High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc © 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³ Published version Ge, Zhuang; Eronen, Tommi; Sevestrean, Vasile Alin; Niţescu, Ovidiu; Stoica, Sabin; Ramalho, Marlom; Suhonen, Jouni; de Roubin, Antoine; Nesterenko, Dmitrii; Kankainen, Anu; Ascher, Pauline; Ayet, San Andres Samuel; Beliuskina, Olga; Delahaye, Pierre; Flayol, Mathieu; Gerbaux, Mathias; Grévy, Stéphane; Hukkanen, Marjut; Jaries, Arthur; Jokinen, Ari; Husson, Audric; Kahl, Daid; Kostensalo, Joel; Kotila, Jenni; Moore, Iain; Nikas, Stylianos; Stryjczyk, Marek; Virtanen, Ville Ge, Z., Eronen, T., Sevestrean, V. A., Niţescu, O., Stoica, S., Ramalho, M., Suhonen, J., de Roubin, A., Nesterenko, D., Kankainen, A., Ascher, P., Ayet, S. A. S., Beliuskina, O., Delahaye, P., Flayol, M., Gerbaux, M., Grévy, S., Hukkanen, M., Jaries, A., . . . Virtanen, V. (2024). High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc. Physics Letters B, 859, Article 139094. https://doi.org/10.1016/j.physletb.2024.139094 2024 Phys. Lett. B 859 (2024) 139094 Available online 24 October 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter High-precision measurements of the atomic mass and electron-capture decay 𝑄value of 95Tc Zhuang Gea, ,∗, Tommi Eronena,, Vasile Alin Sevestreanb,c,d, ,∗∗, Ovidiu Niţescub,d,, Sabin Stoicab,, Marlom Ramalhoa,, Jouni Suhonena,b, ,∗, AntoinedeRoubine,f,, Dmitrii Nesterenkoa,, Anu Kankainena,, Pauline Ascherf,, Samuel Ayet San Andresg,, Olga Beliuskinaa,, Pierre Delahayeh,, Mathieu Flayolf,, Mathias Gerbauxf,, Stéphane Grévyf,, Marjut Hukkanena,i,, Arthur Jariesa,, Ari Jokinena,, Audric Hussonf,, Daid Kahlj, ,1, Joel Kostensalok,, Jenni Kotila b,l,m,, Iain Moore a,, Stylianos Nikasa, Marek Stryjczyka,, Ville Virtanena, aDepartment of Physics, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland bInternational Centre for Advanced Training and Research in Physics (CIFRA), POB MG-12, RO-077125, Bucharest-Măgurele, Romania cFaculty of Physics, University of Bucharest, 405 Atomiştilor, POB MG-11, RO-077125, Bucharest-Măgurele, Romania d“Horia Hulubei” National Institute of Physics and Nuclear Engineering, 30 Reactorului, POB MG-6, RO-077125, Bucharest-Măgurele, Romania eKU Leuven, Instituut voor Kernen Stralingsfysica, B-3001, Leuven, Belgium fUniversité de Bordeaux, CNRS/IN2P3, UMR 5797, F-33170, Gradignan, France gInstituto de Fisica Corpuscular, CSIC-UV, 46980, Gradignan, Spain hGANIL, CEA/DSM-CNRS/IN2P3, Bd Henri Becquerel, 14000, Caen, France iUniversité de Bordeaux, CNRS/IN2P3, LP2I Bordeaux, UMR 5797, F-33170, Gradignan, France jExtreme Light Infrastructure -Nuclear Physics, Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH), 077125, Bucharest-Magurele, Romania kNatural Resources Institute Finland, Yliopistokatu 6B, FI-80100, Joensuu, Finland lFinnish Institute for Educational Research, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland mCenter for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120, USA A R T I C L E I N F O A B S T R A C T Editor: H. Gao Keywords: Penning trap Mass measurements Ultra-low 𝑄value Electron capture A direct measurement of the ground-state-to-ground-state electron-capture decay 𝑄value of 95Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The 𝑄value was determined to be 1695.92(13) keV by taking advantage of the high resolving power of the phase-imaging ion-cyclotron-resonance technique to resolve the low-lying isomeric state of 95Tc (excitation energy of 38.910(40) keV) from the ground state. The mass excess of 95Tc was measured to be −86015.95(18) keV/c2, exhibiting a precision of about 28 times higher and in agreement with the value from the newest Atomic Mass Evaluation (AME2020). Combined with the nuclear energy-level data for the decay-daughter 95Mo, two potential ultra-low 𝑄-value transitions are identified for future long-term neutrino-mass determination experiments. The atomic self-consistent many-electron Dirac– Hartree–Fock–Slater method and the nuclear shell model have been used to predict the partial half-lives and energy-release distributions for the two transitions. The dominant correction terms related to those processes are considered, including the exchange and overlap corrections, and the shake-up and shake-off effects. The normalized distribution of the released energy in the electron-capture decay of 95Tc to excited states of 95Mo is compared to that of 163Ho currently being used for electron-neutrino-mass determination. * Corresponding authors at: Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland. ** Corresponding author at: International Centre for Advanced Training and Research in Physics (CIFRA), POB MG-12, RO-077125, Bucharest-Măgurele, Romania. E-mail addresses: zhuang.z.ge@jyu.fi (Z. Ge), [email protected] (V.A. Sevestrean), jouni.t.suhonen@jyu.fi (J. Suhonen). 