Scattering experiments with three free nucleons in the ingoing channel are extremely challenging in terrestrial laboratories. Recently, the ALICE Collaboration successfully measured the scattering of three protons indirectly, by using the femtoscopy method in high-energy proton-proton collisions at the Large Hadron Collider. In order to establish a connection with current and future measurements of femtoscopic three-particle correlation functions, we analyze the scenarios involving $nnn$ and $ppp$ systems using the hyperspherical adiabatic basis. The correlation function is a convolution of the source function and the corresponding scattering wave function. The finite size of the source allows for the use of the free scattering wave function in most of the adiabatic channels except the lowest ones. The scattering wave function has been computed using two different potential models: ($i$) a spin-dependent Gaussian potential with parameters fixed to reproduce the scattering length and effective range and ($ii$) the Argonne $v_{18}$ nucleon-nucleon interaction. Moreover, in the case of three protons, the Coulomb interaction has been considered in its hypercentral form. The results presented here have to be considered as a first step in the description of three-particle correlation functions using the hyperspherical adiabatic basis, opening the door to the investigation of other systems, such as the $pp\mathrm{\Lambda }$ system. For completeness, the comparison with the measurement by the ALICE Collaboration is shown assuming different values of the source radius.

The astrophysical origin for the chemical elements between the first and second $r$-process peaks is a matter of intense debate, with a number of nucleosynthesis processes at explosive stellar environments possibly contributing to their production. Reliable data on the trends of neutron separation energies of neutron-rich isotopes are required to model neutron-capture processes that would produce these elements. Masses of ${}^{104}\mathrm{Y}$, ${}^{106}\mathrm{Zr}$, ${}^{112}\mathrm{Mo}$, and ${}^{115}\mathrm{Tc}$ have been measured with the time-of-flight-magnetic-rigidity $\left(\mathrm{ToF}\text{−}B\rho \right)$ technique at the National Superconducting Cyclotron Laboratory at Michigan State University. The experiment is the first application of the $\mathrm{ToF}\text{−}B\rho$ technique at the S800 spectrograph that reached the mass region relevant to heavy-element nucleosynthesis. The two-neutron separation energy deduced from the measured masses exhibits a smooth trend consistent with the theoretical predictions within the range of experimental uncertainty, indicating that there is no sudden shape transition in these isotopes as hinted at by previous data.

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.

We perform a first-principles calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with ab initio self-consistent Green's function theory with a nucleon-nucleon $t$ matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off calcium and nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65–200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the calcium and nickel isotopic chains.

Deciphering the conditions under which neutron captures occur in the Universe to synthesize heavy elements is an endeavor pursued since the 1950s, but has proved elusive up to now due to the experimental difficulty of generating the extreme neutron fluxes required. It has been evoked that laser-driven (pulsed) neutron sources could produce neutron beams with characteristics suitable to achieve nucleosynthesis in the laboratory. In this scheme, the laser first generates an ultra-high-current, high-energy proton beam, which is subsequently converted into a dense neutron beam. Here we model, in a self-consistent manner, the transport of laser-accelerated protons through the neutron converter, the subsequent neutron generation and propagation, and finally the neutron capture reactions in gold (${}^{197}\mathrm{Au}$), chosen as an illustrative example. Using the parameters of present-day available lasers, as well as of those foreseeable in the near future, we find that the final yield of the isotopes containing two more neutrons than the seed nuclei is negligible. Our investigation highlights that the areal density of the laser-driven neutron source is a critical quantity and that it would have to be increased by several orders of magnitude over the current state of the art in order to offer realistic prospects for laser-based generation of neutron-rich isotopes.

