We present the first direct measurement of the neutron incoherent scattering length of ${}^{199}\mathrm{Hg}$. The measurement was performed with the Ramsey apparatus of the neutron electric dipole moment experiment located at the Paul Scherrer Institute. The incoherent scattering length $b_{\text{i}}$ was determined by investigating the pseudomagnetic effect due to the strong interaction between the neutron spins and the nuclear spins of mercury atoms. The resulting frequency shift of the neutron Larmor precession frequency was determined for various ${}^{199}\mathrm{Hg}$ density and polarization values. The obtained value of $b_{\text{i}}=(-16.2\pm 2.0)\mathrm{fm}$ agrees in magnitude with previous determinations and provides the so-far unknown sign of the quantity.

A high-precision measurement of the electron-capture (EC) decay $Q$ value for the ground-state-to-ground-state (gs-to-gs) transition of ${}^{113}\mathrm{Sn}$ to ${}^{113}\mathrm{In}$ has been performed using the JYFLTRAP double Penning trap mass spectrometer. Employing the phase-imaging ion-cyclotron-resonance technique, the isomeric state of ${}^{113}\mathrm{Sn}$ at 77.389(19) keV was resolved, and the cyclotron frequency ratio was measured between the isomer ${}^{113m}\mathrm{Sn}$ and the daughter nucleus ${}^{113}\mathrm{In}$. This yielded an isomer-to-ground-state $Q$ value of 1116.64(19) keV and gs-to-gs $Q$ value of 1039.25(19) keV. The atomic mass excess of ${}^{113}\mathrm{Sn}$ was determined as $-88327.87\left(27\right)\mathrm{keV}/c^2$, in excellent agreement with the Atomic Mass Evaluation 2020 (AME2020) but with a sixfold precision improvement. Using nuclear energy-level data for ${}^{113}\mathrm{In}$, we identified two low $Q$-value transitions of the ground state of ${}^{113}\mathrm{Sn}$ to excited states of ${}^{113}\mathrm{In}$ at 1024.280(50) keV ($Q_{\mathrm{EC}}^{*}=14.97\left(20\right)$ keV, second forbidden non-unique) and 1029.650(50) keV ($Q_{\mathrm{EC}}^{*}=9.60\left(20\right)$ keV, allowed). The allowed transition exhibits small energy differences [${\mathrm{\Delta }}_{\mathrm{L}1}=5.58\left(20\right)$ keV, ${\mathrm{\Delta }}_{\mathrm{L}2}=5.87\left(20\right)$ keV] from L1 and L2 shell binding energies, enhancing endpoint events. Partial half-lives and energy-release spectra were calculated using the self-consistent Dirac-Hartree-Fock-Slater method (including exchange, overlap, shake-up, and shake-off corrections) together with the nuclear shell model and showed enhanced endpoint sensitivity for the allowed transition to the state at 1029.650 keV. Including subthreshold atomic states in the spectral function enhances the EC rate near the zero-neutrino-momentum region by a factor of 5, enabling new approaches for low-$Q$-value EC decays in neutrino mass studies.

The cryogenic approach to the search for the neutron electric dipole moment—performing the experiment in superfluid liquid helium—holds promise for a substantial increase in sensitivity, potentially enabling a sensitivity level of ${10}^{-28}$ $e\mathrm{cm}$. A crucial component in realizing such an experiment is the high-voltage and electrode system capable of providing an electric field of 75 kV/cm. This, in turn, requires an electric potential of 635 kV to be applied to the high-voltage electrode, while simultaneously satisfying other experimental constraints, such as those on heat load and magnetic noise requirements. This paper describes the outcome of a comprehensive development program addressing these challenges. It outlines the system requirements, discusses new insights into relevant physical phenomena, and details selected technical solutions with their corresponding experimental demonstrations and expected performance. The results collectively demonstrate the successful development of the necessary technology for the high-voltage and electrode system for this approach.