1Present address: Facility for Rare Isotope Beams, Michigan State University, 640 South Shaw Lane East Lansing, MI 48824, USA. https://doi.org/10.1016/j.physletb.2024.139094 Received 7 June 2024; Received in revised form 18 August 2024; Accepted 22 October 2024 Physics Letters B 859 (2024) 139094 2 Z. Ge, T. Eronen, V.A. Sevestrean et al. Neutrino oscillations in atmospheric, solar, and reactor neutrinos have confirmed that at least two neutrino mass eigenstates have nonzero rest mass. However, these oscillations cannot assess the absolute mass scale, but only the squared differences of the mass eigenstates [1–3]. Neutrinos are the second most abundant particles in the universe, and play an important role on cosmological scales [4]. Accurate measurements of the total neutrino mass involve their imprint on the cosmic microwave background (CMB) as well as on structure formation in the early universe. The most direct method to measure the absolute mass scale of antineutrinos involves studying the electron energy spectrum of 𝛽−decay. Though the neutrinoless double 𝛽−-decay experiments can be used to infer the effective Majorana-neutrino mass from the measured lifetime, the exact relation depends on the mediator model and relies on the calculation of the involved transition matrix elements [5–8]. The ongoing leading experiment for the absolute neutrino mass scale determination is the Karlsruhe Tritium Neutrino (KATRIN) 𝛽−-decay experiment [9–11] which is designed to measure the electron-antineutrino mass, 𝑚𝜈𝑒, with a sensitivity of 0.2 eV/c2at 90% C.L. Most recently, KATRIN has set a limit of 𝑚𝜈𝑒< 0.45 eV/c2(90% C.L.) [12]. Another experiment, Project 8, takes advantage of the cyclotron radiation emission spectroscopy (CRES) technique via measurements of the tritium end-point spectrum. The new technique CRES will allow for an eventual sensitivity to m𝜈𝑒down to 0.04 eV/c2. The first frequency-based neutrino mass limit of electron-weighted neutrino mass < 155 eV/c2is extracted from the background-free measurement of the continuous tritium 𝛽spectrum in a Bayesian (frequentist) analysis [13]. An alternative method in the ECHo [14–17]and HOLMES [18,19] experiments, uses electron capture (EC) on 163Ho, and has reached a current limit of 150 eV/c2for the electron-neutrino mass [16]. A 𝑄value as small as possible is desired in these single decay experiments for electron (anti)neutrino mass determination. The effective fraction of decays in a given energy interval Δ𝐸at the endpoint area will be larger with a lower 𝑄value [20,21]. Currently, only ground-stateto-ground-state (gs-to-gs) decay cases 3H (𝛽decay) and 163Ho (electron capture), are being used for direct neutrino-mass-determination experiments. Ongoing intensive searches for isotopes undergoing 𝛽/EC decays from the ground state to an excited state with a low 𝑄value are actively conducted at JYFLTRAP, LEBIT, CPT, ISOTRAP and SHIPTRAP Penning traps [22–37]. Penning trap mass spectrometry (PTMS) is the leading technique for accurate and precise mass and 𝑄value determination, and it is hitherto the only direct method to measure the decay 𝑄value to a sub-keV precision or better to verify whether a potential candidate is an ultra-low (< 1 keV) 𝑄-value transition or not. If an ultra-low 𝑄-value EC/𝛽transition is identified with a sufficiently high decay rate, the idea that involves operating mechanical quantum sensors to reach the required sensitivity as proposed in [38]could be used for the neutrino mass measurement. In this article, we report on the first direct measurement of the gsto-gs EC 𝑄value of 95Tc with JYFLTRAP PTMS. The precise 𝑄value obtained in this study, in conjunction with nuclear energy level data for excited states of 95Mo, is utilized to ascertain their ground-state-toexcited-state (gs-to-es) 𝑄values. In the case of 95Tc, there are two potential low 𝑄-value gs-to-es EC transitions, that could be used for neutrinomass detection. To explore this potential, we have utilized two computational approaches, the atomic self-consistent many-electron Dirac– Hartree–Fock–Slater method and the nuclear shell model, to predict the partial half-lives and energy-release distributions for the EC-decay transitions in question. 