Background: Cluster radioactivity is a rare nuclear decay phenomenon that emits clusters heavier than the alpha particle but lighter than the smallest fission fragment observed. The experimentally observed clusters, as well as other possible cluster emitters, are theoretically studied based on preformed cluster models, fission-like models, and empirical models.

Purpose: The purpose of this paper is to establish reliable empirical models with fewer parameters for predicting half-lives of cluster decay using symbolic regression.

Methods: The experimentally measured half-lives of the 22 cluster decay of various parents and different clusters in the trans-lead region, along with their mass number, proton number, neutron number, and decay energy (Q) are used to train the interpretable symbolic regression model (pysr). The trained model extracts empirical formulas for intricate physical phenomena from the experimental data. The model traverses an immense mathematical expression space using an evolutionary search strategy to discover the most interpretable and precise formulas to be used to predict logarithmic half-lives of cluster decay. The obtained empirical equations are tested with statistical metrics such as root-mean-square error (RMSE) and mean absolute error (MAE) with respect to the experimental data.

Results: Within the model limits, several empirical equations are obtained with varying score and loss values. The half-lives calculated using the empirical relations are compared with available experimental data and with the results of other empirical formulas available in the literature. Further, the obtained empirical formula is used to predict the half-lives for 51 energetically possible nuclei in the trans-actinide region.

Conclusions: The generated expressions for half-lives are found to have strong correlations between Q values, barrier penetration probabilities, and charge numbers of the decay fragments. The consistency of pysr-derived predictions with known decay systematics suggests that symbolic regression can be a valuable tool for predicting half-lives of exotic cluster decay modes in the unexplored regions of the nuclear chart.

Spallation-induced fission reactions, in combination with state-of-the-art dynamical calculations, provide a robust framework for studying the nuclear dissipation mechanism in nuclear matter over a wide range of deformations. Experimental datasets of neutron- and proton-induced fission, accumulated over the last decades, cover a wide range of nuclei from the preactinide to the actinide region. In this work, these datasets are used to benchmark the dynamical Liège intranuclear cascade model $\mathrm{INCL}++$ integrated with the ABLA++ de-excitation code, which has been improved by updating the calculation of particle separation energies to the atomic mass evaluation (AME2020) and incorporating phenomenological corrections to enhance the description of fission-barrier heights. The results show good agreement with the available experimental data of total fission cross sections induced by protons and neutrons, thereby confirming the applicability and predictive capability of these models. Moreover, the improved framework is used to investigate the fission cross sections of exotic heavy fissile nuclei, far from the valley of stability, with masses $A>155$.

The cumulants of the distribution of anisotropic flow are measured accurately in $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider as a function of centrality classifiers (charged multiplicity and/or transverse energy). Using Bayesian inference, we reconstruct from these measurements the probability distribution of anisotropic flow in the “theorists' frame” where the impact parameter has a fixed magnitude and orientation, up to $\approx 70\%$ centrality. The variation of flow fluctuations with impact parameter displays direct evidence of viscous damping, which is larger for higher Fourier harmonics, in line with expectations from hydrodynamics. We use intensive measures of non-Gaussian flow fluctuations, which have reduced dependence on centrality. We infer from ATLAS data the magnitude of these intensive non-Gaussianities in each Fourier harmonic. They provide data-driven estimates of response coefficients to initial anisotropies, without resorting to any specific microscopic model of initial conditions. These estimates agree with viscous hydrodynamic calculations.

Background: Reliable theoretical predictions of nuclear dipole excitations are crucial for various nuclear applications, particularly in nuclear astrophysics. Calculations of radiative capture cross sections often rely on theoretical $\gamma$ strength functions, with the electric dipole response being the dominant component. Recent experimental and theoretical efforts in this area have focused on nuclei with mass numbers $A\le 60$ which appear of interest to model intergalactic propagation of ultra-high-energy cosmic rays.

Purpose: We aim at a systematic description of the $E1$ strength of nuclei with mass numbers between 17 and 40 of interest for various applications. Additionally, we seek to better understand the nature of the low-energy dipole strength in neutron-rich nuclei, known as pygmy dipole resonances.

Methods: We use the configuration interaction shell-model framework in the $p\text{−}sd\text{−}pf$ valence space with a previously established empirical Hamiltonian. Full $1\hslash \omega$ configuration space is considered to describe $E1$ excitations. Systematic calculations are carried out for the $sd$-shell nuclei and compared to available data and other models. The nature of different resonances is assessed based on calculations of transition densities and analysis of the wave functions.

