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Author(s): Zhuang Ge, Tommi Eronen, Vasile Alin Sevestrean, Ovidiu Niţescu, Sabin Stoica, Marlom Ramalho, Jouni Suhonen, Antoine de Roubin, Dmitrii Nesterenko, Anu Kankainen, Pauline Ascher, Samuel Ayet San Andres, Olga Beliuskina, Pierre Delahaye, Mathieu Flayol, Mathias Gerbaux, Stéphane Grévy, Marjut Hukkanen, Arthur Jaries, Ari Jokinen, Audric Husson, Daid Kahl, Joel Kostensalo, Jenni Kotila, Iain Moore, Stylianos Nikas, Marek Stryjczyk, Ville Virtanen Title: High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc Year: 2024 Version: Published version Copyright: The Author(s) 2024 Rights: CC BY 4.0 Rights url: https://creativecommons.org/licenses/by/4.0/ Please cite the original version: Zhuang Ge, Tommi Eronen, Vasile Alin Sevestrean, Ovidiu Niţescu, Sabin Stoica, Marlom Ramalho, Jouni Suhonen, Antoine de Roubin, Dmitrii Nesterenko, Anu Kankainen, Pauline Ascher, Samuel Ayet San Andres, Olga Beliuskina, Pierre Delahaye, Mathieu Flayol, Mathias Gerbaux, Stéphane Grévy, Marjut Hukkanen, Arthur Jaries, Ari Jokinen, Audric Husson, Daid Kahl, Joel Kostensalo, Jenni Kotila, Iain Moore, Stylianos Nikas, Marek Stryjczyk, Ville Virtanen, High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc, Physics Letters B, Volume 859, 2024, 139094, https://doi.org/10.1016/j.physletb.2024.139094. https://creativecommons.org/licenses/by/4.0/ Phys. Lett. B 859 (2024) 139094 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 𝑄 value of 95Tc Zhuang Ge a, ,∗, Tommi Eronen a, , Vasile Alin Sevestrean b,c,d, ,∗∗, Ovidiu Niţescu b,d, , Sabin Stoica b, , Marlom Ramalho a, , Jouni Suhonen a,b, ,∗, Antoine de Roubin e,f , , Dmitrii Nesterenko a, , Anu Kankainen a, , Pauline Ascher f , , Samuel Ayet San Andres g, , Olga Beliuskina a, , Pierre Delahaye h, , Mathieu Flayol f , , Mathias Gerbaux f , , Stéphane Grévy f , , Marjut Hukkanen a,i, , Arthur Jaries a, , Ari Jokinen a, , Audric Husson f , , Daid Kahl j, ,1, Joel Kostensalo k, , Jenni Kotila b,l,m, , Iain Moore a, , Stylianos Nikas a, Marek Stryjczyk a, , Ville Virtanen a, a Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland b International Centre for Advanced Training and Research in Physics (CIFRA), POB MG-12, RO-077125, Bucharest-Măgurele, Romania c Faculty 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 e KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001, Leuven, Belgium f Université de Bordeaux, CNRS/IN2P3, UMR 5797, F-33170, Gradignan, France g Instituto de Fisica Corpuscular, CSIC-UV, 46980, Gradignan, Spain h GANIL, CEA/DSM-CNRS/IN2P3, Bd Henri Becquerel, 14000, Caen, France i Université de Bordeaux, CNRS/IN2P3, LP2I Bordeaux, UMR 5797, F-33170, Gradignan, France j Extreme Light Infrastructure - Nuclear Physics, Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH), 077125, Bucharest-Magurele, Romania k Natural Resources Institute Finland, Yliopistokatu 6B, FI-80100, Joensuu, Finland l Finnish Institute for Educational Research, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland m Center 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 𝑄 value Electron capture A direct measurement of the ground-state-to-ground-state electron-capture decay 𝑄 value of 95Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The 𝑄 value 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. Available online 24 October 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded b (http://creativecommons.org/licenses/by/4.0/). E-mail addresses: zhuang.z.ge@jyu.fi (Z. Ge), sevestrean.alin@theory.nipne.ro (V 1 Present address: Facility for Rare Isotope Beams, Michigan State University, 640 https://doi.org/10.1016/j.physletb.2024.139094 Received 7 June 2024; Received in revised form 18 August 2024; Accepted 22 Octo y SCOAP³. This is an open access article under the CC BY license .A. Sevestrean), jouni.t.suhonen@jyu.fi (J. Suhonen). South Shaw Lane East Lansing, MI 48824, USA. ber 2024 http://www.ScienceDirect.com/ http://www.elsevier.com/locate/physletb http://orcid.org/0000-0001-8586-6134 http://orcid.org/0000-0003-0003-6022 http://orcid.org/0009-0009-9658-2386 http://orcid.org/0000-0002-9598-8415 http://orcid.org/0000-0003-4632-7327 http://orcid.org/0000-0003-3514-6678 http://orcid.org/0000-0002-9898-660X http://orcid.org/0000-0002-6817-7254 http://orcid.org/0000-0002-6103-2845 http://orcid.org/0000-0003-1082-7602 http://orcid.org/0000-0002-1990-0848 http://orcid.org/0000-0002-0053-1691 http://orcid.org/0000-0003-4448-7650 http://orcid.org/0000-0002-8851-7826 http://orcid.org/0000-0002-1215-2269 http://orcid.org/0000-0002-3852-2643 http://orcid.org/0000-0003-2680-1802 http://orcid.org/0000-0002-4317-3628 http://orcid.org/0000-0002-5279-0820 http://orcid.org/0000-0002-0451-125X http://orcid.org/0000-0001-9798-0655 http://orcid.org/0000-0003-3368-7307 http://orcid.org/0000-0001-9883-1256 http://orcid.org/0000-0001-9207-5824 