2]. It should be pointed out here that Ref. [17] employed the NSM in their analysis, adopting the CVC value for the sNME withoutfittingittotheexperimentalhalf-lifeofβ-decay. A systematic comparison of various theoretical models with the measured spectrum offers a more robust frame- work for extracting the geff from high-precision spectral A data. Experiment.— Metallic magnetic calorimeters (MMCs) are some of the most advanced cryogenic FIG. 1. The detector setup used for the β-decay measure- ment. The gold sample containing the 99Tc source is ther- detectors for precision energy measurements. These mally coupled to the MMC sensor via gold wire bonds. A devices utilize paramagnetic ions embedded in metal- support washer with a Kapton tape on top for thermal insu- lic hosts—typically Au:Er or Ag:Er—as temperature lation was placed below the sample to align its height with sensors thermally coupled to metallic absorbers. The that of the MMC sensor. paramagnetic material is placed in a weak magnetic field (<10 mT) and operated at temperatures below The detector setup consists of an MMC and a Mag- 100 mK. When an incident particle deposits energy nicon SQUID (Model X1) for signal readout (see Fig- E in the absorber, it induces a temperature rise ∆T ure 1). The detector was installed and operated in a in the paramagnetic bath. This temperature increase pulsed tube pre-cooled 3He/4He dilution refrigerator at leads to a decrease in the total magnetization of the Lawrence Livermore National Laboratory (LLNL). The paramagneticions,whichissensedbyasuperconducting signal was amplified using an additional array SQUID pickupcoil. Themagneticsignalisthentransmittedtoa (Model X16) installed at the 4 K stage. superconducting quantum interference device (SQUID) The output was low-pass filtered using a Stanford Re- for precise readout. In this work, we employed an search Systems SRS 560 amplifier [30] with a 30 kHz MMC fabricated at the Korea Research Institute of cutoff frequency. Data acquisition was performed over Standards and Science (KRISS), incorporating 420 ppm 34 hours at 15 mK in un-triggered continuous mode to of Ag:168Er as the sensor material Refs [26, 27]. capture the full information, with a sampling rate of Radionuclide sources were prepared in the form of 4π 200 kS/s. A software trigger was applied using a trape- solid-angle absorbers. A solution of 99Tc dissolved in ni- zoidal filter with a 1-ms shaping time. tric acid was dropped onto a gold foil (2 mm × 2 mm For energy calibration, an external 133Ba source was × 33 µm) and subsequently dried. The foil, containing used as a reference, while a 148Gd source was introduced approximately 10 Bq of 99Tc activity, was then folded inside the setup for internal calibration. Although the α androlledthreetimesinaprocessknownasthekneading signals from 148Gd were not observed due to slight mis- method[28,29]. Thistechniqueenhancestheuniformity alignment, characteristic X-rays from 148Gd interactions of 99Tc distribution within the absorber and improves weresuccessfullydetected. Thesimultaneousobservation energyresolution. Aportionofthekneadedfoilwascut, ofγraysfrom133BaandX-raysresultingfrom148Gdpro- encapsulated between two 25 µm thick gold foils, and videdmultiplereferencepointsforaccuratecalibrationof compressed using a rolling machine. The final encapsu- the energy scale. lated sample, measuring 1.2 mm × 1.3 mm × 50 µm, Two trapezoidal filters with different shaping parame- was thermally coupled to the MMC sensor. The total ters were applied to the raw pulses. The long trapezoid absorber mass was 1.75 mg, and the total heat capacity, was used to obtain information about the entire DC sig- includingthecontributionfromtheparamagneticionsin nal, while the short trapezoid was designed to capture the MMC sensor, was approximately 400 pJ in the 15- information corresponding only to the rise time of the 50 mK temperature range. The final 99Tc activity was DC signal [31, 32]. All data were analyzed using custom 4 MATLAB○R scripts [33]. five most prominent γ peaks from 133Ba: 383.8 keV, Results.—Inthebackgrounddataset,atotalof130,001 356.0 keV, 302.8 keV, 276.4 keV, and 80.9 keV. The re- sultingcalibrationfunctionwasthenappliedtotheanal- | events | were | recorded. | Among | them, | 80,903 | events ex- | | | | | | | | | | ------ | ---- | --------- | ----- | ----- | ------ | ---------- | --- | --- | --- | --- | --- | --- | --- | --- | ceededtheenergythresholddefinedfortheanalysisas10 ysis dataset. The positions of the Gd X-ray peaks were keV. A pulse shape discrimination (PSD) cut was sub- compared between the calibration and analysis datasets, sequently applied to select events consistent with 99Tc andnosignificantdiscrepancieswereobserved. Thiscon- signal-like pulses. After that, 77,487 events remained for sistency validated the use of the same calibration func- further analysis. tion for both datasets. Specifically, the 42.3097 keV, Similarly, the calibration dataset obtained with an ex- 42.9968 keV, and 48.6957 keV peaks in the two datasets | | 133Ba | | | | | | differedby0.14(11)keV,0.093(18)keV,and0.38(5)keV, | | | | | | | | | ------ | ----- | ------ | --------- | ------ | ------- | ------ | ------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | | ternal | | source | contained | 47,491 | events. | Out of | | | | | | | | | these, 35,821 events passed the energy threshold. Af- respectively—well within the corresponding uncertain- | ter applying | | the same | PSD | criteria, | 23,596 | events were | ties. | | | | | | | | | ------------ | --- | -------- | --- | --------- | ------ | ----------- | ----- | --- | --- | --- | --- | --- | --- | --- | retained. FIG.2. 99Tcspectrumwithexternal133Bacalibrationsource. | Details | of the | X-ray peaks | are | provided | in Table | I. | | | | | | | | | | ------- | ---------- | ----------- | -------- | -------- | -------- | ---- | -------- | -------- | ---- | ----------- | ----- | ----------- | ----- | ------- | | | | | | | | | FIG. 3. | Spectrum | of | calibrated | 99Tc, | plotted | with | a 1 keV | | Figure | 2 presents | | the 99Tc | spectrum | measured | with | | | | | | | | | | | | | | | | | binning, | compared | with | theoretical | | predictions | based | on the | the external 133Ba source in place. Characteristic X-ray farCVC variants of the glekpn, jj45pnb, and MQPM models. peaksfromGdandPtfluorescence,aswellasγlinesfrom Themodelswerefittedusingaχ2 method. Theresidualgraph ν 133Ba, are clearly visible [34]. These peaks, along with below was calculated over the energy range from 0–280 keV, | | | 133Ba | | | | | corresponding | | to the | χ2 fitting | range. | | | | | -------- | ----------- | ----- | --------------- | ------------ | ----------- | ---------- | ------------- | ---- | ------ | ---------- | ------ | --------- | --- | --------- | | the γ | lines from | | and | escape peaks | due | to partial | | | | ν | | | | | | energy | deposition, | were | used | for energy | calibration | [35]. | | | | | | | | | | The peak | positions | | were determined | | by Gaussian | fitting | | | | | | | | | | | | | | | | | In our | ESSM | theory | framework, | | templates | | of the β- | 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 | 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. [1] J. Engel and J. Menendez, Rep. Prog. Phys. 60, 046301 [19] A. Kumar, P. C. Srivastava, and J. 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