In a recent Letter [Phys. Rev. Lett. 130, 052501 (2023)], we suggested the quasi-SU(3) coupling across the $N=50$ and 82 shell gaps as the main source driving shape evolution and phase transitions. The present article extends the discussion in the Letter. We demonstrate that by varying the coupling strengths of the quasi-SU(3) partner orbits, $(1g_{9/2},$ $2d_{5/2})$ for protons and $(1h_{11/2}$, $2f_{7/2})$ for neutrons, we can well reproduce the features of the IBM U(5), O(6), SU(3), and $\overline{\mathrm{SU}\left(3\right)}$ symmetries and the Iachello E(5), X(5), and $\overline{\mathrm{X}\left(5\right)}$ with critical behavior. Therefore, all known dynamical and critical-point symmetries are realized in our shell-model parameter space. Moreover, in the phase diagram of the parameter space, we find that the line connecting U(5), E(5), and O(6) is characterized by the vanishing spectroscopic quadrupole moment of the first $2^{+}$ state [i.e., $Q_s\left(2_1^{+}\right)=0]$. It gives a new physical meaning to the central axis of the extended Casten triangle and implies that any shape evolution passing through this line can be naturally considered as a prolate-oblate shape phase transition. Thus, we have found microscopic origins for all symmetries originally suggested by algebraic or geometric models. By visualizing the shape using the constrained Hartree-Fock-Bogolyubov (HFB) method based on our shell-model results, we conclude that ${}^{134}\mathrm{Ba}$ is likely the softest nucleus in the nuclear chart, having no definite shape at all in its ground state.

Modern nuclear theory provides qualitative insights into the fundamental mechanisms of nuclear fission and is increasingly capable of making reliable quantitative predictions. Most quantities of interest pertain to the primary fission fragments, whose subsequent decay is typically modeled using statistical reaction models. Consequently, a key objective of fission theory is to inform these models by predicting the initial conditions of the primary fragments. In this work, we employ a framework that combines joint angular momentum and particle number projection with time-dependent configuration mixing to calculate the angular momentum distributions of primary fragments. Focusing on the benchmark cases of neutron-induced fission of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$, we predict—for the first time—microscopic angular momentum distributions for all fragments observed in experiments. Our results reveal a pronounced sawtooth pattern in the average angular momentum as a function of fragment mass, consistent with recent measurements. Additionally, we observe substantial variations in angular momentum distributions along isobaric chains, indicating that commonly used empirical formulas lack sufficient accuracy. We also quantify a strong correlation between the angular momentum and the deformation of the fragments at scission, and a weak correlation in the magnitude of the angular momentum between fragment partners. The generated data will enable estimation of the impact of microscopic distributions on fission spectra, paving the way toward fission modeling based on microscopic inputs.

This Letter deals with the so-called nuclear polarization correction to the 1S levels in light to intermediate muonic atoms. An easy to use recipe to compute it is given. The calculation includes the effect of the nucleon polarization, i.e. the contribution from inelastic states in the hadronic range, and Coulomb corrections beyond the leading-logarithm approximation to both nuclear and nucleon polarization.

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.