http://orcid.org/0000-0003-0934-8727 http://orcid.org/0000-0001-6515-2409 http://orcid.org/0000-0003-0276-6483 mailto:zhuang.z.ge@jyu.fi mailto:sevestrean.alin@theory.nipne.ro mailto:jouni.t.suhonen@jyu.fi https://doi.org/10.1016/j.physletb.2024.139094 https://doi.org/10.1016/j.physletb.2024.139094 http://crossmark.crossref.org/dialog/?doi=10.1016/j.physletb.2024.139094&domain=pdf http://creativecommons.org/licenses/by/4.0/ 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 non- zero rest mass. However, these oscillations cannot assess the abso- lute mass scale, but only the squared differences of the mass eigen- states [1–3]. Neutrinos are the second most abundant particles in the universe, and play an important role on cosmological scales [4]. Accu- rate measurements of the total neutrino mass involve their imprint on the cosmic microwave background (CMB) as well as on structure forma- tion in the early universe. The most direct method to measure the absolute mass scale of an- tineutrinos 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 cal- culation 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/c2 at 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 spec- troscopy (CRES) technique via measurements of the tritium end-point spectrum. The new technique CRES will allow for an eventual sensitiv- ity to m𝜈𝑒 down to 0.04 eV/c2. The first frequency-based neutrino mass limit of electron-weighted neutrino mass < 155 eV/c2 is extracted from the background-free measurement of the continuous tritium 𝛽 spectrum 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/c2 for the electron-neutrino mass [16]. A 𝑄 value as small as possible is desired in these single decay ex- periments for electron (anti)neutrino mass determination. The effective fraction of decays in a given energy interval Δ𝐸 at the endpoint area will be larger with a lower 𝑄 value [20,21]. Currently, only ground-state- to-ground-state (gs-to-gs) decay cases 3H (𝛽 decay) and 163Ho (electron capture), are being used for direct neutrino-mass-determination experi- ments. Ongoing intensive searches for isotopes undergoing 𝛽/EC decays from the ground state to an excited state with a low 𝑄 value are ac- tively 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 𝑄 value determi- nation, and it is hitherto the only direct method to measure the decay 𝑄 value 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/𝛽 transition is identified with a sufficiently high decay rate, the idea that involves operating mechanical quantum sen- sors 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 gs- to-gs EC 𝑄 value of 95Tc with JYFLTRAP PTMS. The precise 𝑄 value obtained in this study, in conjunction with nuclear energy level data for excited states of 95Mo, is utilized to ascertain their ground-state-to- excited-state (gs-to-es) 𝑄 values. In the case of 95Tc, there are two poten- tial low 𝑄-value gs-to-es EC transitions, that could be used for neutrino- mass detection. To explore this potential, we have utilized two com- putational 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 tran- sitions 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 2 spectrometer [39] at the University of Jyväskylä, Finland [40,41]. Physics Letters B 859 (2024) 139094 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 accu- mulation time) plot. The used angular gates are highlighted. The vertical dashed blue line shows the chosen optimal frequency to transmit 95Tc ions while sup- pressing 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 Accel- erator Laboratory of the University of Jyväskylä. A helium-filled small volume gas cell was used to stop the recoils produced from the proton- induced fusion-evaporation reaction, and the ions were extracted using gas flow and guided through a sextupole ion guide [42] with a com- bination 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 reac- tion 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 of- fline glow-discharge ion source. A 90◦ electrostatic bender selected ions either from the online target station or the offline ion source for down- stream transmission. JYFLTRAP comprises two cylindrical Penning traps in a 7-T super- conducting 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 ≈ 105. In the pu- rification 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 exci- tation 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 sam- ples 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 de- scribed 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 𝐵 is the magnetic field strength, 𝑞 is the charge and 𝑚 the mass of the stored ion. The PI- ICR 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, sep- arated in time by the defined phase-accumulation time, 𝑡𝑎𝑐𝑐 . The phase images of these two are projected onto a position-sensitive MCP detec- 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 mo- tions with