The development of emulators for the evaluation of many-body observables has gained increasing attention over the last years. In particular the framework of eigenvector continuation (EC) has been identified as a powerful tool when the Hamiltonian admits for a parametric dependence. By training the emulator on a set of training data the many-body solution for arbitrary parameter values can be robustly predicted in many cases. Furthermore, it can be used to resum perturbative expansions that otherwise diverge. In this work, we apply EC to the pairing Hamiltonian and show that EC-resummed perturbation theory is in qualitative agreement with the exact solution and that EC-based emulators robustly predict the ground-state energy once the training data are chosen appropriately. In particular the phase transition from the normal to the superfluid regime is quantitatively predicted using a very low number of training points.

The microscopic framework of time-dependent covariant density functional theory is applied to a systematic study of ternary quasifission in collisions of pairs of ${}^{238}\mathrm{U}$ nuclei. It is shown that the inclusion of octupole degree of freedom in the case of head-to-head collisions extends the energy window in which ternary quasifission occurs, and greatly enhances the number of nucleons contained in a middle fragment. Dynamical pairing correlations, included here in the time-dependent Bardeen-Cooper-Schrieffer approximation, prevent the occurrence of ternary quasifission in head-to-head collisions, and have an effect on the location of the energy window in which a middle fragment is formed in tail-to-tail collisions. In the latter case, as well as for tail-to-side collisions, the formation of very heavy neutron-rich systems in certain energy intervals is predicted.

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.

Background: The triple-alpha process is a vital reaction in nuclear astrophysics, characterized by two consecutive reactions [$2\alpha \leftrightarrows {}^8\mathrm{Be}(\alpha ,\gamma ){}^{12}\mathrm{C}$] that drive carbon formation. The second reaction occurs through the Hoyle state, a 7.65 MeV excited state in ${}^{12}\mathrm{C}$ with $J^{\pi }=0^{+}$. The rate of the process depends on the radiative width, which can be determined by measuring the branching ratio for electromagnetic decay. Recent measurements by Kibédi et al. conflicted with the adopted value and resulted in a significant increase of nearly 50% in this branching ratio, directly affecting the triple-alpha reaction.

Purpose: This work aims to utilize charged-particle spectroscopy with magnetic selection as a means to accurately measure the total radiative branching ratio (${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }$) of the Hoyle state in ${}^{12}\mathrm{C}$.

Methods: The Hoyle state in ${}^{12}\mathrm{C}$ was populated via ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime }){}^{12}{\mathrm{C}}^{*}$ inelastic scattering. The scattered $\alpha$-particles were detected using a $\mathrm{\Delta }E-E$ telescope, while the recoiled ${}^{12}\mathrm{C}$ ions were identified in a magnetic spectrometer.

Results: A radiative branching ratio value of ${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }\times {10}^4=4.0\pm 0.3\left(\mathrm{stat}.\right)\pm 0.16\left(\mathrm{syst}.\right)$ was obtained.

Conclusions: The radiative branching ratio for the Hoyle state obtained in this work is in agreement with the original adopted value. Our result suggests that the proton-$\gamma -\gamma$ spectroscopy result reported by Kibédi et al. may be excluded.

Interference terms between monopole and quadrupole Coulomb form factors that contribute to the cross section of electron scattering from polarized nuclei are studied within the plane wave Born approximation. By experimentally exploring the effect of this nuclear response, valuable insights into the sign of the quadrupole deformation can be obtained. The nuclear structure is evaluated numerically using a self-consistent deformed Hartree-Fock approximation with Skyrme effective interactions and accounting for pairing correlations. To illustrate the practical applicability, several examples of odd-$A$ nuclei with different spins and deformations are examined. Comparison of unpolarized and polarized cross sections becomes a tool to discriminate between the oblate and prolate nature of the nuclear shape, providing a deeper understanding of the nuclear deformation.