In this paper we present our results on the decay of ${}^{64}\mathrm{Se}$. It is the heaviest $T_z=-2$ nucleus that both $\beta$ decays and has a stable mirror partner ($T_z=+2$), thus allowing comparison with charge exchange reaction studies. The $\beta$ decays of ${}^{64}\mathrm{Se}$ and its descendants were studied at the RIKEN Nishina Center (Japan) following their production in the fragmentation of ${}^{78}\mathrm{Kr}$ on a beryllium target. $\beta$-Delayed $\gamma$-ray and particle radiation was identified for each of the nuclei in the decay chain allowing us to obtain decay schemes for ${}^{64}\mathrm{Se}$, ${}^{64}\mathrm{As}$, and ${}^{63}\mathrm{Ge}$. Thus new excited states could be found for the descendant nuclei, including the interesting case of the $N=Z$ nucleus ${}^{64}\mathrm{Ge}$. Furthermore, we observed for the first time the $\beta$-delayed proton emission of ${}^{64}\mathrm{Se}$ and ${}^{64}\mathrm{As}$. Based on these results we obtained proton branching ratios of $48.0\left(9\right)\%$ in ${}^{64}\mathrm{Se}$ decay and $4.4\left(1\right)\%$ in ${}^{64}\mathrm{As}$ decay. We obtained a half-life value of $22.5\left(6\right)\mathrm{ms}$ for ${}^{64}\mathrm{Se}$ decay and half-lives slightly more precise than those in the literature for each nucleus involved in the decay chain. Using our results on the excited levels of ${}^{64}\mathrm{As}$ and the mass excess in the literature for ${}^{63}\mathrm{Ge}$ we obtained $-39588\left(50\right)\mathrm{keV}$ for the mass excess of ${}^{64}\mathrm{As}$. Then based on the isobaric mass multiplet equation we obtained the mass excess of $-27429\left(88\right)\mathrm{keV}$ for ${}^{64}\mathrm{Se}$ by extrapolation. The mirror process of ${}^{64}\mathrm{Se}\beta$ decay, the charge exchange reaction ${}^{64}\mathrm{Zn}{({}^3\mathrm{He},t)}^{64}\mathrm{Ga}$, has already been measured allowing us to study the mirror symmetry through the comparison of the weak force ($\beta$a decay) and strong force (charge exchange reaction). An interpretation of the decay schemes based on the idea of the antisnalogue tate is proposed.

Optical potentials are a standard tool in the study of nuclear reactions, as they describe the interaction between a target nucleus and a projectile. The use of phenomenological optical potentials built using experimental data on stable isotopes is widespread. Although successful in their dedicated domain, it is unclear whether these phenomenological potentials can provide reliable predictions for unstable isotopes. To address this problem, optical potentials based on microscopic nuclear structure input calculations prove to be crucial and are an important current line of research. In this work we present an explicit implementation of the Feshbach formalism for the systematic derivation of optical potentials using input from nuclear structure models. Numerical tools for the derivation of Green's functions associated with nonlocal potentials are presented. The new optical potential, based on the valence shell model, is applied to the calculations of $n+{}^{24}\mathrm{Mg}$ elastic scattering and yields a close agreement with the experimental data.

We develop a calculation method for describing the direct and pre-equilibrium processes in neutron-induced reactions based on the framework of noniterative finite amplitude method (FAM) and distorted-wave Born approximation (DWBA). The noniterative FAM is used to derive equations of quasiparticle random-phase approximation for neutron-induced inelastic scatterings to both the discrete and continuum states in a consistent manner. The Skyrme force is employed as an interaction between the projectile neutron with nucleons inside the target nucleus. We apply this method to the neutron-induced reaction on ${}^{208}\mathrm{Pb}$. We demonstrate that the calculated differential inelastic scattering cross-sections to low-lying states reproduce available experimental data without any phenomenological parameters that are often introduced in conventional DWBA calculations. The calculated double differential cross-section to the continuum state also agrees with the experimental data in the energy region relevant to the direct and pre-equilibrium processes. These results are used to investigate the spin distribution of the populated states in the residual nucleus.

We present a method to calculate neutron scattering cross sections for deformed nuclei using many-body wave functions described with multiple reference states. Nuclear states are calculated with the generator coordinate method using a low energy effective Hamiltonian. Using these states, a nonlocal and energy dependent optical potential is consistently constructed, allowing one to directly investigate the role of nuclear structure properties in nuclear scattering. The case of neutron scattering on ${}^{24}\mathrm{Mg}$ is presented. The results are compared to experiment and to phenomenological optical potentials at energies below 13 MeV, demonstrating the importance of low-energy collectivity in elastic and nonelastic scattering.

Background: The use of theranostic isotope pairs is an emerging field in contemporary medicine, yet their clinical availability is often constrained by production and supply chain challenges. Among them, ${}^{67}\mathrm{Cu}$ has gained significant interest as the therapeutic counterpart in the ${}^{67}\mathrm{Cu}\text{/}{}^{64}\mathrm{Cu}$ theranostic pair. Traditional production methods rely on reactor-based or charged-particle accelerator routes, both of which face limitations in scalability and isotopic purity.

