Since its beginnings, fission theory has assumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Nevertheless, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the generator coordinate method (GCM). Simple reaction-theoretic models are constructed with the Gaussian overlap approximation to parametrize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor $T$. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. The bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.

For even-odd isotopes of actinides and superheavy nuclei, spontaneous fission and $\alpha$-decay half-lives are calculated within the dinuclear system model and compared with the existing experimental data. All these processes are considered as the evolution of a nucleus in the charge (mass) asymmetry coordinate and in the relative distance between the centers of clusters formed. The important role of the spin dependence of total potential energy in the charge asymmetry coordinate is shown and the origin of the fission hindrance in even-odd nuclei is explained.

Using the string melting version of a multiphase transport model, we focus on the evolution of thermodynamic properties of the central cell of parton matter produced in $\text{Au}+\text{Au}$ collisions ranging from 200 GeV down to 2.7 GeV. The temperature and chemical potentials have been calculated based on both Boltzmann and quantum statistics in order to locate their evolution trajectories in the QCD phase diagram. We demonstrate that the trajectories can depend on many physical factors, especially the finite nuclear thickness at lower energies. However, from the evolution of pressure anisotropy, only partial thermalization can be achieved when the partonic systems reach the predicted QCD phase boundary. It provides some helpful insights to studying the QCD phase structure through relativistic heavy-ion collisions.

We argue that a detailed analysis of the spin alignment of vector mesons can serve as a probe of two little-understood aspects of spin dynamics in a vortical fluid: The degree of relaxation between vorticity and particle spin polarization, and the degree of coherence of the hadron wave function at freeze-out. We illustrate these with a coalescence model.

We include effects of chiral symmetry and its restoration in the kinetic equations for baryon propagation and explore the consequences for $\eta , {\pi }^0, \rho$, and dilepton production in heavy-ion collisions at $\left(112\right)A\mathrm{GeV}$. Numerical calculations are performed using the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) microscopic transport model supplemented by the parity-doublet model for the mean fields of the nucleon and the $N^{*}\left(1535\right)$ resonance. In this chiral model, a strong drop of the Dirac mass of the $N^{*}\left(1535\right)$ in the high-density stage of a collision leads to a considerable enhancement in the production of this resonance as compared to the standard (nonlinear) Walecka model. As the system expands, the Dirac masses of these abundant soft $N^{*}\left(1535\right)$ resonances gradually increase and ultimately cross the $N\eta$ decay threshold. As a result, an enhanced low-energy $\eta$ production is observed in the calculations with chiral mean fields. Comparing with data from the TAPS experiment on $\eta$ and ${\pi }^0$ production, we find that the chiral model improves the agreement for the $m_t$ spectra of $\eta$'s at small $m_t$ in heavy colliding systems. A similar enhancement is also observed in the soft $\rho$ production due to chiral symmetry and its partial restoration. The resulting dilepton yields at low and intermediate invariant masses are slightly enhanced due to these chiral effects, which further improves the agreement between GiBUU transport simulations and data from the HADES experiment for $\mathrm{C}+\mathrm{C}$ at $1A\mathrm{GeV}$.

Based on the three-fluid model, the global $\mathrm{\Lambda }$ polarization in $\mathrm{Au}+\mathrm{Au}$ collisions at 2.4 $\le \sqrt{s_{NN}}\le$ 7.7 GeV is calculated, including its rapidity and centrality dependence. Contributions from the thermal vorticity and meson-field term (proposed by Csernai, Kapusta, and Welle) to the global polarization are considered. The results are compared with data from recent and ongoing STAR and HADES experiments. It is predicted that the polarization maximum is reached at $\sqrt{s_{NN}}\approx 3$ GeV, if the measurements are performed with the same acceptance. The value of the polarization is very sensitive to interplay of the aforementioned contributions. In particular, the thermal vorticity results in quite strong increase of the polarization from the midrapidity to forward/backward rapidities, while the meson-field contribution considerably flattens the rapidity dependence. The polarization turns out to be very sensitive to details of the equation of state. While collision dynamics become less equilibrium with decreasing collision energy, the present approach to polarization is based on the assumption of thermal equilibrium. It is found that equilibrium is achieved at the freeze-out stage, but this equilibration takes longer at moderately relativistic energies.

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasiparticle (qp) configurations. Detailed derivation is provided and the validity of the new formula is checked numerically. The corresponding efficiency is discussed, which turns out to be about five times (one order of magnitude) higher than the conventional method when four (less than four) qp operators are considered.