1. Experimental method The experiment was performed at the Ion Guide Isotope Separator On-Line facility (IGISOL) using JYFLTRAP double Penning trap mass spectrometer [39]at the University of Jyväskylä, Finland [40,41]. Fig. 1. (a) Ramsey-type dipole excitation frequency scan with a 5 ms (On) - 17 ms (Off) -5 ms (On) excitation pattern in the second trap filtered by the positional gates shown in (b) using the PI-ICR identification (755 ms phase accumulation time) plot. The used angular gates are highlighted. The vertical dashed blue line shows the chosen optimal frequency to transmit 95Tc ions while suppressing the others. To generate 95Tc ions, a natural Mo target foil was irradiated with a few 𝜇A proton beam at 45 MeV from the K-130 cyclotron at the Accelerator Laboratory of the University of Jyväskylä. A helium-filled small volume gas cell was used to stop the recoils produced from the protoninduced fusion-evaporation reaction, and the ions were extracted using gas flow and guided through a sextupole ion guide [42]with a combination of DC and RF fields. Subsequently, the ions were accelerated with a 30 kV electric potential, followed by mass separation using a 55◦dipole magnet with a typical mass resolving power of 𝑀∕Δ𝑀≈ 500. After isobaric separation for ions of 𝐴∕𝑞=95, including the reaction products 95Nb+, 95𝑚Tc+, 95Tc+and 95Mo+, they were directed to a radiofrequency-quadrupole cooler-buncher (RFQ-CB) [43], where they underwent accumulation, cooling, and bunching. Decay-daughter ions of 95Mo+were prepared using the upstairs offline glow-discharge ion source. A 90◦electrostatic bender selected ions either from the online target station or the offline ion source for downstream transmission. JYFLTRAP comprises two cylindrical Penning traps in a 7-T superconducting solenoid. The first trap, functioning as a purification trap, is filled with helium buffer gas and is used for isobaric purification through the sideband buffer gas cooling technique [44]. This method achieves purification with a mass resolving power of ≈10 5. In the purification trap, all cooled and centered ions (95Nb+, 95𝑚Tc+, 95Tc+, and 95Mo+) are initially excited to a large magnetron motion orbit. This is accomplished by applying a dipole excitation at the magnetron motion frequency 𝜈−for approximately 11 ms. Subsequently, a quadrupole excitation is executed for approximately 100 ms to center the ions of interest through collisions with the buffer gas. The buffer gas cooling technique eliminated 95Mo+but did not have enough mass resolving power to remove the other aforementioned ions. To prepare mono-isotopic samples of 95Tc+, the coupling of the dipolar excitation with Ramsey’s method of time-separated oscillatory fields [45]and the phase-imaging ion-cyclotron-resonance (PI-ICR) technique [46,47]was utilized, as described in details in [35]. A plot of the Ramsey-type dipole excitation frequency scan with a 5 ms (On) -17 ms (Off) -5 ms (On) excitation pattern in the second (precision) trap, filtered by the positional gates using the PI-ICR identification with a 755 ms phase accumulation time, is shown in Fig. 1. For 𝑄-value measurements, the PI-ICR method is used to measure the cyclotron frequency, 𝜈𝑐=𝑞𝐵∕(2𝜋𝑚), where 𝐵is the magnetic field strength, 𝑞is the charge and 𝑚the mass of the stored ion. The PIICR technique [47]provides around 40 times better resolving power than the conventional time-of-flight ion-cyclotron-resonance (TOF-ICR) method [47–49]. Two timing patterns are needed for the determination of 𝜈𝑐. The patterns differ only in their quadrupolar conversion pulse, separated in time by the defined phase-accumulation time, 𝑡𝑎𝑐𝑐 . The phase images of these two are projected onto a position-sensitive MCP detec- Physics Letters B 859 (2024) 139094 3 Z. Ge, T. Eronen, V.A. Sevestrean et al. tor after the trap. Additionally a center point, measured without any excitations, is needed for angle determination. The angle between two phase images of the projected radial motions with respect to the center spot is denoted as 𝛼𝑐=𝛼+−𝛼−, where 𝛼+and 𝛼−represent the polar angles of the cyclotron and magnetron motion phases. The cyclotron frequency 𝜈𝑐is derived from: 𝜈𝑐=(𝛼𝑐+2𝜋𝑛𝑐)∕2𝜋𝑡𝑎𝑐𝑐 , where 𝑛𝑐represents the full number of revolutions made by the measured ions during the phase accumulation time 𝑡𝑎𝑐𝑐 . Different accumulation times for 95Tc+were utilized to unambiguously assign 𝑛𝑐. An accumulation time of 574 ms was employed for the actual measurements to determine the final 𝜈𝑐for both 95Tc+and 95Mo+ ions; the choice also ensures that any leaked isobaric contaminant