Results: Systematic results of photoabsorption strength show good agreement with experimental data, provided a renormalization of the dipole operator is applied to account for the correlations outside the model space. Transition densities are computed in ${}^{26}\mathrm{Ne}$ and confirm the pure isovector character of the giant dipole resonance. The strength at 7–10 MeV is shown to have a distinct structure from the giant resonance and from the lowest-energy excitations, with largely fragmented wave functions and transition densities of isovector character at the edge of the nucleus.

Conclusions: The configuration-interaction shell model is proved to be a valuable tool in the description of the photoresponse of light nuclei, providing more accurate results than the usually employed approaches. It gives additional and valuable insight into the nature of low-energy dipole strength, supporting the interpretation of the pygmy dipole strength as an oscillation of the neutron skin against the proton-neutron core.

The relativistic configuration-interaction density functional theory is extended to odd-$A$ nuclear systems, and applied to study a pair of negative-parity bands observed in the odd-$A$ nucleus ${}^{135}\mathrm{Pr}$, regarded as candidate wobbling bands in previous studies. The calculated energy spectra and electromagnetic transition probabilities agree satisfactorily with the experimental data. By examining the probability amplitudes of the microscopic wave functions as functions of total angular momenta, the importance of the three-quasiparticle configurations is clearly revealed. The underlying pictures of the studied bands are illustrated by using the azimuthal plot, showcasing a clear evolution from tilted precession to wobbling motion, and finally to tilted axis rotation. The present work represents the first microscopic and quantal description for nuclear wobbling motions within the framework of relativistic density functional theory.

The cluster decay half-lives and their decay characteristics are systematically investigated within the framework of the preformed cluster-decay model (PCM), focusing on the doubly closed-shell ${}^{208}\mathrm{Pb}$ daughter nucleus and extending the analysis to other daughter nuclei. The cluster-daughter interaction potential is calculated using the Skyrme energy density functional theory and a double-folding procedure with the M3Y nucleon-nucleon potential, incorporating densities derived from two different approaches: the phenomenological two-parameter Fermi (2pF) model and the microscopic Skyrme Hartree-Fock (SHF) radial densities. A key objective of the present work is to compare the 2pF and SHF densities to assess their impact on the cluster decay half-lives. The penetration probability through the interaction potential, a crucial factor in determining decay half-lives, is obtained using the Wentzel-Kramers-Brillouin approximation. The decay energies ($Q$ values) used in this work are calculated from various binding energy, including those from Möller et al., Audi et al., the deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc), and the binding energy plus rotational correction energy from DRHBc calculations. These $Q$ values, in conjunction with the total interaction potential, serve as inputs in the PCM to compute the half-lives $T_{1/2}$ of experimentally observed clusters. It is observed that experimental $Q$ values reproduce the experimental half-lives well for all spherical cases considered, making them a more reliable choice for the spherical choice of the nuclei. By keeping the same $Q$ values, calculations for deformed nuclei are also carried out using experimental $Q$ values, incorporating deformation effects along with the optimal cold orientations. Furthermore, the standard deviation obtained for deformed nuclei is found to be nearly comparable to that of the spherical case, indicating the reliability of the PCM approach in both scenarios. Additionally, our analysis reveals that 2pF densities yield better agreement with experimental data compared to SHF densities, which may be attributed to their phenomenological nature, effectively capturing nuclear surface properties. The standard root-mean-square (rms) deviation for both the 2pF and SHF approaches could be further minimized if precise experimental half-lives were available for 15 of the 45 clusters considered in this study, for which only lower limits are currently available. The present analysis provides the theoretical predictions for the upcoming experiments on the heavier-mass region.

This study examines charge-changing cross sections for ${}^{12}\mathrm{C}$, ${}^{14}\mathrm{N}$, ${}^{16}\mathrm{O}$, and ${}^{20}\mathrm{Ne}$ projectiles on elemental targets (C, Al, Cu) at a beam energy of around 290 MeV/nucleon. The two-stage abrasion-ablation model is used, with the abrasion stage described via the Glauber model, incorporating validated single-nucleon density distributions from proton elastic scattering data. In the ablation stage, where particle evaporation occurs, the contribution to charge-changing cross sections is estimated using two approaches. First, a statistical decay model is employed to analyze the evaporation of protons following neutron removal in the abrasion stage. The second approach estimates evaporation contributions by subtracting the direct process component (abrasion) from the experimental charge-changing cross-section data. A comparison between these estimated contributions from the experimental data and the predictions of the statistical model enables a systematic evaluation of the evaporation process. The key factors influencing evaporation, such as excitation energy distribution parameters, decay width of the emitted particles, and nucleon separation energies, are analyzed. A strong correlation is observed between the maximum excitation energy available for evaporation and the neutron separation energy of the projectiles across different targets, highlighting the role of evaporation dynamics in the charge-changing cross sections.