respect to the center spot is denoted as 𝛼𝑐 = 𝛼+ − 𝛼−, where 𝛼+ and 𝛼− represent the polar angles of the cyclotron and mag- netron motion phases. The cyclotron frequency 𝜈𝑐 is derived from: 𝜈𝑐 = (𝛼𝑐 + 2𝜋𝑛𝑐)∕2𝜋𝑡𝑎𝑐𝑐 , where 𝑛𝑐 represents the full number of revo- lutions made by the measured ions during the phase accumulation time 𝑡𝑎𝑐𝑐 . Different accumulation times for 95Tc+ were utilized to unambigu- ously assign 𝑛𝑐 . An accumulation time of 574 ms was employed for the actual measurements to determine the final 𝜈𝑐 for 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 main- tain an angle 𝛼𝑐 within a few degrees. This choice aimed to minimize the shift in the 𝜈𝑐 ratio of the 95Tc+-95Mo+ pair due to the conversion of the cyclotron motion to magnetron motion and the possible distor- tion 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 cy- clotron motion that might have shifted the different spots. The total data accumulation time of interleaved measurements of 𝜈𝑐 for 95Tc+-95Mo+ ions was ≈ 4.9 hours, respectively. The gs-to-gs electron-capture 𝑄 value, 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 𝑀𝑝 and 𝑀𝑑 represent the masses of the parent and daughter atoms, respectively, and 𝑅 (=𝜈𝑐,𝑑∕𝜈𝑐,𝑝) denotes their cyclotron fre- quency ratio for singly charged ions (𝑞 = 1), with 𝑚𝑒 being the mass of an electron. The electron binding energies of the parent and daughter atoms, denoted as 𝐵𝑝 and 𝐵𝑑 , are neglected due to their small values (on the order of a few eV [50]), and 𝑅 is close to 1. Since both the parent and daughter ions have the same 𝐴∕𝑞 and their relative mass dif- ference 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 𝑄 value from the mass uncer- tainty of the reference (daughter), which is 0.12 keV/c2 for 95Mo [51], can be neglected. 2. Results and discussion The determination of 𝑄EC depends on the measured cyclotron fre- quency ratio 𝑅 via Eq. (1). Two data sets for 95Tc+-95Mo+ were col- lected. 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 𝜈𝑐 of the daughter 95Mo+ as a refer- ence 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 Δ𝑡 is 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 3 thus ignored in the calculation of the final uncertainty. Furthermore, Physics Letters B 859 (2024) 139094 Fig. 2. The measured experimental results from this work compared to the lit- erature 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 𝑄 value (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 𝑅 is depicted by the solid red line, and its 1𝜎 uncertainty band is shaded in red. The dashed blue line illustrates the difference between our new value and the one referenced in AME2020, with its 1𝜎 uncertainty 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 𝑅 of all single ratios was calculated along with the inner and outer errors to deduce the Birge ratio [58]. The max- imum 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 fre- quency ratio 𝑅 with their uncertainty is determined to be 1.000 019 183 9(15). The corresponding gs-to-gs 𝑄 value 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 mea- sured 𝑄EC value has a deviation of 4.9(50) keV from the AME2020 value and is ≈1𝜎 larger. The 𝑄EC value in AME2020 is derived pri- marily from two 𝛽+-decay experiments 95Tc(𝛽+)95Mo [60,61]. Com- bined with the atomic mass of 95Mo (mass excess: −87711.87(12) keV/c2) from AME2020 [51,59], we deduce the mass excess of its par- ent 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%, re- spectively [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 al- lowed. In case of EC, the closer the 𝑄 value 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 non- vanishing neutrino mass are relevant. The event-rate dependence on the 𝑄 value near the end-point for EC is steeper than that for 𝛽− decay. As tabulated in Table 1, Δ𝑥 gives the distance of the 𝑄∗ EC value to the com- puted atomic relaxation energy 𝜀𝑥 following the capture of electrons in the allowed daughter atomic shells (𝑥 = K, L1, L2, and other elec- trons 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) 139094Z. 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 𝑄 values. The first column lists the excited final state of 95Mo for the low 𝑄 value 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 𝜀𝑥 in 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 ex- citation 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 possi- bly 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 relax- ation 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, fur- ther high-precision measurements of the excitation energy of the state are required. The parity of the 1683.0(10) keV state needs to be deter- mined to verify the decay type of the transition to this state. The gs-to-gs 𝑄 value 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 dis- tance (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 sug- gest 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 𝑛 is the principal quantum number and 𝜅 is the relativistic quantum number. The atomic relaxation energy following the capture of an electron from the 𝑥 shell is denoted as 𝜀𝑥. It is calculated according to the refined energy con- servation in [65], as 𝜀𝑥 = |𝑇g.s.