would not overlap with the ions of interest. The positions of the phase spots for magnetron and cyclotron motion were carefully selected to maintain an angle 𝛼𝑐within a few degrees. This choice aimed to minimize the shift in the 𝜈𝑐ratio of the 95Tc+-95Mo+pair due to the conversion of the cyclotron motion to magnetron motion and the possible distortion of the ion-motion projection onto the detector to a level well below 10−10 [48]. The excitation of the 𝜈+delay was systematically scanned over one magnetron period, while the extraction delay varied over one cyclotron period. This accounted for any residual magnetron and cyclotron motion that might have shifted the different spots. The total data accumulation time of interleaved measurements of 𝜈𝑐for 95Tc+-95Mo+ ions was ≈4.9 hours, respectively. The gs-to-gs electron-capture 𝑄value, 𝑄EC, can be derived from the mass difference of the decay pair: 𝑄EC =(𝑀𝑝−𝑀𝑑)𝑐2=(𝑅−1)(𝑀𝑑−𝑞𝑚𝑒)𝑐2+(𝑅⋅𝐵𝑑−𝐵𝑝),(1) where 𝑀𝑝and 𝑀𝑑represent the masses of the parent and daughter atoms, respectively, and 𝑅(=𝜈𝑐,𝑑∕𝜈𝑐,𝑝) denotes their cyclotron frequency ratio for singly charged ions (𝑞=1), with 𝑚𝑒being the mass of an electron. The electron binding energies of the parent and daughter atoms, denoted as 𝐵𝑝and 𝐵𝑑, are neglected due to their small values (on the order of a few eV [50]), and 𝑅is close to 1. Since both the parent and daughter ions have the same 𝐴∕𝑞and their relative mass difference Δ𝑀∕𝑀<10−4, the mass-dependent error becomes negligible compared to the statistical uncertainty achieved in the measurements. Also, the contribution of uncertainty to the 𝑄value from the mass uncertainty of the reference (daughter), which is 0.12 keV/c2for 95Mo [51], can be neglected. 2. Results and discussion The determination of 𝑄EC depends on the measured cyclotron frequency ratio 𝑅via Eq. (1). Two data sets for 95Tc+-95Mo+were collected. A full scanning measurement of the magnetron phase, cyclotron phase and center spot in sequence (one cycle) was completed in less than 5 minutes for each ion species. In the analysis, the position of each spot was fit with the maximum likelihood method. A few cycles were summed to have reasonable statistics for fitting. The phase angles were calculated accordingly to deduce the cyclotron frequencies of each ion species. The cyclotron frequency 𝜈𝑐of the daughter 95Mo+as a reference was linearly interpolated to the time of the measurement of the parent 95Tc+(ion of interest) to deduce the cyclotron frequency ratio 𝑅. Only the bunches with less than five detected ions were considered in the data analysis in order to reduce a possible cyclotron frequency shift due to ion-ion interactions [56,57]. The count-rate related frequency shifts were not observed in the analysis. The temporal fluctuation of the magnetic field 𝛿𝐵(𝜈𝑐)∕𝜈𝑐=Δ𝑡 ×2.01(25) ×10 −12/min [46], where Δ𝑡is the time interval between two consecutive reference measurements, is considered in the final results. Contribution of temporal fluctuations of the magnetic field to the final frequency ratio uncertainty was less than 10−10 since the parent-daughter measurements were interleaved with Δ𝑡< 10 minutes. The frequency shifts in the PI-ICR measurement due to ion image distortions were well below the statistical uncertainty and thus ignored in the calculation of the final uncertainty. Furthermore, Fig. 2. The measured experimental results from this work compared to the literature values [59,51]. The deviations of the individually measured cyclotron frequency ratios 𝑅(𝜈𝑐(95Mo+)/𝜈𝑐(95Tc+)) from the measured value 𝑅(left axis) and 𝑄value (right axis) in this work are compared to values adopted from AME2020. The red points with uncertainties represent individual measurements using the PI-ICR method. Vertical brown dashed lines separate measurements conducted at different time slots. The weighted average value 𝑅is depicted by the solid red line, and its 1𝜎uncertainty band is shaded in red. The dashed blue line illustrates the difference between our new value and the one referenced in AME2020, with its 1𝜎uncertainty area shaded in blue. decay pair ions 95Tc+-95Mo+, being mass doublets, cancel many of the systematic uncertainties in the cyclotron frequency ratio. The weighted mean ratio 𝑅of all single ratios was calculated along with the inner and outer errors to deduce the Birge ratio [58]. The maximum of the inner and outer errors was taken as the weight to calculate 𝑅. In Fig. 2, results of the analysis including all data with comparison to literature values are demonstrated. The final parent-to-daughter