Background: The fusion excitation function of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ contains many resonances from above the Coulomb barrier towards sub-barrier energies. These oscillations might be linked to molecular states in the compound nucleus ${}^{12}\mathrm{C}$ with drastic consequences for stellar carbon burning. Moreover, these structures render the common extrapolations from measurements into the astrophysics region of interest at deep sub-barrier energy extremely uncertain.

Purpose: We have investigated the cross section around the lowest direct-coincident gamma-particle measurements, where previously only limits could be established with the aim of obtaining a detailed description of the excitation function. We have furthermore analyzed the ratio of extreme decay branching into the first excited state of daughter nuclei with alpha or proton emission at relative kinetic energies where previous measurements are in disagreement with each other.

Methods: The experiments were carried out at the Andromède accelerator, IJCLab Orsay (France), with carbon-beam intensities of up to 3 $\mathrm{p}\mu \mathrm{A}$ on thin rotating carbon-target foils. Light charged particles and gamma decays were detected using silicon strip detectors and ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ crystals, respectively, in coincidence measurements with nanoseconds precision.

Results: We establish data points with highly improved accuracy at the high-energy tail of the lowest resonance detected so far in direct measurements, right in the astrophysics region of interest (RoI). The findings are in agreement with an earlier interpretation of the fusion excitation function composed of resonances on top of a global trend of empirically determined fusion hindrance behavior. At a relative energy between 3.1 MeV and 3.3 MeV, an oscillating behavior of the branching ratio into the first excited final state with alpha or proton emission is observed, with extreme values significantly deviating from data at higher energy.

Conclusions: Our findings in the astrophysics RoI support reaction-rate models with a lower average $S$-factor trend, that deviates significantly from standard extrapolations between 2.2 MeV and 2.6 MeV, for stellar carbon-burning simulations of up to 25 $M_{\odot }$ stars. Based on our data, an overall increase of the $S$-factor at deep sub-barrier energy cannot be confirmed. The extremely low ratio of the branching into the first excited state with proton over alpha emission of $\approx 2\%$ at 3.23 MeV might indicate the presence of alpha-cluster compound states in ${}^{12}\mathrm{C}$. This highly favors $\alpha$ emission with fundamental consequences in possible stellar carbon-burning sites.

We investigate dilepton production in heavy-ion, proton-proton, and proton-nucleus collisions from low energies of 1 AGeV (SIS) to ultrarelativistic energies (LHC) using the parton-hadron-string dynamics (PHSD) transport approach. PHSD is a microscopic, nonequilibrium approach that integrates hadronic and partonic degrees of freedom, providing a comprehensive description of relativistic heavy-ion collisions—from initial nucleon-nucleon interactions to quark-gluon plasma (QGP) formation, hadronization, and final-state interactions. Key dilepton sources in PHSD include hadronic decays, bremsstrahlung, QGP radiation ($q+\overline{q}\to e^{+}{e}^{-}$, $q+\overline{q}\to g+e^{+}{e}^{-}$, $q+g\to q+e^{+}{e}^{-}$), primary Drell-Yan production, and semileptonic decays of correlated charm and bottom pairs. PHSD well describes dilepton data from HADES, STAR, and ALICE experiments. We examine in-medium effects, such as the vector-meson spectral function broadening, and present the excitation function for the dilepton “excess” in the invariant mass range $0.4<M_{\text{ee}}<0.75\mathrm{GeV}/{\mathrm{c}}^2$ and its centrality dependence at various energies. For the first time we report on the baryon chemical potential ${\mu }_B$ dependence of the QGP radiation calculated on a basis of the dynamical-quasiparticle model (DQPM) in PHSD. The influence of ${\mu }_B$ on the QGP yield grows at lower collision energies, where ${\mu }_B$ becomes large; however, its impact on the total dilepton spectra is small due to the lowering of the QGP volume with decreasing energy. The excitation function of QGP dileptons, including the ${\mu }_B$-dependent quasiparticle masses and widths, is presented versus correlated charm, confirming that the QGP radiation overshines charm contributions at $\sqrt{s}\simeq 25-30$ GeV in central $\mathrm{Au}+\mathrm{Au}$ collisions, providing access to thermal QGP dileptons at BES RHIC and FAIR. Additionally, we find that the contribution from partonic processes to dilepton spectra in $\mathrm{p}+\mathrm{p}$ collisions at intermediate masses—although being small—increases with energy, suggesting that after subtracting correlated charm and bottom contributions the QGP radiation in high multiplicity $\mathrm{p}+\mathrm{p}$ collisions might also be experimentally accessible at LHC energies.