Benchmarking simulation codes for electron transport and scattering in matter is a crucial step for estimating uncertainties in many applications. However, experimental data for electron energies of a few MeV are too scarce to make such comparisons. We report here the measurement and the quantitative analysis of backscattering probabilities of electrons in the energy range 0.1 to 3.4 MeV impinging on a Ce-doped ${\mathrm{YAlO}}^3$ (YAP:Ce) scintillator. The setup consists of a $2\times 2\pi$ calorimeter which enables, in particular, the inclusion of large incidence angles. The results are used to benchmark various scattering models incorporated in Geant4, showing relative deviations smaller than 5% between experiment and simulations. They demonstrate the current rather high reliability of the simulations when employing appropriate electromagnetic physics lists.

One method of determining the free neutron lifetime involves the absolute counting of neutrons and trapped decay protons. In such experiments, a cold neutron beam traverses a segmented proton trap inside a superconducting solenoid while the neutron flux is continuously monitored. Protons that are born within the fiducial volume of the trap are confined radially by the magnetic field and axially by the electrostatic potential supplied by trap electrodes. They are periodically released and counted, and the ratio of the absolute number of neutrons to protons is proportional to the neutron lifetime. Systematic error can be introduced if protons in the trap are lost, gained, or misidentified. The influence of molecular hydrogen interactions is of particular interest because of its ubiquitous presence in ultrahigh vacuum systems. To understand how it could affect the neutron lifetime, measurements were performed on the production and detection of molecular hydrogen in an apparatus used to measure the neutron lifetime. We demonstrate that charge exchange with molecular hydrogen can occur with trapped protons, and we determine the efficiency with which the molecular hydrogen ions in the trap are detected. Finally, we comment on the potential impact on a neutron lifetime experiment using this beam technique. We find that the result of the beam neutron lifetime performed at NIST is unlikely to have been significantly affected by charge exchange with molecular hydrogen.

We present a calculation of the nuclear matrix element for the two-neutrino double-beta ($2\nu \beta \beta$) decay of ${}^{48}\mathrm{Ca}\to {}^{48}\mathrm{Ti}$ using a post-Hartree-Fock (HF) density functional theory–based no-core configuration-interaction framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent mean-field configurations obtained by solving the HF equations with the density-independent local Skyrme interaction. Our calculations yield $|{\mathcal{M}}_{2\nu \beta \beta }|=0.056\left(6\right){\mathrm{MeV}}^{-1}$ for the nuclear matrix element describing this process. This result is in very good agreement with shell-model studies—for example, with the calculations by Horoi et al. [Phys. Rev. C 75, 034303 (2007)], which yielded $0.054\left(0.064\right){\mathrm{MeV}}^{-1}$ for the GXPF1A (GXPF1) interactions, respectively. It is also in a reasonable agreement with the most recent experimental estimate from the review by Barabash, which is $0.068\left(6\right){\mathrm{MeV}}^{-1}$, assuming quenching $q{g}_{\text{A}}\approx 1$. The consistency of our prediction with the shell-model results increases our confidence in the nuclear modeling of this second-order, very rare process which is of paramount importance for further modeling of the neutrinoless double-beta ($0\nu \beta \beta$) decay process.

Mu2e and COMET will search for electrons produced via the neutrinoless conversion of stopped muons bound in 1s atomic orbits of ${}^{27}\mathrm{Al}$, improving existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. Conventionally, $\mu \to e$ conversion experiments are optimized to detect electrons originating from transitions where the nucleus remains in the ground state, thereby maximizing the energy of the outgoing electron. Clearly, detection of a positive signal in forthcoming experiments would stimulate additional work—including subsequent conversion experiments using complementary nuclear targets—to further constrain the new physics responsible for CLFV. Here we argue that additional information can be extracted without the need for additional experiments, by considering inelastic conversion in ${}^{27}\mathrm{Al}$. Transitions to low-lying nuclear excited states can modify the near-endpoint spectrum of conversion electrons, with the ratio of the elastic and inelastic responses being sensitive to the underlying CLFV operator. We extend the nuclear effective theory of $\mu \to e$ conversion to the inelastic case, which adds five new response functions to the six that arise for the elastic process. We evaluate these nuclear response functions in ${}^{27}\mathrm{Al}$ and calculate the resulting conversion-electron signal, taking into account the resolution anticipated in Mu2e/COMET. We find that ${}^{27}\mathrm{Al}$ is an excellent target choice from the perspective of the new information that can be obtained from inelastic $\mu \to e$ conversion.