High-energy heavy-ion collisions have been suggested as a favorable environment for the production of $B_c$ mesons, due to a much larger abundance of charm and bottom quarks compared to elementary reactions. Motivated by recent CMS data for $B_c^{+}$ production in Pb-Pb(5.02 TeV) collisions at the Large Hadron Collider (LHC), we deploy a previously developed transport approach for charmonia and bottomonia to evaluate the kinetics of $B_c$ mesons throughout the fireball formed in these reactions. The main inputs to our approach are two transport parameters: the $B_c$'s reaction rate and equilibrium limit. Both quantities are determined by previous calculations via a combination of charm and bottom sectors. In-medium binding energies of $B_c$ mesons are calculated from a thermodynamic $T$ matrix with a lattice-QCD constrained potential, and figure in their inelastic reaction rates. Temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. We compute the centrality dependence of inclusive $B_c$ production and transverse-momentum $\left(p_T\right)$ spectra using two different recombination models: instantaneous coalescence and resonance recombination. The main uncertainty in the resulting nuclear modification factors, $R_{\mathrm{AA}}$, is currently associated with the $B_c$ cross section in elementary $pp$ collisions, caused by the uncertainty in the branching ratio for the $B_c^{-}\to J/\psi {\mu }^{-}\overline{\nu }$ decay. Our results indicate a large enhancement of the $R_{\mathrm{AA}}$ at low $p_T$, with significant regeneration contributions up to $p_T\simeq 20\mathrm{GeV}$. Comparisons to CMS data are carried out but firm conclusions will require a more accurate value of the branching ratio, or alternative channels to measure the $B_c$ production in $pp$ collisions.

Nuclear energy density functionals successfully reproduce properties of nuclei across almost the entire nuclear chart. However, nearly all available functionals are phenomenological in nature and lack a rigorous connection to systematically improvable nuclear forces. This issue might be solved with an energy density functional obtained from first principles. As an intermediate step towards this goal we construct the GUDE family of functionals that is obtained from a hybrid scheme consisting of long-range pion-exchange contributions derived from chiral effective field theory at the Hartree-Fock level and a phenomenological Skyrme part. When including pion contributions beyond next-to-leading order in the chiral expansion, we find significant improvements over a reference Skyrme functional constructed following the same protocol. We analyze the importance of different pion contributions and identify which terms drive the observed improvements. Since pions are incorporated without adding further optimization parameters to the functionals, the improvements can be attributed to the functional form of these terms. Our work therefore suggests that the considered chiral contributions constitute useful ingredients for true ab initio energy density functionals.

We present a detailed study of the contribution from two-body currents to the one-nucleon knockout process induced by electromagnetic interaction. The framework is a relativistic mean-field model in which bound and scattering nucleons are consistently described as solutions of Dirac equation with potentials. We show results obtained with the most general expression of the two-body operator, in which the intermediate nucleons are described by relativistic mean-field bound states; then, we propose two approximations consisting in describing the intermediate states as nucleons in a relativistic Fermi gas, preserving the complexity and consistency in the initial and final states. These approximations simplify the calculations considerably, allowing us to provide outcomes in a reasonable computational time. The results obtained under these approximations are validated by comparing with those from the full model. Additionally, the theoretical predictions are compared with experimental data of the longitudinal and transverse responses of carbon 12. The agreement with data is outstanding for the longitudinal response, where the contribution from the two-body operator is negligible. In the transverse sector, the two-body current increases the response from 30 to 15 %, depending on the approximations and kinematics, in general, improving the agreement with data.

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.

High-energy backward $\left(u\text{−}\text{channel}\right)$ reactions can involve very large momentum transfers to the target baryons, shifting them by many units of rapidity. These reactions are difficult to understand in conventional models in which baryon number is carried by the valence quarks. Backward Compton scattering is an especially attractive experimental target, because of its simple final state. There is currently limited data on this process, and those data are at low center-of-mass energies. In this paper, we examine the prospects for studying backward Compton scattering at the future Electron Ion Collider (EIC). We model the cross section and kinematics using the limited data on backward Compton scattering and backward meson production, and then simulate Compton scattering at EIC energies in a simple model of the ePIC detector. Generally, the proton is scattered toward midrapidity, while the produced photon is in the far-forward region, visible in a Zero Degree Calorimeter (ZDC). We show that the background from backward ${\pi }^0$ production can be rejected using a high-resolution, well-segmented ZDC.