Purpose: This work investigates the photonuclear production of ${}^{67}\mathrm{Cu}$ via the ${}^{68}\mathrm{Zn}(\gamma ,p){}^{67}\mathrm{Cu}$ reaction, using high-energy bremsstrahlung photons from an electron accelerator. In addition to quantifying production yields and radionuclidic purity, the work provides spectrum-weighted average cross sections for multiple emission channels, serving as a test of reaction modeling under broad excitation conditions. The results inform both the optimization of ${}^{67}\mathrm{Cu}$ production for theranostic applications and the improvement of nuclear reaction theory in an underexplored energy regime.

Method: Natural zinc targets were irradiated using bremsstrahlung photons from an 855 MeV electron beam at the Mainzer Mikrotron (MAMI). The photon energy spectrum was measured via tagging and extended beyond the tagged range using Geant4 simulations. Reaction products were identified via gamma-ray spectroscopy, and spectrum-weighted average cross sections were derived. Theoretical cross sections were calculated using talys, incorporating giant dipole resonance and quasideuteron components of the photon absorption cross section. A model sensitivity analysis was performed to assess the influence of level density and photon strength function variations on the predicted cross sections.

Results: A production yield of 0.410(16) MBq $\mu {\mathrm{A}}^{-1}{\mathrm{h}}^{-1}{\mathrm{g}}^{-1}$ was measured for ${}^{67}\mathrm{Cu}$, with corresponding average cross sections determined from the bremsstrahlung spectrum. Yields and average cross sections were also measured for coproduced isotopes including ${}^{64}\mathrm{Cu}, {}^{61}\mathrm{Cu}, {}^{60}\mathrm{Cu}, {}^{69m}\mathrm{Zn}, {}^{65}\mathrm{Zn}, {}^{63}\mathrm{Zn}$, and ${}^{62}\mathrm{Zn}$. The relatively low production of nontarget isotopes indicates that the ${}^{68}\mathrm{Zn}(\gamma ,p){}^{67}\mathrm{Cu}$ reaction proceeds with favorable radionuclidic selectivity under the applied irradiation conditions. talys calculations showed good agreement with the ($\gamma ,p$) channel, but neutron-emission and multi-particle channels were systematically overestimated. Model sensitivity points to assumptions in the photon strength function and level density, as well as the absence of explicit pion-resonance dynamics at high energies, as likely contributors to this behavior.

Conclusions: Photonuclear reactions provide a promising approach for high-purity ${}^{67}\mathrm{Cu}$ production. Theoretical discrepancies highlight limitations in current reaction models, especially for ($\gamma ,\mathit{xn}$) channels at high energy. Beyond this, the scalability of electron-driven methods, enabled by existing high-current infrastructure and compact low-energy linacs, offers flexibility for both centralized and decentralized isotope production. Continued development of accelerator technologies and nuclear models will be essential for expanding access to photonuclear-produced medical isotopes.

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.

We develop a framework that allows us to calculate integrated properties of the nuclear response from first principles. Using the ab initio in-medium similarity renormalization group (IMSRG), we calculate the expectation values of moment operators that are linked to the multipole response of nuclei. This approach is applied to the isoscalar mono- and quadrupole as well as the isovector dipole response of closed-shell nuclei from ${}^4\mathrm{He}$ to ${}^{78}\mathrm{Ni}$ for different chiral two- and three-nucleon interactions. We find that the inclusion of many-body correlations in the nuclear ground state significantly impacts the multipole response when going from the random-phase approximation to the IMSRG level. Our IMSRG calculations lead to an improved description of experimental data in ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$, including a good reproduction of the Thomas-Reiche-Kuhn enhancement factor. These findings highlight the utility of the moment method as a benchmark for other ab initio approaches that describe nuclear response functions through the explicit treatment of excited states.

Converged results for $E2$ observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the $E2$ operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated $E2$ and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form $Q/r^2$ for nuclei throughout the $p$ shell. Meaningful predictions for electric quadrupole moments may then be made by calibrating to the ground-state charge radius, if experimentally known, or vice versa. Moreover, these dimensionless ratios provide ab initio insight into the nuclear quadrupole deformation.