We propose two novel constraints for the theoretical corrections to Gamow-Teller transition rates. The first, derived from a two-level model, predicts forbidden regions within the plane defined by the isospin-mixing correction ${\delta }_{C1}$ and the ratio $\eta$ of the isospin-symmetry Gamow-Teller matrix elements between the upper and lower admixed states. It serves as a filter for the theoretical calculations, particularly effective for small values of $\left|\eta \right|$. The other employs experimental $ft$ values, incorporating the upper admixed states, and exploits mirror symmetry to eliminate isospin-invariant and nuclear structure-independent quantities presented in the master decay formula. Within the standard model, this approach offers an alternative means for collectively testing the theoretical corrections for isospin and radiative effects beyond tree level. Additionally, it enables an experimental extraction of ${\eta }^2$, yielding a sensitive test for the isospin-conserving component of the nuclear Hamiltonian. Our investigation also reveals a substantial cancellation among radiative correction contributions in these tests, suggesting that these corrections are largely invariant under mirror symmetry. Importantly, the remarkable consistency of the nuclear structure corrections achieved in this axial-vector process provides a robust validation for the underlying theoretical approach in the purely vector process, especially the superallowed $0^{+}\to 0^{+}$ nuclear $\beta$ decay—the most accurate tool for extracting the $V_{ud}$ matrix element.

Radiative corrections are essential for an accurate determination of $V_{ud}$ from superallowed $\beta$ decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for $V_{ud}$. In this work, we provide a detailed account of the electroweak corrections to superallowed $\beta$ decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. We present a first numerical evaluation of the dominant corrections in light nuclei based on quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parametrize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in $V_{ud}$, as illustrated in detail for the ${}^{14}\mathrm{O}\to {}^{14}\mathrm{N}$ transition.

Observations of anomalies in the electron-positron angular correlations in high-energy decays in ${}^4\mathrm{He}, {}^8\mathrm{Be}$, and ${}^{12}\mathrm{C}$ have been reported recently by the ATOMKI collaboration. These could be explained by the creation and subsequent decay of a new boson with a mass of $\approx 17\mathrm{MeV}$. Theoretical understanding of pair creation in the proton capture reactions used in these experiments is important for the interpretation of the anomalies. We apply the ab initio no-core shell model with continuum (NCSMC) to the proton capture on ${}^7\mathrm{Li}$. The NCSMC describes both bound and unbound states in light nuclei in a unified way with chiral two- and three-nucleon interactions as the only input. We investigate the structure of ${}^8\mathrm{Be}$, the $p+{}^7\mathrm{Li}$ elastic scattering, the ${}^7\mathrm{Li}(p,\gamma ){}^8\mathrm{Be}$ cross section, and the internal pair creation ${}^7\mathrm{Li}(p,e^{+}{e}^{-}){}^8\mathrm{Be}$. We discuss the impact of a proper treatment of the initial scattering state on the electron-positron angular correlation spectrum and compare our results to available ATOMKI data sets. Finally, we calculate ${}^7\mathrm{Li}(p,X){}^8\mathrm{Be}$ cross sections for several proposed models of the hypothetical X17 particle.