frequency ratio 𝑅with their uncertainty is determined to be 1.000 019 183 9(15). The corresponding gs-to-gs 𝑄value is 1695.92(13) keV. The gs-to-gs 𝑄EC value of 1695.92(13) keV from this work is ≈37 times more precise than that evaluated in AME2020 [59,51]. The measured 𝑄EC value has a deviation of 4.9(50) keV from the AME2020 value and is ≈1𝜎larger. The 𝑄EC value in AME2020 is derived primarily from two 𝛽+-decay experiments 95Tc(𝛽+)95Mo [60,61]. Combined with the atomic mass of 95Mo (mass excess: −87711.87(12) keV/c2) from AME2020 [51,59], we deduce the mass excess of its parent nucleus 95Tc (9/2+) to be −86015.95(18) keV/c2. The mass of 95Tc in AME2020 is primarily evaluated from 𝛽+-decay experiments 95Tc(𝛽+)95Mo and 95Ru(𝛽+)95Tc with influence of 97.4% and 2.6%, respectively [60,62,63]. The high-precision electron-capture energy from this work, together with the nuclear energy level data from Ref. [52–54]of the excited states of 95Mo as tabulated in Table 1, was used to determine the gs-to-es 𝑄 (𝑄∗ EC) values of three candidate states as shown in Table 1. The newly determined 𝑄∗ EC values confirm that the decay transitions of the ground state of 95Tc to the three excited states of interest are energetically allowed. In case of EC, the closer the 𝑄value of the decay to one of the ionization energies of the captured electrons, the larger the resonance enhancement of the rate near the end-point, where the effects of a nonvanishing neutrino mass are relevant. The event-rate dependence on the 𝑄value near the end-point for EC is steeper than that for 𝛽−decay. As tabulated in Table 1, Δ𝑥gives the distance of the 𝑄∗ EC value to the computed atomic relaxation energy 𝜀𝑥following the capture of electrons in the allowed daughter atomic shells (𝑥 =K, L1, L2, and other electrons from s-levels and p1∕2-levels from the third and higher shells). For the state with the excitation energy of 1675.40(60) keV, the captures of electrons occupying the K and higher shells for the transition 95Tc Physics Letters B 859 (2024) 139094 4 Z. Ge, T. Eronen, V.A. Sevestrean et al. Table 1 Potential candidate transitions of initial state (ground state) of parent nuclei 95Tc (9/2+) to the final states (excited states) of daughter 95Mo with ultra-low 𝑄values. The first column lists the excited final state of 95Mo for the low 𝑄value transition. The decay type is provided in the second column. The third and fourth columns present the derived decay 𝑄EC values in keV, sourced from literature (Lit.) [51]and this work (T. W.), respectively. The fifth column displays the experimental excitation energy 𝐸∗ with its experimental error [52–54]in keV. The sixth column shows the confidence (𝜎) of the 𝑄∗ EC being positive/negative. Columns seven to nine, denoted as Δ𝑥, represent the distance of 𝑄EC values to the computed atomic relaxation energy following the electron capture 𝜀𝑥in the daughter atoms [55]. FNU means forbidden non-unique. Spin-parity assignments and energy values enclosed in braces {} signify uncertain assignments or uncertainties in excitation energy, resulting in uncertainties in the decay type or decay energy. All the energies are in unit of keV. Final state Decay type 𝑄∗ EC (Lit.) 𝑄∗ EC (T. W.) E∗𝑄∕𝛿𝑄 (T. W.) ΔK (T. W.) ΔL1 (T. W.) ΔL2 (T. W.) 95Mo (9/2+) allowed 15.6(50) 20.52(61) 1675.40(60) 33 0.47(61) 17.64(61) 17.89(61) 95Mo ({7/2+,9/2 +}) {allowed} 8.0(51) 12.9(10) 1683.0(10) 13 10.0(10) 10.3(10) 95Mo (1/2+) 4th FNU -1.0({51}) 3.92({13}) 1692({}) {29} 1.04({13}) 1.29({13}) (9/2+) →95Mo∗are energetically allowed, while for states with the excitation energy of 1683.0(10) keV and 1692 keV, only electrons from s-levels and p1∕2-levels from the second (L) and higher shells can possibly be captured due to angular momentum conservation and the finite overlap of their wave function with the nucleus. The transition 95Tc (9/2−) →95Mo∗(1692 keV), giving the values of 1.04({13}) keV and 1.29({13}) keV for the distance of 𝑄∗ EC to the computed atomic relaxation energy following the electron capture 𝜀𝐿1= 2.878 keV and 𝜀𝐿2= 2.632 keV, is of the decay type of 4th FNU (forbidden non-unique). It has a long half-life which will result in an extremely low fraction of events landing near the endpoint. This transition is not of interest for future neutrino mass determination due to the low branching ratio. To confirm whether the emitted neutrino energy 1.04({13}) keV is ultra-low, further high-precision measurements of the excitation energy of the state are required. The parity of the 1683.0(10) keV state needs to be determined to verify the decay type of the transition to this state. The gs-to-gs 𝑄value of 95Tc is now well refined to sub keV uncertainty, combined with the energy level of 1675.40(60)-keV state, a possible ultra-low distance (0.47(61) keV) of 𝑄∗ EC to the computed atomic relaxation energy following the electron capture 𝜀𝑘= 20.054 keV [55]is observed to suggest it a suitable transition for potential neutrino mass measurements. Achieving precision below 100 eV for the 1675.40-keV state is highly desirable to unambiguously confirm whether the transition represents an energetically allowed decay. 