Converged results for $E2$ observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the $E2$ operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated $E2$ and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form $B\left(E2\right)/\left(e^2{r}^4\right)$ for nuclei throughout the $p$ shell. Meaningful predictions for $E2$ transition strengths may then be made by calibrating to the ground-state charge radius if experimentally known.

A benchmark study is performed for the excited state of ${}^4\mathrm{He}$. When the Coulomb interaction is switched off, the ${}^4\mathrm{He}$ nucleus exhibits a bound excited state in the vicinity of the $p-{}^3\mathrm{H}$ threshold. As the Coulomb interaction is gradually introduced, the excited state crosses the threshold and eventually becomes a resonant state. Using three numerical methods, we track the evolution of this excited state and determine the resonance energy and width. Comparisons of the theoretical predictions reveal a significant discrepancy with commonly used $R$-matrix values based on the analysis of the experimental data. We explain the origin for this discrepancy. Additionally, the two-level energy spectrum of ${}^4\mathrm{He}$ in the absence of the Coulomb force exhibits characteristics linked to Efimov physics, suggesting a reduced sensitivity to interaction details.

Three new behaviors have been found in comparisons of fusion cross sections for different collision systems. (1) Replacing the energy $E$ with a scaling one, $E_{\mathrm{scal}}=(E-V_g)/\left(\sqrt{2}{W}_g\right)$, is successful for washing out the Coulomb interaction in the spectra of fusion cross sections, where $V_g$ and $W_g$ are barrier height and width of the single-Gaussian barrier distribution model. (2) In a representation of $\sigma E$ vs the scaling energy, $E_{\mathrm{scal}}$, all data sets display in parallel. The ratio for $\sigma E$ from any two fusion systems over the whole range is a constant value. That behavior is also studied in another representation, in which the data sets display as parallel horizontal lines for any heavy-ion fusion system. (3) The constant ratio value is the ratio of parameter products, $R_g^2{W}_g$, of the two systems; where $R_g$ is the barrier radius obtained in the single-Gaussian barrier distribution model. Moreover, when comparing neighboring collision systems at the same $E_{\mathrm{scal}}$, the ratio of $\sigma$ is near a constant value within a few percent over the whole range. Thus a quantitative comparison for the fusion enhancement for neighboring systems is developed. The present finding could be beneficial for predicting unmeasured fusion cross sections.

Techniques from artificial intelligence and machine learning are increasingly employed in nuclear theory; however, the uncertainties that arise from the complex parameter manifold encoded by the neural networks are often overlooked. Epistemic uncertainties arising from training the same network multiple times for an ensemble of initial weight sets offer a first insight into the confidence of machine learning predictions, but they often come with a high computational cost. Instead, we apply a single-model uncertainty quantification method called $\mathrm{\Delta }$-UQ that gives epistemic uncertainties with one-time training. We demonstrate our approach on a two-feature model of nuclear binding energies per nucleon with proton and neutron number pairs as inputs. We show that $\mathrm{\Delta }$-UQ can produce reliable and self-consistent epistemic uncertainty estimates and can be used to assess the degree of confidence in predictions made with deep neural networks.

The $\alpha$-decay spectroscopy of ${}^{247}\mathrm{Md}$ was investigated via the fusion-evaporation reaction ${}^{209}\mathrm{Bi}({}^{40}\mathrm{Ar},2n){}^{247}\mathrm{Md}$ by means of $\alpha$-, $\gamma$-, and electron-coincidence measurements. While measuring the previously known $\alpha$-decay properties, a new isomeric state in ${}^{243}\mathrm{Es}$, the daughter nucleus of ${}^{247}\mathrm{Md}$, with a half-life of $5.0\left(5\right)\mu \mathrm{s}$ was observed. Based on the suggested decay scheme of ${}^{247}\mathrm{Md}$, the new isomer in ${}^{243}\mathrm{Es}$ was assigned as the $7/2^{+}\left[633\right]$ Nilsson level, which is the first observation of an isomer in $Z=99$ Es isotopes. The single-particle structure around the $Z=100$ deformed shell gap was discussed.