Background: Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $\alpha$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remains elusive.

Purpose: The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from neon to germanium, in order to monitor and understand its nature and conditions of emergence.

Methods: We perform covariant quasiparticle random phase approximation calculations, formulated within the finite amplitude method, on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states.

Results: Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, clusterlike excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecularlike orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases.

Conclusions: The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\approx$5–10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\approx$10–15 MeV) as well as pair excitation ($<$5 MeV), with possible mixing, depending on neutron excess, deformation, and pairing energy.

Excited states of the ${}^{93}\mathrm{Nb}$ nucleus are produced through the fusion-evaporation reactions ${}^{82}\mathrm{Se}({}^{14}\mathrm{N},3n){}^{93}\mathrm{Nb}$ and ${}^{82}\mathrm{Se}({}^{16}\mathrm{O},1p4n){}^{93}\mathrm{Nb}$. On the basis of new experimental data, the previously known level scheme is extended. Level structure is discussed in comparison to a shell-model calculation. The calculation results demonstrate that the low-lying states can be interpreted as the excitation of the protons from the $1p_{1/2}$ orbit, through the $Z=40$ subshell closure, to the $0g_{9/2}$ orbit. The moderate-spin states involve not only the proton excitation through the $Z=38$ or 40 subshell ($0f_{5/2}1p_{3/2}1p_{1/2}\to 0g_{9/2}$), but also the neutron excitation through the $N=56$ subshell ($1d_{5/2}\to 0g_{7/2}$). For the high-spin states above 9.1 MeV, the neutron excitation across the $N=50$ closed shell plays a dominant role.

We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring diagrams in terms of effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to those particle-hole interactions. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.

We investigate ground states properties of Pb isotopes located between neutron and proton drip-lines estimated by two-neutron (two-proton) separation energies and Fermi energies within the deformed relativistic Hartree-Bogoliubov theory in continuum. First, we report some candidates of nuclear shape coexistence in the isotope chain. They are accessed by calculating total energy as a function of the deformation parameter ${\beta }_2$, and for the coexistence candidates we take a few deformation regions bringing about minima of the energy within energy difference $\mathrm{\Delta }E<1$ MeV. Second, the Pb isotopes near neutron drip-lines are also investigated and compared to the results by other nuclear mass models. We find out 11 neutron emitters, ${}^{278\text{–}296,300}\mathrm{Pb}$, giving rise to the Pb peninsular near the neutron drip-line. Finally, by exploiting the neutron and proton density we deduce the neutron skin thickness (NST) of the Pb isotopes and compare to the available experimental data. The recent reports regarding the shape coexistence of ${}^{184,186,188}\mathrm{Pb}$ and the NST of ${}^{208}\mathrm{Pb}$ are shown to be well matched with the present results.

Background: Sr isotopes are located in the mass region $A\approx 100$, where a very quick onset of nuclear deformation exists; other notable examples of this area are Yb, Zr, and Nb nuclei. The presence of the proton subshell closure $Z=40$ allows the existence of particle-hole excitations that produce low-lying intruder bands.

Purpose: The goal of this work is the study of the nuclear structure of the even-even ${}^{92\text{–}102}\mathrm{Sr}$ isotopes through the accurate description of excitation energies, $B\left(E2\right)$ transition rates, nuclear radii, and two-neutron separation energies.

Method: The interacting boson model with configuration mixing will be the framework to calculate all the observables of the Sr isotopes. Only two types of configurations will be considered, namely, 0-particle–0-hole and 2-particle–2-hole excitations. The parameters of the model are determined using a least-squares procedure for the excitation energies and the $B\left(E2\right)$ transition rates.

Results: For the whole chain of isotopes, the value of excitation energies, $B\left(E2\right)$'s, two-neutron separation energies, nuclear radii, and isotope shifts have been obtained, with a good agreement between theory and experiment. Also, a detailed analysis of the wave functions have been performed and, finally, the mean-field energy surfaces and the value of the nuclear deformation, $\beta$, have been obtained.

Conclusions: The presence of low-lying intruder states in even-even Sr isotopes has been confirmed and its connection with the onset of deformation has been clarified. The lightest Sr isotopes present a spherical structure while the heaviest ones are clearly deformed. The rapid onset of deformation at neutron number 60 is due to the crossing of the regular and intruder configurations and, moreover, both families of states present an increase of deformation with the neutron number.

Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates, leading to missing or incorrect results.

Purpose: This work aims to produce efficient and physically motivated computational algorithms to refine potential energy surfaces by removing discontinuities.

Method: Procedures based on tree-search algorithms are developed which are capable of smoothing discontinuities in one- and two-dimensional potential energy surfaces while minimizing their overall energy.

Results: Each of the new methods is applied to smooth candidate discontinuities in ${}^{252}\mathrm{Cf}$, ${}^{222}\mathrm{Th}$, and ${}^{218}\mathrm{Ra}$. The effectiveness of each case is analyzed both qualitatively and quantitatively. The one-dimensional method is also compared to the adiabatic and linear interpolation approaches which are commonly used to remove discontinuities.

Conclusions: The smoothing methods presented in this work are resource efficient and successful for one- and two-dimensional discontinuities; they will improve the fidelity of potential energy surfaces as well as their subsequent uses in beyond mean-field applications. Complex discontinuities occurring in higher dimensions may require alternative approaches which better utilize prior knowledge of the potential energy surface to narrow their searches.

To study the bulk properties of quark-gluon plasma produced at beam-energy scan (BES) energies at the Relativistic Heavy Ion Collider (RHIC), we extend the $(3+1)$-dimensional viscous hydrodynamics clvisc to include net baryon number conservation and Israel-Stewart–like equations for baryon diffusion with the neos-bqs equation of state, fluctuating initial conditions from the Monte Carlo Glauber model and the afterburner smash. This integrated framework is shown to provide a good description of identified particle spectra, mean transverse momenta, and anisotropic flows for different centralities and over a wide range of collision energies (7.7–62.4 GeV). It is found that the mean momenta of identified particles and anisotropic flows increase mildly with the collision energy due to larger radial flow. We further compute the multiple-particle cumulant ratio $v_2\left\{4\right\}/v_2\left\{2\right\}$ of elliptic flow across BES energies, and find that the relative fluctuations of elliptic flow are insensitive to the collision energy, consistent with the preliminary STAR data. Our model provides a benchmark for understanding the RHIC-BES data and studying the critical properties and phase structure of hot and dense QCD matter.

There have been great improvements in the predictions of nuclear masses, yet it is difficult to exactly reproduce the measured nuclear mass. It has been suggested that the cause of such discrepancies is due to the negligence of many-body effects in the available theoretical models. The errors in the prediction of the nuclear mass show residual correlations due to the missing physics in the mass models. In the present Letter we have tried to learn such correlations by using the neural networks. We have used a neural network architecture which adaptively learns the linear and nonlinear correlations between the data of different fidelity. We have used the theoretical predictions of finite range droplet model and Hartree- Fock-Bogoliubov models in the input of the neural networks. The present approach show significant improvements in the accuracy of the predictions. It has been clearly presented that the difference between the predictions from the present approach and the experimental data behave more, such as white noise, showing that using the present approach the residual correlations arising due to the missing physics from the available mass models can be learned.

Short range correlated nucleon-nucleon ($NN$) pairs are an important part of the nuclear ground state. They are typically studied by scattering an electron from one nucleon in the pair and detecting its spectator correlated partner (“spectator-nucleon tagging”). The Electron Ion Collider (EIC) should be able to detect these nucleons, since they are boosted to high momentum in the laboratory frame by the momentum of the ion beam. To determine the feasibility of these studies with the planned EIC detector configuration, we have simulated quasielastic scattering for two electron and ion beam energy configurations: 5 GeV $e^{-}$ and 41 $\mathrm{GeV}/A$ ions, and 10 GeV $e^{-}$ and 110 $\mathrm{GeV}/A$ ions. We show that the knocked-out and recoiling nucleons can be detected over a wide range of initial nucleon momenta. We also show that these measurements can achieve much larger momentum transfers than current fixed target experiments. By detecting both low and high initial-momentum nucleons, the planned EIC has the potential to provide the data that should allow scientists to definitively show if the European Muon Collaboration effect and short-range correlation are connected, and to improve our understanding of color transparency.

Background: Electric-quadrupole ($E2$) strengths relate to the underlying quadrupole deformation of a nucleus and present a challenge for many nuclear theories. Mirror nuclei in the vicinity of the line of $N=Z$ represent a convenient laboratory for testing deficiencies in such models, making use of the isospin symmetry of the systems.

