The number of low-energy constants (LECs) in chiral effective field theory ($\chi \mathrm{EFT}$) grows rapidly with increasing chiral order, necessitating the use of Markov chain Monte Carlo techniques for sampling their posterior probability density function. For this we introduce a Hamiltonian Monte Carlo (HMC) algorithm and sample the LEC posterior up to next-to-next-to-leading order (NNLO) in the two-nucleon sector of $\chi \mathrm{EFT}$. We find that the sampling efficiency of HMC is three to six times higher compared to an affine-invariant sampling algorithm. We analyze the empirical coverage probability and validate that the NNLO model yields predictions for two-nucleon scattering data with largely reliable credible intervals, provided that one ignores the leading-order EFT expansion parameter when inferring the variance of the truncation error. We also find that the NNLO truncation error dominates the error budget.

We apply the charge-exchange subtracted second random-phase approximation (SSRPA), based on Skyrme functionals, to investigate Gamow-Teller resonances in several closed-shell and closed-subshell nuclei, located in different regions of the nuclear chart. After having discussed the SSRPA findings obtained within different approximation schemes in ${}^{48}\mathrm{Ca}$, we compare our results with ab initio coupled-cluster predictions available for C and O isotopes, where two-body currents are included. Our integrated strengths, obtained by using one-body transition operators, are lower compared to the corresponding ab initio results. This indicates that, within our model, the inclusion of two-particle–two-hole configurations is indeed very effective and has an impact on the integrated strengths which is comparable to (and even stronger than) the one produced by the inclusion of two-body currents in ab initio results. By analyzing heavier nuclei, ${}^{90}\mathrm{Zr}$ and ${}^{132}\mathrm{Sn}$, we confirm the same conclusions that we have recently drawn for ${}^{48}\mathrm{Ca}$: the inclusion of two-particle–two-hole configurations is very effective in our model for providing strengths which are significantly more quenched than in other theoretical models and, thus, in better agreement with the experimental measurements. This occurs because two-particle–two-hole configurations have a density which strongly increases with the excitation energy. Their inclusion thus pushes a significant amount of the strength to higher energies, compared to what happens in other theoretical models, reducing in this way the cumulative sum of the strength up to excitation energies around 20–30 MeV.

Innovative experiments using the inverse kinematics technique to accelerate light, medium-mass, and heavy nuclei at relativistic energies have become excellent tools to produce and study hypernuclei. We investigate hypernuclei created in spallation reactions, where multifragmentation, particle evaporation, and fission processes play an important role in the formation of final hypernuclei residues. For the description of spallation reactions, we couple the Liège intranuclear cascade model, extended recently to the strange sector, to a new version of the ablation (ABLA) model that accounts for the evaporation of $\mathrm{\Lambda }$ particles from hot hyperremnants produced during the intranuclear cascade stage. These state of the art models are then used to study the production of hypernuclei close to drip lines through spallation-evaporation and fission reactions.

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provide the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.

The newly derived relativistic energy density functional [Phys. Rev. C 103, 024305 (2021)], which stems from the effective field theory motivated relativistic mean field (E-RMF), is employed to establish the appearance of peaks and/or kinks in the symmetry energy over the isotopic chain of Pb nuclei. The coherent density fluctuation model parametrization procedure for finite nuclei is adopted here to obtain the relativistic energy density functional at local density. The relativistic energy density functional from relativistic mean-field theory takes precedence over the Brückner energy density functional as it accurately predicts the empirical saturation density and binding energy per nucleon $E/A$, so-called coester band problem. Interestingly, using the relativistic energy density functional, it is possible to predict the peak at $N=126$ for recently developed G3 and widely used NL3 parameter sets, which is not observed for Brückener's functional in spite of using the relativistic mean-field density. From the present analysis, the newly fitted energy density functional is found to be minutely sensitive to the choice of the parameter sets employed.