Recent discussions about the origin of the so-called gallium anomaly have motivated a remeasurement of the half-life of ${}^{71}\mathrm{Ge}$. We have conducted three separate measurements using dedicated planar Ge detectors—one with ${}^{55}\mathrm{Fe}$ as a standard, one with ${}^{57}\mathrm{Co}$ as a standard, and one standalone ${}^{71}\mathrm{Ge}$ measurement. Our results yield a half-life of $11.468\pm 0.008$ days, which is consistent with, but significantly more precise than, the currently accepted value. With this experiment, the potential explanation of the gallium anomaly being due to an unexpectedly long ${}^{71}\mathrm{Ge}$ half-life has been ruled out, leaving the anomaly's origin as an open question.

We present a comprehensive reevaluation of the $ft$ values in superallowed nuclear $\beta$ decays crucial for the precise determination of $V_{ud}$ and low-energy tests of the electroweak standard model. It consists of the first, fully data-driven analysis of the nuclear $\beta$ decay form factor, that utilizes isospin relations to connect the nuclear charged weak distribution to the measurable charge distributions. This prescription supersedes previous shell-model estimations, and allows for a rigorous quantification of theory uncertainties in $f$ which is absent in the existing literature. Our new evaluation shows an overall downward shift of the central values of $f$ at the level of 0.01%.

Project 8 has developed a novel technique, cyclotron radiation emission spectroscopy (CRES), for direct neutrino mass measurements. A CRES-based experiment on the beta spectrum of tritium has been carried out in a small-volume apparatus. We provide a detailed account of the experiment, focusing on systematic effects and analysis techniques. In a Bayesian (frequentist) analysis, we measure the tritium endpoint as $18{553}_{-19}^{+18}$ ($18{548}_{-19}^{+19}$) eV and set upper limits of 155 (152) eV (90% C.L.) on the neutrino mass. No background events are observed beyond the endpoint in 82 days of running. We also demonstrate an energy resolution of $1.66\pm 0.19\mathrm{eV}$ in a resolution-optimized magnetic trap configuration by measuring ${}^{83\mathrm{m}}\mathrm{Kr}17.8$-keV internal-conversion electrons. These measurements establish CRES as a low-background, high-resolution technique with the potential to advance neutrino mass sensitivity.

In this paper, we re-examine one of the most promising candidates for determining the neutrino mass scale—the unique first forbidden $\beta$ transition from ${}^{187}\mathrm{Re}(5/2^{+}$) to ${}^{187}\mathrm{Os}(1/2^{-})$. With the lowest-known ground-state to ground-state $Q$ value for a $\beta$ transition at 2.4709 keV, rhenium's $\beta$ decay can offer insights into the neutrino mass scale puzzle. However, understanding its electron spectrum is a complex task. Besides involving a mixture of $s_{1/2}$-state and $p_{3/2}$-state electrons, the rhenium $\beta$ spectrum could be strongly influenced by various atomic corrections. In addition to our previous paper [R. Dvornický, K. Muto, F. Šimkovic, and A. Faessler, Phys. Rev. C 83, 045502 (2011)], we have incorporated finite nuclear size, diffuse nuclear surface, screening, and exchange corrections into the rhenium $\beta$ decay model. We have accounted for the last two effects within the framework of the Dirac-Hartree-Fock-Slater self-consistent method. We have discovered that both screening and exchange effects significantly alter the partial decay rates for the $s_{1/2}$- and $p_{3/2}$-state emission channels, while still maintaining the experimentally confirmed dominance of the $p_{3/2}$-state emission. The ratio between the respective decay rates has been found to be approximately ${10}^4$. When compared to the other corrections, the exchange effect stands out due to the modification it induces in the spectrum shape. We demonstrate that calculations with and without the exchange effect lead to entirely different shape factors for the decay spectrum. Finally, we illustrate that to preserve the linearity of the Kurie plot, it is essential to include the exchange correction in its definition. We conclude that atomic effects, especially the exchange effect, should be taken into account in current and future investigations of the neutrino mass scale from $\beta$ decays.