| − |𝑇𝑥|, where 𝑇g.s. and 𝑇𝑥 are the total binding energy of the final atom in the ground state and in the excited 4 state with a hole in the 𝑥 shell. For allowed transitions the energy distribution of an EC event is cal- culated as a sum over all atomic shells with 𝜅 = ±1 as 𝜌(𝐸) = 𝐺2 𝛽 (2𝜋)2 𝐶 ∑ 𝑥 𝑛𝑥𝛽 2 𝑥 𝐵𝑥𝑆𝑥𝑝𝜈𝐸𝜈 Γ𝑥∕(2𝜋)( 𝐸 − 𝜀𝑥 )2 + Γ2 𝑥 ∕4 , (2) where 𝐵𝑥 and 𝑆𝑥 are 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 𝐸 is related to the energy of the neutrino 𝐸𝜈 and 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 𝑛𝑥 is the relative occupancy of the shell. The intrinsic line-widths of Breit– Wigner resonances centered at 𝜀𝑥 are denoted as Γ𝑥 and are taken from [67]. The Fermi constant 𝐺F and the Cabibbo angle 𝜃C are combined in 𝐺𝛽 = 𝐺F cos𝜃C. For allowed transitions, the nuclear structure infor- mation is contained in the shape factor 𝐶 in 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 shell- model interactions. Our findings indicated that the jj45pna and jj45pnb interactions showed a stronger agreement with the available experimen- tal data compared to the glekpn. Then, for the value of the weak axial coupling 𝑔A we 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 𝑔A value equal to 0.857. The half-life for the values in the selected interval of 𝑔A are between −33.3% and +36.1% of each mean value. The total decay constant𝜆 is obtained by integrating the energy dis- tribution over the entire energy range (0, 𝑄∗ EC −𝑚𝜈). Using the narrow- width approximation, the decay rate can be written as: 𝜆 = 𝐺2 𝛽 (2𝜋)2 𝐶 ∑ 𝑥 𝑛𝑥𝛽 2 𝑥 𝐵𝑥𝑆𝑥𝑝𝜈𝑥 ( 𝑄∗ EC − 𝜀𝑥 ) , (4) √( ) where 𝑝𝜈𝑥 = 𝑄∗ EC − 𝜀𝑥 2 −𝑚2 𝜈 . Physics Letters B 859 (2024) 139094Z. 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∗ = 1675.4 keV and 1683 keV), using three shell-model interactions for the Gamow-Teller matrix element, with their experimental 𝑄 values 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 L2 M1 M2 N1 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 81.6 47.4 39.4 25.8 87.1 glekpn 0.0070667 850 19.4 114 587 446 259 216 141 477 12.9 jj45pna −0.02412 173 - 24.1 143 79.7 46.0 37.5 24.5 82.6 jj45pnb -0.0198667 255 - 35.6 210 117 67.9 55.3 36.1 122 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 exper- imental excitation energies are 𝐸∗ = 1675.40 keV and 𝐸∗ = 1683.0 keV, while the corresponding 𝑄 values are 𝑄∗ EC = 20.52 keV (green) and 𝑄∗ EC = 12.9 keV (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 (1675.4 keV, 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∕2 and 𝐸∗ = 1675.4 keV 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. 3 the 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 5 keV, situated 0.47 keV relative to the computed atomic relaxation en- Fig. 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 1𝜎 range 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 high- est 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 vari- ations of the 𝑄 value 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 1𝑠 level, relative to the endpoint. Assuming 𝑄EC∗ = 20.06 keV, which is consistent with the 1𝜎 range 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. 4 shows 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 𝑠1 level, 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- Z. Ge, T. Eronen, V.A. Sevestrean et al. larged scale in the inset of Fig. 4. Assuming a 𝑄 value 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 tech- nique at JYFLTRAP Penning trap mass spectrometer. A 𝑄 value of 1695.92(13) keV was obtained and the precision was improved by a factor of around 37 compared to literature. The measurement also im- proved 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 𝑄 value of 95Tc allows us to find a possible ultra-low en- ergy 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 tran- sition 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 𝑄 value. The atomic self-consistent many-electron Dirac–Hartree–Fock–Slater method and three nuclear shell-model interactions were utilized to pre- dict the partial decay half-lives and energy distributions of gs-to-es EC transitions in 95Tc with low 𝑄 values. 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 cal- culations, 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 innova- tion program under grant No. 771036 (ERC CoG MAIDEN) is acknowl- edged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agree- ment 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, Con- tract No. 760100/23.05.2023 of the Romanian Ministry of Research, Innovation and Digitization. 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