We employ a microscopic approach that examines the impact of isospin dynamics on the process of low-energy nuclear fusion along an isotope chain and dependence on deformation. Our method utilizes the density constrained time-dependent Hartree-Fock theory (DC-TDHF), where isoscalar and isovector characteristics of the energy density functional (EDF) are examined in turn. This approach is applied to a series of fusion interactions of ${}^{176}\mathrm{Yb}$ with increasingly neutron rich isotopes of calcium. By evaluating the contributions from the isoscalar and isovector components of the EDF, we look to quantify the influence of isospin composition on the conditions under which fusion is most likely to take place. Our findings reveal that, in nonsymmetric systems, the isovector dynamics plays a significant role. Its typical effect is a reduction in the potential barrier, which turns into enhancement for neutron-rich systems.

The fragmentation of a projectile into a number of pieces can lead to the creation of many resonances in different nuclei. We discuss application of the invariant-mass method to the products from such reactions to find some of the most exotic resonances located furthest beyond the proton drip line. We show examples from fragmentation of a fast ${}^{13}\mathrm{O}$ beam including the production of the newly identified ${}^9\mathrm{N}$ resonance. In extracting resonance parameters from invariant-mass spectra, accurate estimates of the background from nonresonant prompt protons are needed. These prompt protons are correlated with the resonances due to long-range Coulomb interactions and will suppress events when resonance decay products and the prompt protons have small invariant masses. The shape of this background is especially important in determining the widths of wide resonances typically found at the edge of the chart of nuclides. An event-mixing recipe is proposed to describe this background, where the mixed events have reduced weighting for the smaller invariant masses to account for the effect of the Coulomb final-state interactions. The weighting is based on the measured correlations of heavier hydrogen isotopes with the resonances or the projectile residues. We also show that the relative magnitude of the background can be reduced in some cases by selecting events where the resonance decay products are accompanied by a deuteron or triton cluster. The deuteron and triton clusters are largely not products of resonant decay and thus events with an accompanying cluster are associated with fewer background protons than events without them. The width of the $5/2^{-}$ state in ${}^9\mathrm{C}$ with the new background prescription was found to be consistent with the value obtained using proton elastic scattering on ${}^8\mathrm{B}$. Improved values for the widths of ${}^{10}\mathrm{C}, {}^{10,11}\mathrm{N}$, and ${}^{12}\mathrm{O}$ resonances were also obtained using the new background prescription.

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.

Hexadecapole collectivity and its interplay with quadrupole degrees of freedom is studied in an axial symmetry preserving framework based on the Hartree-Fock-Bogoliubov plus generator coordinate method. Results are obtained for several even-even isotopes of Sm and Gd with various parametrizations of the Gogny force. The analysis of the results indicates the strong coupling between the quadrupole and hexadecapole degrees of freedom. The first two excited states are vibrational in character in most of the cases. The impact of prolate-oblate shape mixing in the properties of hexadecapole states is analyzed.

Over the past decade, machine learning has been successfully applied in various fields of science. In this study, we employ a deep learning method to analyze a Skyrme energy density functional (Skyrme-EDF), which is a Kohn-Sham type functional commonly used in nuclear physics. Our goal is to construct an orbital-free functional that reproduces the results of the Skyrme-EDF. To this end, we first compute energies and densities of a nucleus with the Skyrme Kohn-Sham $+$ Bardeen-Cooper-Schrieffer method by introducing a set of external fields. Those are then used as training data for deep learning to construct a functional which depends only on the density distribution. Applying this scheme to the ${}^{24}\mathrm{Mg}$ nucleus with two distinct random external fields, we successfully obtain a new functional which reproduces the binding energy of the original Skyrme-EDF with an accuracy of about 0.04 MeV. The rate at which the neural network outputs the energy for a given density is about ${10}^5–{10}^6$ times faster than the Kohn-Sham scheme, demonstrating a promising potential for applications to heavy and superheavy nuclei, including the dynamics of fission.