3. Theoretical predictions In the following we employed two calculation methods in order to predict the transition half-life and the distribution of energy released in the decay, namely atomic many-electron Dirac–Hartree–Fock–Slater (DHFS) self-consistent method and the Nuclear Shell Model (NSM) many-nucleon framework using the code NuShellX@MSU [64]. The DHFS framework has been proven adequate for this type of calculations in our previous work [65]. Using the DHFS method we obtained the wave-functions and the energy levels of the atomic electrons. The calculations were performed for both the initial atom and the final atom. The initial atom was in its ground state. For the final atom, we considered all possible states with the electron configuration of the initial atom having a hole in each shell from which the electron could be captured. For the atomic-structure calculations we made use of the RADIAL subroutine package [66], which also contains the DHFS.F code. We denote the electron shell as 𝑥 =(𝑛, 𝜅), where 𝑛is the principal quantum number and 𝜅is the relativistic quantum number. The atomic relaxation energy following the capture of an electron from the 𝑥shell is denoted as 𝜀𝑥. It is calculated according to the refined energy conservation in [65], as 𝜀𝑥=|𝑇g.s.| −|𝑇𝑥|, where 𝑇g.s.and 𝑇𝑥are the total binding energy of the final atom in the ground state and in the excited state with a hole in the 𝑥shell. For allowed transitions the energy distribution of an EC event is calculated as a sum over all atomic shells with 𝜅=±1as 𝜌(𝐸)= 𝐺2 𝛽 (2𝜋)2𝐶∑ 𝑥 𝑛𝑥𝛽2 𝑥𝐵𝑥𝑆𝑥𝑝𝜈𝐸𝜈 Γ𝑥∕(2𝜋) (𝐸−𝜀𝑥)2+Γ 2 𝑥∕4 ,(2) where 𝐵𝑥and 𝑆𝑥are the exchange and overlap corrections, and the shake-up and shake-off corrections, respectively, presented in detail in [65]. Here we go beyond the formalism used in [28]by adding the shake-up and shake-off corrections into the energy distribution 𝜌(𝐸). Here 𝐸is related to the energy of the neutrino 𝐸𝜈and the Q value as 𝐸=𝑄∗ EC −𝐸𝜈. The momentum of the neutrino is denoted as 𝑝𝜈= √𝐸2 𝜈−𝑚2 𝜈. The Coulomb amplitude is represented as 𝛽𝑥, while 𝑛𝑥is the relative occupancy of the shell. The intrinsic line-widths of Breit– Wigner resonances centered at 𝜀𝑥are denoted as Γ𝑥and are taken from [67]. The Fermi constant 𝐺Fand the Cabibbo angle 𝜃Care combined in 𝐺𝛽=𝐺Fcos𝜃C. For allowed transitions, the nuclear structure information is contained in the shape factor 𝐶in terms of the nuclear form factor 𝐴𝐹(0) 101 [68]: 𝐶=[𝐴𝐹(0) 101]2 =[−𝑔A √2𝐽𝑖+1 𝑀GT]2 ,(3) where 𝑀GT is the Gamow–Teller nuclear matrix element [69]. The angular momentum of the initial nucleus is denoted as 𝐽𝑖, while the strength of the weak axial coupling is represented as 𝑔A. For the 𝑀GT calculation we used the NSM interactions jj45pna [70], a two-nucleon potential with a perturbative G-matrix approach with the single-particle energies adjusted in the Coulomb part to reproduce the recent results in [71]and jj45pnb [72], both sharing the same jj45pn model space. Additionally, we employed the interaction glekpn [73]. We computed the level scheme of the parent and daughter nuclei along with a few electromagnetic moments to evaluate the validity of three shellmodel interactions. Our findings indicated that the jj45pna and jj45pnb interactions showed a stronger agreement with the available experimental data compared to the glekpn. Then, for the value of the weak axial coupling 𝑔Awe used the conservative range of 0.7 to 1 [74–76]and presented the partial half-life corresponding to the mean decay rate in Table 2. The mean rate corresponds to a 𝑔Avalue equal to 0.857. The half-life for the values in the selected interval of 𝑔Aare between −33.3% and +36.1% of each mean value. The total decay constant𝜆is obtained by integrating the energy distribution over the entire energy range (0, 𝑄∗ EC −𝑚𝜈). Using the narrowwidth approximation, the decay rate can be written as: 𝜆= 𝐺2 𝛽 (2𝜋)2𝐶∑ 𝑥 𝑛𝑥𝛽2 𝑥𝐵𝑥𝑆𝑥𝑝𝜈𝑥 (𝑄∗ EC −𝜀𝑥),(4) where 𝑝𝜈𝑥 =√(𝑄∗ EC −𝜀𝑥)2−𝑚2 𝜈. Physics Letters B 859 (2024) 139094 5 Z. Ge, T. Eronen, V.A. Sevestrean et al. Table 2 Computed mean half-lives using 𝑔A=0.857 (see the main text) for the EC decay of 95Tc to the two excited states in 95Mo (with experimental energies 𝐸∗= 1675.4keV and 1683 keV), using three shell-model interactions for the Gamow-Teller matrix element, with their experimental 𝑄values shown in column 1. The second column indicates the used interactions and the third column the Gamow–Teller nuclear matrix element [69]. The computed total half-life and partial half-lives are demonstrated in columns 4-12. The atomic subshells are denoted using the X-ray notation. 