The ground-state properties of neutron-rich exotic Na and Mg isotopes with even numbers of neutrons, $N$, are studied up to drip lines. The shell-model calculations with an ab initio effective nucleon-nucleon interaction reported by Tsunoda, Otsuka, Takayanagi et al. [Nature (London) 587, 66 (2020)] are extended to observables such as magnetic dipole and electric quadrupole moments, and charge and matter radii. Good agreements with experimental data are found, and predictions are shown up to drip lines. A prescription to extract the deformation parameters for the eigenstates of the Monte Carlo shell model is presented, and the obtained values are used to calculate charge and matter radii. The increase of these radii from the droplet model is described as the consequences of the varying deformation of the surface and the growing neutron excitations or occupations in the $pf$ shell, consistent with the drip-line mechanism presented in the above reference. The neutron skin thickness is shown to be about 0.1 fm for $N=20$, which can be compared to the value for ${}^{208}\mathrm{Pb}$ in an $A^{1/3}$ scaling. The relation of the neutron skin thickness to the electromagnetic moments is discussed for an exotic nucleus, ${}^{31}\mathrm{Na}$.

In the first part of this paper, we present a study of the symmetry energy $a_s$ and its slope parameter $L$ for nuclear matter in the framework of the Fermi-liquid theory of Landau and Migdal. We derive an exact relation between $a_s$ and $L$, which involves the nucleon effective masses and three-particle Landau-Migdal parameters. We present simple estimates which suggest that there are two main mechanisms to explain the empirical values of $L$: The proton-neutron effective-mass difference in isospin asymmetric matter and the $\ell =0$ moment of the isovector in-medium three-particle scattering amplitude. In the second part of this paper, we discuss the general structure of three-particle interactions in nuclear matter in the framework of the Fermi-liquid theory. The connections to the Bethe-Brueckner-Goldstone theory and other approaches are also discussed. We show explicitly how the first few terms in the Faddeev series, together with medium-induced three-particle interactions, emerge naturally in the Fermi-liquid theory.

Background: In recent years, we constructed a microscopic optical potential (OP) for elastic nucleon-nucleus (NA) scattering using modern approaches based on chiral theories for the nucleon-nucleon (NN) interaction. The OP was derived at first order of the spectator expansion in Watson multiple scattering theory and its final expression was a folding integral between the NN $t$ matrix and the nuclear density of the target. Two- and three-body forces are consistently included both in the target and in the projectile description.

Purpose: The purpose of this work is to apply our microscopic OP to nuclei characterized by a ground state of spin-parity quantum numbers $J^{\pi }\ne 0^{+}$.

Methods: We extended our formalism to include the spin of the target nucleus. The full amplitudes of the NN reaction matrix are retained in the calculations starting from two- and three-body chiral forces.

Results: The microscopic OP can be applied in the energy range $100\le E\le 350$ MeV. We show a remarkable agreement with experimental data for the available observables and, simultaneously, provide reliable estimates for the theoretical uncertainties.

Conclusions: This work paves the way toward a full microscopic approach to inelastic NA scattering, showing that the derivation of optical potentials between states with $J^{\pi }\ne 0^{+}$ is completely under control.

Background: Both ($e,e^{\prime }p$) and ($p,2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e,e^{\prime }p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy.

Purpose: We apply the DOM wave functions to the traditional ($p,2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e,e^{\prime }p$) cross section with the result of the ($p,2p$) analysis. Additionally, we make a comparison with a phenomenological single-particle wave function and optical potential. Uncertainty arising from a choice of $p\text{−}p$ interaction is also investigated.

Method: We implement the DOM wave functions to the nonrelativistic distorted-wave impulse approximation (DWIA) framework for ($p,2p$) reactions.

Results: DOM $+$ DWIA analysis on ${}^{40}\mathrm{Ca}(p,2p){}^{39}\mathrm{K}$ data generates a proton $0d_{3/2}$ spectroscopic factor of 0.560, which is meaningfully smaller than the DOM value of 0.71 shown to be consistent with the ($e,e^{\prime }p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p\text{−}p$ interaction do not explain this inconsistency.

Conclusions: The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p\text{−}p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.

We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J\ge 3$ and $L\le 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for ${}^{3}D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable description of the phase shifts can only be obtained with a particular cutoff. Furthermore, we compare the so-obtained nonperturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic nonperturbative TPE are more moderate than those from the nonrelativistic TPE obtained in the dimensional regularization scheme. A proper convergence pattern is observed for most of the partial waves studied except for ${}^{3}F_3$, ${}^{3}F_4$, and ${}^{3}H_6$, for which the subleading TPE contributions are a bit strong. We find that for $H$ and $I$ partial waves, the OPE alone can already describe the phase shifts reasonably well.