Purpose: Uncertainties associated with literature $E2$ strengths in ${}^{23}\mathrm{Mg}$ are some of the largest in $T_z=\left|\frac{1}{2}\right|$ nuclei in the $sd$ shell. The purpose of the present paper is to improve the precision with which these values are known, to enable better comparison with theoretical models.

Methods: Coulomb-excitation measurements of ${}^{23}\mathrm{Mg}$ and ${}^{23}\mathrm{Na}$ were performed at the TRIUMF-ISAC facility using the TIGRESS spectrometer. They were used to determine the $E2$ matrix elements of mixed $E2/M1$ transitions.

Results: Reduced $E2$ transition strengths, $B\left(E2\right)$, were extracted for ${}^{23}\mathrm{Mg}$ and ${}^{23}\mathrm{Na}$. Their precision was improved by factors of approximately 6 for both isotopes, while agreeing within uncertainties with previous measurements.

Conclusions: A comparison was made with both shell-model and ab initio valence-space in-medium similarity renormalization group calculations. Valence-space in-medium similarity renormalization group calculations were found to underpredict the absolute $E2$ strength, in agreement with previous studies.

Background: Recent developments in ab initio nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, $E2$, strength associated with collectivity.

Purpose: The valence-space in-medium similarity renormalization group (VS-IMSRG) is a particularly powerful method for accessing medium- and high-mass nuclei but has been found to underpredict $E2$ strengths. The purpose of this work is to evaluate the isospin dependence of this underprediction.

Methods: We perform a systematic comparison of VS-IMSRG calculations with available literature. We make use of isoscalar and isovector contributions to the $E2$ matrix elements to assess isoscalar and isovector contributions to the missing strength.

Results: It is found that the $E2$ strength is consistent throughout $T_z=\left|\frac{1}{2}\right|, T_z=\left|1\right|, T_z=\left|\frac{3}{2}\right|$, and $T_z=2$ pairs within the $sd$ shell. Furthermore, no isovector contribution to the deficiency is identified.

Conclusions: A comparison with toy-models and coupled-cluster calculations is used to discuss potential origins of the missing strength, which arises from missing many-particle, many-hole excitations out of the model space. The absence of any significant isovector contribution to the missing $E2$ strength indicates that the $E2$ strength discrepancy, and therefore any correction, is largely independent of the isospin of the nuclei in question.

The $\beta$-decay scheme of ${}^{138}\mathrm{Te}$ and the level structure of ${}^{138}\mathrm{I}$ is reported for the first time. The experiment was performed at the Radioactive Isotope Beam Factory of RIKEN, as one of the EUROBALL-RIKEN Cluster Array campaigns. Secondary radioactive ions, including ${}^{138}\mathrm{Te}$ and ${}^{138}\mathrm{Sb}$, were produced by the in-flight fission of a ${}^{238}\mathrm{U}$ beam with the energy of 345 MeV per nucleon. From the $\beta$ decay of ${}^{138}\mathrm{Te}$, the level scheme of ${}^{138}\mathrm{I}$ was supplemented with new spin and parity assignments, such as the low-lying negative-parity states and a positive-parity $1^{+}$ state. This $1^{+}$ state can be interpreted as being associated with the $\pi 0h_{11/2}\otimes \nu 0h_{9/2}$ partner orbital configuration populated by the Gamow-Teller transition between a neutron in the $0h_{9/2}$ orbital and a proton in the $0h_{11/2}$ orbital. Details of the structure of ${}^{138}\mathrm{I}$ are discussed in terms of the proton-neutron interactions and Gamow-Teller transition strength within the theoretical context of shell-model calculations.

Magnetic dipole strength functions are determined for the series of germanium isotopes from $N=Z=32$ to $N$ = 48 on the basis of a large number of transition strengths calculated within the shell model. The evolution of the strength with increasing neutron number in the $1g_{9/2}$ orbital is analyzed. A bimodal structure comprising an enhancement toward low transition energy and a resonance in the region of the scissors mode is identified. The low-energy enhancement is strongest near closed shells, in particular at the almost completely filled $1g_{9/2}$ orbital, while the scissorslike resonance is most pronounced in the middle of the open shell, which correlates with the magnitude of the also deduced electric quadrupole transition strengths. The results are consistent with previous findings for the shorter series of iron isotopes and prove the occurrence and correlation of the two low-lying magnetic dipole modes as a global structural feature.