𝑄∗ EC interaction 𝑀GT Total half-life K L1 L2M1M2N1 N2 O1 (keV) (103yr) (107yr) (104yr) (105yr) (104yr) (106yr) (105yr) (107yr) (106yr) 20.52 jj45pna −0.00696 877 20.0 117 708 640 267 223 146 491 jj45pnb -0.016533 155 3.55 20.8 125 81.647.4 39.425.887.1 glekpn 0.0070667 850 19.4 114 587 446 259 216 141 477 12.9 jj45pna −0.02412 173 -24.1 143 79.746.0 37.524.582.6 jj45pnb -0.0198667 255 -35.6 210 117 67.9 55.336.1 122 glekpn 0.2296 1.9-0.266 1.57 0.880 0.508 0.414 0.271 0.911 Fig. 3. Normalized distributions of released energy in the EC decay of 95Tc in the transitions to the excited states of 95Mo, as functions of 𝐸−𝑄∗ EC. The experimental excitation energies are 𝐸∗= 1675.40 keV and 𝐸∗= 1683.0keV, while the corresponding 𝑄values are 𝑄∗ EC =20.52 keV (green) and 𝑄∗ EC =12.9keV (orange). The K, L1, L2, M1 and N1 notations indicate sub-shells from which the electron was captured. The M2, N2 and O1 sub-shells are harder to distinguish and are not labeled. The inset indicates an enlarged endpoint region showing the effect of neutrino masses of 0.45 eV and 0 eV. The dotted lines depict the spectra for a massless neutrino, while the solid lines correspond to a neutrino mass of 0.45 eV. While an electron is captured by the nucleus, the other electrons (the spectator electrons) can undergo some processes which affect the decay rate. Multiple corrections, including exchange, overlap, shake-up, and shake-off effects, were considered as explained in detail in a forthcoming theory paper [77]. The energy levels of the daughter nucleus were computed to identify the theoretical states corresponding to the experimental states of interest (1675.4keV, 1683 keV). We compared the theoretical energies with the experimental ones and concluded that the following are the theoretical states closest to the experimental ones: for the experimental state with 𝐽𝑓=9∕2and 𝐸∗= 1675.4keV the best matches were 𝐸∗ th = 1748 keV for jj45pna, 𝐸∗ th = 1897 keV for jj45pnb, and 𝐸∗ th = 1703 keV for glekpn. All the mentioned theoretical states have 𝐽𝑓=9∕2. For the experimental state having the energy 𝐸∗= 1683 keV and with the angular momentum and parity uncertain {7/2+, 9/2+}, the closest correspondence is for jj45pna the energy 𝐸∗ th = 1584 keV, for jj45pnb the energy 𝐸∗ th = 1642 keV, and for glekpn the energy 𝐸∗ th = 1707 keV. The mentioned three theoretical states have the angular momentum and parity 7∕2+. In Table 2, we present the predicted half-lives for the decay of 95Tc to the two excited states of 95Mo for all relevant atomic shells. In Fig. 3the normalized distribution of the released energy in the EC decay of 95Tc to excited states of 95Mo is demonstrated. The transition spectrum of 95Tc (9/2+) →95Mo∗(1675.4 keV) is indicated in green, with 𝑄∗ EC of 20.52 keV, situated 0.47 keV relative to the computed atomic relaxation enFig. 4. Normalized distribution of released energy in the EC decay of 95Tc in the transition to the excited state 𝐸∗= 1675.40 keV of 95Mo, with 𝑄∗ EC =20.06 keV, as function of 𝐸−𝑄∗ EC in comparison to that of 163Ho with gs-to-gs 𝑄EC = 2.8632 keV [78]. The red line corresponds to the on-resonance EC decay using the experimental 𝑄∗ 𝐸𝐶 of 20.06 keV within 1𝜎range of the central value 20.52 keV, while the blue line corresponds to the 𝑄∗ EC of 2.8632 keV. For the sub-shell notation and the inset the reader is referred to the caption of Fig. 3. ergy following the electron capture in the allowed K shell. In contrast, the transition 95Tc (9/2+) →95Mo∗(1683.0 keV), shown in orange, with a 𝑄∗ EC value of 12.9 keV, is relatively farther from the computed atomic relaxation energy following the electron capture of the allowed L1 shell (giving a value of 10 keV for the distance). As illustrated in the inset of Fig. 3, a more pronounced resonance enhancement in the last 0.45 eV region near the endpoint for the former transition is observed, suggesting a preference for choosing this transition as a candidate for determining