An empirical approach, called E-GOS ($E$-gamma over spin) curves, which is used for discerning the evolution between vibration and rotation in nuclei as a function of spin, is discussed. Considering the possible mechanisms and the results of total-Routhian-surface calculations, we find that the decrease in an E-GOS plot may be misinterpreted as the onset of vibration behavior along the yrast line. The insufficiency of the vibration-like criterion of the E-GOS curves to determine the transition from rotation to vibration is emphasized. It is pointed out that the crossing between the ground-state and $S$ bands, especially with a strong interaction, will be responsible for such vibration-like evolution of nuclear excitation modes.

A systematic analysis of nuclear deformation is made for neutron-rich Ti, Cr, and Fe isotopes to explore the nuclear structure in the island of inversion near $N=40$, where strong nuclear deformation is predicted. The nuclear ground states are obtained by the Skyrme-Hartree-Fock method in three-dimensional coordinate space, which properly describes any nuclear shape. Three types of Skyrme interactions are employed to generate various deformed states in its isotopic chain. We find that in the island of inversion the occupation of highly elongated intruder orbits induces not only large quadrupole deformation but also large hexadecapole deformation. This appears as a sizable enhancement of the nuclear matter radius, showing the characteristic shell effect of the density profile near the nuclear surface. We show that the edge of the island of inversion, where the intruder orbit starts being occupied, can be determined by measuring the enhancement of the total reaction cross section at high incident energy. The possibility of constraining the hexadecapole deformation by a measurement of the total reaction cross sections is discussed.

Experiments searching for very rare processes such as neutrinoless double-beta decay require a detailed understanding of all sources of background. Signals from radioactive impurities present in construction and detector materials can be suppressed using a number of well-understood techniques. Background from in situ cosmogenic interactions can be reduced by siting an experiment deep underground. However, the next generation of such experiments have unprecedented sensitivity goals of ${10}^{28}$ years half-life with background rates of ${10}^{-5}\text{cts/(keV kg yr)}$ in the region of interest. To achieve these goals, the remaining cosmogenic background must be well understood. In the work presented here, Majorana Demonstrator data are used to search for decay signatures of metastable germanium isotopes. Contributions to the region of interest in energy and time are estimated using simulations and compared to Demonstrator data. Correlated time-delayed signals are used to identify decay signatures of isotopes produced in the germanium detectors. A good agreement between expected and measured rate is found and different simulation frameworks are used to estimate the uncertainties of the predictions. The simulation campaign is then extended to characterize the background for the LEGEND experiment, a proposed tonne-scale effort searching for neutrinoless double-beta decay in ${}^{76}\mathrm{Ge}$.

The combined dinuclear system (DNS) model and statistical model incorporated in kewpie2 have been used to study the prospects for the synthesis of a superheavy element (SHE) with $Z=119$ in the ${}^{54}\mathrm{Cr}+{}^{243}\mathrm{Am}$ fusion reaction. The method of calculation has been verified by description of the evaporation residue cross sections measured for the ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$ reaction. The calculated results of the partial and total cross sections for the complete fusion, quasifission, fast fission, and evaporation residues formation for both reactions are discussed.

Background: A quantitative microscopic understanding of the fission-fragment yield distributions represents a major challenge for nuclear theory as it involves the intricate competition between large-amplitude nuclear collective motion and single-particle nucleonic motion.

Purpose: A recently proposed approach to global modeling of fission fragment distributions is extended to account for odd-even staggering in charge yields and for neutron evaporation.

Method: Fission trajectories are obtained within the density functional theory framework, allowing for a microscopic determination of the most probable fission prefragment configurations. Mass and charge yield distributions are constructed by means of a statistical approach rooted in a microcanonical ensemble.

Result: We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields, including the odd-even staggering for a wide range of fissioning nuclei. Experimental isotopic yields can be described within a simple neutron evaporation scheme. We also explore fission fragment distributions of exotic neutron-rich and superheavy systems and compare our predictions with other state-of-the art global calculations.