The summation method for the calculation of reactor ${\overline{\nu }}_e$ fluxes and spectra is methodically revised and improved. For the first time, a complete uncertainty budget accounting for all known effects likely to impact these calculations is proposed. Uncertainties of a few percent at low energies and ranging up to 20% at high energies are obtained on the calculation of a typical reactor ${\overline{\nu }}_e$ spectrum. Although huge improvements have been achieved over the past decade, the quality and incompleteness of the present day evaluated nuclear decay data still limit the accuracy of the calculations and therefore dominate by far these uncertainties. Pushing the $\beta$-decay modeling of the thousands of branches making a reactor ${\overline{\nu }}_e$ spectrum to a high level of details comparatively brings modest changes. In particular, including nuclear structure calculations in the evaluation of the nonunique forbidden transitions gives a smaller impact than anticipated in past studies. Finally, this new modeling is challenged against state-of-the-art predictions and measurements. While a good agreement is observed with the most recent inverse $\beta$ decay measurements of reactor ${\overline{\nu }}_e$ fluxes and spectra, it is unable to properly describe the reference aggregate $\beta$ spectra measured at the Institut Laue-Langevin High-Flux Reactor in the 1980s. This result adds to recent suspicions about the reliability of these data and preferentially points toward a misprediction of the ${}^{235}\mathrm{U}$ ${\overline{\nu }}_e$ spectrum.

In the recent Baksan Experiment on Sterile Transitions (BEST), a suppressed rate of neutrino absorption on a gallium target was observed, consistent with earlier results from neutrino source calibrations of the SAGE and GALLEX/GNO solar neutrino experiments. The BEST Collaboration, utilizing a 3.4 MCi ${}^{51}\mathrm{Cr}$ neutrino source, found observed-to-expected counting rates at two very short baselines of $R=0.791\pm 0.05$ and $0.766\pm 0.05$, respectively. Among recent neutrino experiments, BEST is notable for the simplicity of both its neutrino spectrum, line neutrinos from an electron-capture source whose intensity can be measured to a estimated precision of 0.23%, and its absorption cross section, where the precisely known rate of electron capture to the gallium ground state, ${}^{71}\mathrm{Ge}(e^{-},{\nu }_e){}^{71}\mathrm{Ga}\left(\text{g.s.}\right)$, establishes a minimum value. However, the absorption cross section uncertainty is a common systematic in the BEST, SAGE, and GALLEX/GNO neutrino source experiments. Here we update that cross section, considering a variety of electroweak corrections and the role of transitions to excited states, to establish both a central value and reasonable uncertainty, thereby enabling a more accurate assessment of the statistical significance of the gallium anomalies. Results are given for ${}^{51}\mathrm{Cr}$ and ${}^{37}\mathrm{Ar}$ sources. The revised neutrino capture rates are used in a reevaluation of the BEST and gallium anomalies.

We analyze the axial $\gamma W$-box diagram for $I\left(J^P\right)=1\left(0^{+}\right)$ nuclei and provide a dispersion representation of the nuclear-structure correction ${\delta }_{\text{NS}}$ including its energy-dependent part. We also summarize useful isospin rotation formula and representations in nuclear theory that could facilitate the calculation of the parity-odd nuclear structure function $F_3(\nu ,Q^2)$. They provide a rigorous theory framework for the future, high-precision calculation of the nuclear structure correction ${\delta }_{\text{NS}}$ necessary for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ud}|$ from superallowed nuclear $\beta$ decays.