a non-vanishing neutrino mass. This phenomenon guides us to search for cases that have the smallest distance of 𝑄∗ EC to the highest ionization energy of the captured electron of all allowed shells for neutrino-mass determination experiments. The decay rate close to the endpoint is highly sensitive to small variations of the 𝑄value as demonstrated by the K level, manifesting as a resonance itself, and thus can radically increase the number of recorded events near the endpoint. The current accuracy of measurement of the 𝑄∗ EC value does not allow to make an unambiguous conclusion about the position of the 1𝑠level, relative to the endpoint. Assuming 𝑄EC∗= 20.06 keV, which is consistent with the 1𝜎range of experimental error and is shifted by -0.46 keV relative to the central value, the resonance at the endpoint provides the highest EC event rate in the neutrino-mass sensitive region. Fig. 4shows the normalized EC energy spectrum as a function of the energy, 𝐸−𝑄∗ EC, deposited in a calorimeter through the de-excitation of atomic shells for 𝑄∗ EC = 20.06 keV, in comparison to the EC energy spectra in 163Ho atom. The 𝑠1level, K, has a significant EC counting-rate enhancement for the transition 95Tc (9/2+) →95Mo∗ (1675.40 keV) in the neutrino-mass sensitive region, as shown on an en- Physics Letters B 859 (2024) 139094 6 Z. Ge, T. Eronen, V.A. Sevestrean et al. larged scale in the inset of Fig. 4. Assuming a 𝑄value of 𝑄∗ EC = 20.06 keV, technetium is about three orders of magnitude more effective than holmium. Based on these findings, it can be conjectured that we have found a potentially strong transition for direct electron-neutrino mass determination. However, the short half-life of about 1 day for the 95Tc can prove to be a challenge experimentally. 4. Conclusion and outlook A direct high-precision gs-to-gs EC-decay 𝑄-value measurement of 95Tc (9/2+) →95Mo (5/2+) was performed using the PI-ICR technique at JYFLTRAP Penning trap mass spectrometer. A 𝑄value of 1695.92(13) keV was obtained and the precision was improved by a factor of around 37 compared to literature. The measurement also improved the mass excess of 95Tc by a factor of 28 compared to previous experiments. Three candidate transitions of 95Tc (9/2+) →95Mo∗were validated to be energetically allowed. The refined sub-keV precision of the gs-to-gs 𝑄value of 95Tc allows us to find a possible ultra-low energy difference (0.47(61) keV) between 𝑄∗ EC and the atomic relaxation energy 𝜀𝑘= 20.054 keV in the K capture for the allowed gs-to-es transition to the 1675.40-keV state. The spin of the 1683.0-keV state needs to be determined along with its energy with higher precision in order to see if the related transition is allowed and of low 𝑄value. The atomic self-consistent many-electron Dirac–Hartree–Fock–Slater method and three nuclear shell-model interactions were utilized to predict the partial decay half-lives and energy distributions of gs-to-es EC transitions in 95Tc with low 𝑄values. We computed the energy levels of the parent and daughter nuclei and a few electromagnetic moments to assess the validity of the three shell-model interactions (jj45pna, jj45pnb, glekpn). Multiple corrections, such as exchange, overlap, shake-up, and shake-off effects, were accounted for in these predictions. From the calculations, the possible ultra-low distance to the atomic line K, level 1s, for 95Tc (9/2+) →95Mo∗(1675.40 keV) results in a significant increase in the number of EC events in the energy region sensitive to the electron neutrino mass. These findings confirm a potentially powerful transition for direct electron-neutrino mass determination. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We acknowledge the staff of the Accelerator Laboratory of University of Jyväskylä (JYFL-ACCLAB) for providing stable online beam. We thank the support by the Research Council of Finland under the Finnish Centre of Excellence Programme 2012–2017 (Nuclear and Accelerator Based Physics Research at JYFL) and projects No. 306980, 312544, 275389, 284516, 295207, 314733, 315179, 327629, 320062, 354589, 345869 and 354968. The support by the EU Horizon 2020 research and innovation program under grant No. 771036 (ERC CoG MAIDEN) is acknowledged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 861198–LISA–H2020-MSCA-ITN-2019. V.A.S., O.N., S.S., J.S., and J.K. acknowledge support from project PNRR-I8/C9-CF264, Contract No. 760100/23.05.2023 of the Romanian Ministry of Research, Innovation and Digitization. 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