Conclusion: Our paper suggests that the microscopic rearrangement of nucleons into fission fragments occurs well before the scission and that the subsequent dynamics is mainly driven by the thermal excitations and bulk features of the nuclear binding. The proposed simple hybrid approach is well suited for large-scale calculations involving hundreds of fissioning nuclei.

The experimental values of the ratio ${\mathrm{\Gamma }}_{\mathrm{f}}\left(E\right)/{\mathrm{\Gamma }}_{\mathrm{n}}\left(E\right)$ are well described for the nuclei ${}^{180,181,182,184}\mathrm{W}$, ${}^{185}\mathrm{Re}$, ${}^{186,187,188,190}\mathrm{Os}$, ${}^{189,191}\mathrm{Ir}$, ${}^{192,193,194,196}\mathrm{Pt}$, ${}^{197,195}\mathrm{Au}$, ${}^{196,198,199,200}\mathrm{Hg}$, ${}^{201}\mathrm{Tl}$, ${}^{207,209}\mathrm{Bi}$, ${}^{208,210,211,212}\mathrm{Po}$, and ${}^{213}\mathrm{At}$. The values of fission barrier height are deduced using a statistical approach for a description of the ratio ${\mathrm{\Gamma }}_{\mathrm{f}}\left(E\right)/{\mathrm{\Gamma }}_{\mathrm{n}}\left(E\right)$. The dependence of the fission barrier on the thermal excitation energy of the compound nucleus is taken into account in the calculations. The obtained values of 29 fission barrier heights are entirely consistent with the available experimental data as well as with the results of the macroscopic-microscopic finite-range liquid-drop model.

It has been proposed that strong electromagnetic fields produced in the early stages of heavy-ion collisions can lead to splitting of the rapidity-odd directed flow of positive and negative hadrons. For light hadrons, the interpretation of such measurements is complicated by the low magnitude of directed flow as well as by ambiguities arising from transported quarks. To overcome these complications, we propose measurements using only hadrons carrying produced quarks ($\overline{u},\overline{d},s,\overline{s}$). We discuss how to identify the kinematics where such hadrons are produced via the coalescence mechanism and therefore their flow is the sum of the flow of their constituent quarks. With this sum rule verified for certain combinations of hadrons, the expected systematic violation of this rule with increasing electric charge can be measured, which could be a consequence of the electromagnetic fields produced in the collisions. Our approach can be tested with the high statistics data from Phase II of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.

Two-proton decay from excited states in ${}^{10}\mathrm{C}$ and ${}^{11}\mathrm{N}$ has been characterized from an analysis of the $2p+2\alpha$ and $3p+2\alpha$ exit channels. Data from four previously published invariant-mass studies associated with inelastic excitation, multinucleon knockout, and neutron pickup reactions have been considered. A rotational band in ${}^{10}\mathrm{C}$ was identified built on the second $0^{+}$ state which has strong $\alpha$-cluster molecular structure. The members of this band were tentatively identified up to $J^{\pi }=4^{+}$ and all identified states have a prompt $2p$ decay branch. The spins of the $0^{+}$ and $2^{+}$ members were deduced from comparisons of the momentum correlations in their $2p$ branches to those from known $2p$ emitters. The $2^{+}$ and the tentative $4^{+}$ members are both above the $\alpha$ threshold and exhibit large reduced decay widths for $\alpha$ emission. This band exhibits a similar moment of inertia to its analog in the mirror nucleus ${}^{10}\mathrm{Be}$. Evidence is also presented for a molecular band in ${}^{11}\mathrm{N}$ built on the second $3/2^{-}$ state which $2p$ decays. Tentative members of this band have been assigned up to $J^{\pi }=9/2^{-}$ and their excitation energies also match their likely analogs in the mirror nucleus ${}^{11}\mathrm{Be}$.

The expression of dependence of average total kinetic energy release of fission fragments on the excitation energy of the compound nucleus is obtained in the framework of a simple statistical model. The experimental data for the neutron-induced fission of ${}^{233,235,238}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ measured in wide ranges of the excitation energy of the compound nuclei are well described using the obtained expression. The origin of the energy dependence of the average total kinetic energy is discussed in detail.