We calculate the $\beta$ spectrum in the decay of ${}^6\mathrm{He}$ using quantum Monte Carlo methods with nuclear interactions derived from chiral effective field theory and consistent weak vector and axial currents. We work at second order in the multipole expansion, retaining terms suppressed by $\mathcal{O}(q^2/m_{\pi }^2)$, where $q$ denotes low-energy scales such as the reaction's $\mathcal{Q}$ value or the electron energy, and $m_{\pi }$ is the pion mass. We go beyond the impulse approximation by including the effects of two-body vector and axial currents. We estimate the theoretical error on the spectrum by using four potential models in the Norfolk family of local two- and three-nucleon interactions, which have different cutoffs, fit two-nucleon data up to different energies, and use different observables to determine the couplings in the three-body force. We find the theoretical uncertainty on the $\beta$ spectrum, normalized by the total rate, to be well below the permille level, and to receive contributions of comparable size from first- and second-order corrections in the multipole expansion. We consider corrections to the $\beta$ decay spectrum induced by beyond-standard-model charged-current interactions in the standard model effective field theory, with and without sterile neutrinos, and discuss the sensitivity of the next generation of experiments to these interactions.

The Baksan Experiment on Sterile Transitions (BEST) probes the gallium anomaly and its possible connections to oscillations between active and sterile neutrinos. Based on the Gallium-Germanium Neutrino Telescope (GGNT) technology of the SAGE experiment, BEST employs two zones of liquid Ga target to explore neutrino oscillations on the meter scale. Oscillations on this short scale could produce deficits in the ${}^{71}\mathrm{Ge}$ production rates within the two zones, as well as a possible rate difference between the zones. From July 5th to October 13th 2019, the two-zone target was exposed to a primarily monoenergetic, 3.4-MCi ${}^{51}\mathrm{Cr}$ neutrino source 10 times for a total of 20 independent ${}^{71}\mathrm{Ge}$ extractions from the two Ga targets. The ${}^{71}\mathrm{Ge}$ production rates from the neutrino source were measured from July 2019 to March 2020. At the end of these measurements, the counters were filled with ${}^{71}\mathrm{Ge}$ doped gas and calibrated during November 2020. In this paper, results from the BEST sterile neutrino oscillation experiment are presented in details. The ratio of the measured ${}^{71}\mathrm{Ge}$ production rates to the predicted rates for the inner and the outer target volumes are calculated from the known neutrino capture cross section. Comparable deficits in the measured ratios relative to predicted values are found for both zones, with the $4\sigma$ deviations from unity consistent with the previously reported gallium anomaly. If interpreted in the context of neutrino oscillations, the deficits give best-fit oscillation parameters of $\mathrm{\Delta }{m}^2=3.3_{-2.3}^{+\infty }{\mathrm{eV}}^2$ and ${\sin }^{2}2\theta =0.{42}_{-0.17}^{+0.15}$, consistent with ${\nu }_e\to {\nu }_s$ oscillations governed by a surprisingly large mixing angle.

We present high-precision theoretical predictions for the electron energy spectra for the ground-state to ground-state $\beta$ decays of ${}^{214}\mathrm{Pb}$, ${}^{212}\mathrm{Pb}$, and ${}^{85}\mathrm{Kr}$ most relevant to the background of liquid xenon dark matter detectors. The effects of nuclear structure on the spectral shapes are taken into account using large-scale shell-model calculations. Final spectra also include atomic screening and exchange effects. The impact of nuclear structure effects on the ${}^{214}\mathrm{Pb}$ and ${}^{212}\mathrm{Pb}$ spectra below $\approx 100$ keV, pertinent for several searches for new physics, are found to be comparatively larger than those from the atomic effects alone. We find that the full calculation for ${}^{214}\mathrm{Pb}$ (${}^{212}\mathrm{Pb}$) predicts 15.0%–23.2% (12.1%–19.0%) less event rate in a 1–15 keV energy region of interest compared to the spectrum calculated as an allowed transition when using values of the weak axial vector coupling in the range $g_{\mathrm{A}}=0.7$–1.0. The discrepancy highlights the importance of both a proper theoretical treatment and the need for direct measurements of these spectra for a thorough understanding of $\beta$ decay backgrounds in future experiments.