Background: In the mass region with an abnormal shell structure, the so-called island of inversion, the spin-parity of odd-mass nuclei provides quantitative insights into the shell evolution. However, the experimental determination of the spin-parity is often challenging, leaving it undetermined in many nuclei.

Purpose: We discuss how the shell structure affects the density profiles of nuclei in the island of inversion and investigate whether these can be probed from the total reaction and elastic scattering cross sections.

Method: The antisymmetrized molecular dynamics (AMD) is employed to generate various particle-hole configurations and predict the energy levels of these nuclei. The obtained density distributions are used as inputs to the Glauber model, which is employed to calculate the total reaction and elastic scattering cross sections to reveal their relationship to the particle-hole configurations.

Results: In addition to the well-known correlation between nuclear deformation and radius, we show the correlations between the particle-hole configurations and both central density and diffuseness. We show that different particle-hole configurations are well reflected in the total reaction and elastic scattering cross sections.

Conclusion: The total reaction and elastic scattering cross sections are useful probes to identify the spin-parity of nuclei when different particle-hole configurations coexist.

The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudospin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its approach, is an excellent tool to understand the main mechanism driving theses spin and pseudospin symmetries and their breaking. A perturbative expansion of the degeneracy raising related to spin and pseudospin effects is proposed, up to second order. It allows one to understand the main behavior of spin and pseudospin energy doublets, such as their $A$ dependence, as well as their common footing and differences. In the case of the spin symmetry, only the lower component of the Dirac bispinor is involved, whereas, in the case of the pseudospin one, both the upper and lower components are involved. Their interplay with the covariant potentials is also analyzed.

We investigated the contributions of the tensor force to the potential energy and symmetry energy in symmetric nuclear matter (SNM) using three different chiral $NN$ interactions and the Argonne ${\mathrm{V}}_{18}$ (Av18) potential. By isolating the diagonal contributions of the tensor term $3({\vec{\sigma }}_1·\widehat{\vec{r}})({\vec{\sigma }}_2·\widehat{\vec{r}})$ and that of the central term $-({\vec{\sigma }}_1·{\vec{\sigma }}_2)$ in the tensor force through the Hellmann-Feynman theorem, we find that the diagonal contribution from the tensor term nearly cancels out the contribution from the central term within the Brueckner-Hartree-Fock approch. This indicates that the primary contribution of the tensor force to the potential energy in SNM arises from the off-diagonal elements. Furthermore, the tensor force contribution to both the potential energy and symmetry energy is significantly weaker in chiral interactions compared to the Av18 potential. In particular, the role of the tensor force in the symmetry energy in the framework of chiral effective field theory is much less pronounced compared to that based on the Av18 potential. These results reveal significant differences in the tensor force across various interactions, challenging previous expectations and indicating the strong model dependence of the tensor force contribution to the symmetry energy.

Elastic scattering and breakup ${}^8\mathrm{B}+p$ and ${}^7\mathrm{Be}+2p$ angular distributions for ${}^9\mathrm{C}+{}^{208}\mathrm{Pb}$ at an incident energy of 303 MeV, around five times the Coulomb barrier, are reported. The data have been analyzed using the optical model and the three-body continuum discretized coupled channels formalism, assuming ${}^8\mathrm{B}+p$ and ${}^7\mathrm{Be}+2p$ configurations. The elastic scattering angular distributions, both measured and calculated, exhibit a relatively minor suppression of the Coulomb rainbow. Calculations combining the elastic and nonelastic breakup contributions reproduce the breakup angular distributions rather well, apart from a slight overestimation observed for ${}^7\mathrm{Be}$ fragments at forward angles. Analyses of the breakup reactions reveal that the cross section for two-proton-removal from ${}^9\mathrm{C}$ is approximately twice as large as that for one-proton-removal, despite the close proximity of the one- and two-proton separation energies.

We present a comparison of model-space extrapolation methods for No-Core Shell Model calculations of ground-state energies and root-mean-square radii in Li isotopes. In particular, we benchmark the latest machine-learning tools against widely used exponential and infrared extrapolations for energies and crossing point estimates for radii. Our findings demonstrate that, while some machine-learning-based approaches provide reliable predictions with robust statistical uncertainties for both observables even in small model spaces, others perform less consistently. The predictions of the former are compatible with established exponential and infrared extrapolations for energies while also providing a notable improvement over conventional radius estimates.