This paper reports on the measurement of the ground-state spin and nuclear magnetic dipole moment of ${}^{61}\mathrm{Cr}$. The radioactive ion beam was produced at the CERN-ISOLDE facility and was probed using high-resolution resonance ionization laser spectroscopy with the collinear resonance ionization spectroscopy (CRIS) apparatus. The present ground-state spin measurement $I=\frac{1}{2}$, differing from the previously adopted $I=\left(\frac{5}{2}\right)$, has significant consequences on the interpretation of existing beta decay data and nuclear structure in the region. The structure and shape of ${}^{61}\mathrm{Cr}$ is interpreted with state-of-the-art Large-Scale Shell-Model and Discrete NonOrthogonal Shell-Model calculations. From the measured magnetic dipole moment $\mu {(}^{61}\mathrm{Cr})=+0.541\left(6\right){\mu }_N$ and the theoretical findings, its configuration is understood to be driven by two-particle–two-hole neutron excitations with an unpaired $1p_{1/2}$ neutron. This establishes the western border of the $N=40$ island of inversion, characterized by four-particle–four-hole neutron components. We discuss the shape evolution along the Cr isotopic chain as a second-order quantum phase transition at the entrance of the $N=40$ island of inversion.

Background: Electron-capture reactions on iron-group nuclei play a crucial role in the late stages of massive star evolution. Since stellar evolution simulations depend on accurate electron-capture rates—which are highly sensitive to the detailed Gamow-Teller (GT) strength distributions—reliable theoretical models are essential. However, experimental data on GT strength distributions are scarce. High-resolution measurements are therefore vital for benchmarking and improving these theoretical calculations.

Purpose: To provide high-resolution data on Gamow-Teller strength distributions of iron-group nuclei and to compare these results with theoretical calculations within this mass region.

Methods: Differential cross sections for the ${}^{59}\mathrm{Co}(t,{}^3\mathrm{He}){}^{59}\mathrm{Fe}$ charge-exchange reaction at 115 MeV/u were measured using the S800 spectrometer. To resolve individual levels that are not distinguishable in the S800 particle singles data, coincident $\gamma$ rays from the ${}^{59}\mathrm{Fe}$ residual nucleus were detected by using the Gamma-Ray Energy Tracking In-beam Nuclear Array $\gamma$-ray tracking array.

Results: The Gamow-Teller transition strength distribution from the ground state of ${}^{59}\mathrm{Co}$ to ${}^{59}\mathrm{Fe}$ was extracted up to an excitation energy of 10 MeV. Additionally, transition strengths for several low-lying states were determined from coincident $\gamma$-ray measurements. Electron-capture rates calculated using the present data indicate that these low-lying states contribute significantly to the overall rates in relevant stellar environments. The experimental results show reasonable agreement with theoretical predictions based on both shell-model and projected shell-model calculations.

Conclusions: High-resolution data on Gamow-Teller strength distributions—particularly for individual low-lying states—are essential for accurately determining electron-capture rates in iron-group nuclei. Coincident $\gamma$-ray measurements provide a powerful tool for obtaining such detailed information. While the present work demonstrates that shell-model calculations successfully reproduce the experimental results, such comparisons are scarce and more experimental data are desirable.

The reaction ${}^{14}\mathrm{N}(n,p){}^{14}\mathrm{C}$ is one of the main neutron poisons during $s$-process nucleosynthesis. In addition, the reaction provides insight into the yields of atmospheric nuclear weapon testing. Because of their high level of sensitivity, total neutron cross sections provide a great deal of constraint on the modeling of reaction cross sections through the $R$-matrix analyses used for nuclear data evaluations. Yet for ${}^{14}\mathrm{N}+n$ only one high sensitivity measurement is available, and it lacks detailed information about its experimental conditions and uncertainties. With these motivations in mind, a new measurement of the ${}^{14}\mathrm{N}+n$ total cross section was performed at the nELBE facility. The cross sections were found to be in good agreement with previous data over much of the energy range, with the key exception of the lowest energy resonance at a neutron energy of 433 keV.