We employ the Bohr model and nuclear density functional theory to investigate the nuclear structure of the ${}^{116}\mathrm{Sn}$ isotope. Given that vibrational and rotational states are prevalent in midshell nuclei near $Z=50$ with shape coexistence, we applied the $\beta$ and $\gamma$ vibrations of an axially symmetric rotor Hamiltonian to study band mixing. We estimated the mixing of the lowest vibrational and rotational $0^{+}$ and $2^{+}$ states and compared these results with predictions from other models. Our findings indicate that the $\gamma$ bands are significantly more deformed than the $\beta$ bands in ${}^{116}\mathrm{Sn}$.

Theoretical considerations are made for the nuclear excitation from the ground state to the $8\mathrm{eV} {}^{229m}\mathrm{Th}$ isomer via near-resonant electron transitions in Sb-like ($q=39+$) thorium ions. The energy of the first excited atomic state ($J=7/2$) in the ${}^{229}\mathrm{Th}^{39+}$ ion is estimated to be $8.308\pm 0.069\mathrm{eV}$, which is very close to the new reference value for the ${}^{229m}\mathrm{Th}$ nuclear isomer energy, $8.356\mathrm{eV}$ [C. Zhang et al., Nature (London) 633, 63 (2024)]. Therefore, the ${}^{229}\mathrm{Th}^{39+}$ ion provides a unique opportunity to study the nuclear excitation by electron transition process under well-defined atomic conditions in the regime of extremely low nuclear excitation energy. Our results indicate that the upper theoretical limit for the ${}^{229m}\mathrm{Th}$ isomer excitation rate reaches an enormous value of $2.50\times {10}^{16}{\mathrm{s}}^{-1}$ at resonance ($\mathrm{\Delta }=0$ meV), but drops many orders of magnitude for the value of electronic transition energy within its uncertainty interval. Additionally, it was shown that using an electron beam ion trap, the production of the ${}^{229}\mathrm{Th}$ isomer can reach rates ranging from a few to approximately $5\times {10}^{20}{\mathrm{s}}^{-1}$.

Large-scale shell-model calculations are performed for the $9/2_{\mathrm{g}.\mathrm{s}.}^{+}, 1/2_1^{-}, 3/2_1^{-}$, and $5/2_1^{-}$ states in the odd-$A$ indium isotopes with $N=50–82$. The calculated energy levels, electromagnetic moments, and spectroscopic factors exhibit remarkable agreement with the experimental data due to significant configuration mixing for the neutron numbers away from the closed shells. The $1/2_1^{-}$ energy levels closely follow the trend of effective single-particle energies, which are determined using the fractional occupancies of neutron orbitals. However, configuration mixing with the proton $p_{3/2}$ and $f_{5/2}$ orbitals in the actual shell-model calculations plays a crucial role in accurately reproducing the positions of the $1/2_1^{-}$ levels, ensuring better agreement with the experimental data across the entire isotopic chain.

To establish credibility for the use of the Slater determinant harmonic oscillator (SDHO) density in predicting root-mean-square proton and neutron radii for Be, B, C, N, O, and F isotopes [M. Imran et al., Phys. Rev. C 110, 014623 (2024)], in this work we propose to study charge-changing and interaction cross sections for the said isotopes on ${}^{12}\mathrm{C}$ at a wider range of incident energies (200–1050 MeV/nucleon), involving different density distributions; the calculations also assess the importance of nuclear medium effects. Working within the framework of the Glauber model, we involve two-parameter Fermi (2pF) and three-parameter Fermi (3pF) shapes of density distributions, and use the in-medium as well as free behavior of the nucleon-nucleon ($\mathit{NN}$) amplitude. The results provide enough basis to support the matter radii of exotic isotopes obtained using SDHO densities.

We study multiparticle azimuthal correlations in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV. We use initial conditions obtained from a Monte Carlo Glauber model and evolve them within a viscous relativistic hydrodynamics framework that eventually gives way to a transport model in the late hadronic stage of the evolution. We compute the multiparticle symmetric and asymmetric cumulants and present the results for their sensitivity to the shear and bulk viscosities during the hydrodynamic evolution. We also check their sensitivity to resonance decay and hadronic interactions. We demonstrate that while some of these observables are more sensitive to transport properties than traditional flow observables, others are less sensitive, making them suitable for studying different stages of the evolution.