The intermediate neutron-capture process ($i$ process) has gained notable traction within the past decade as a way to describe stellar abundance observations which cannot be explained by the slow and rapid neutron-capture processes. Despite the general success of $i$-process models, many open questions remain. Among the observations, Zr stands out, as its elemental abundance is difficult to replicate with available $i$-process models, while the reactions that affect its production through the $i$ process are close enough to stability to study experimentally. Here, we present the experimental constraint of the nuclear level density and $\gamma$-strength function ($\gamma \mathrm{SF}$) of ${}^{91}\mathrm{Sr}$ using the $\beta$-Oslo method, which were then input into the TALYS Hauser-Feshbach code to produce the first experimental constraint of the ${}^{90}\mathrm{Sr}(n,\gamma ){}^{91}\mathrm{Sr}$ capture reaction. This constraint was used alongside that of ${}^{92}\mathrm{Sr}(n,\gamma ){}^{93}\mathrm{Sr}$ for a reduction in the uncertainty of [Y/Zr] production in the $i$-process relevant environmental neutron density of ${10}^{13.5}$ and ${10}^{14.5} \text{neutrons}/{\mathrm{cm}}^3$.

Alpha decay, a fundamental quantum mechanical phenomenon, serves as a vital tool for exploring nuclear decay properties and stability. In this study, we developed machine learning models based on Random Forest (RF), Support Vector Regression (SVR), and Deep Neural Network (DNN) techniques to predict alpha decay half-life ($T_{1/2}$). A transfer learning (TL) framework is introduced, wherein a pretrained alpha decay energy ($Q_{\alpha }$) model serves as an input for half-life prediction, improving both accuracy and computational efficiency. The performance of RF, SVR, and DNN models are rigorously evaluated using the $R^2$ test to confirm the absence of overfitting or underfitting, with RF emerging as the most robust and reliable model for half-life prediction model. Multiple RF models with varying feature sets are developed to assess the impact of input features, and SHAP (SHapley Additive exPlanations) values is utilized to quantify the influence of each feature on model output. The TL-RF model incorporating $Q\alpha$, neutron number (N), proton number (Z), pairing factor ($\delta$), and promiscuity factor (P) are identified as the optimal-feature space, achieving the lowest root mean square deviation ($\sigma =0.2$). Furthermore, the TL-RF model is extended to the superheavy region, revealing enhanced nuclear stability near $N=184$, supporting its potential as the next magic number beyond 126, also highlighting an additional zone of relative stability in the neutron range $N=158-162$. These findings underscore the effectiveness of transfer-learning-driven machine learning approaches in nuclear physics, offering valuable insights into nuclear decay properties and the stability of exotic nuclei.

Two-proton ($2p$) radioactivity constitutes a pivotal probe for studying the nuclear structure of extreme proton-rich nuclei. To improve the calculated accuracy and predictive power of the generalized liquid drop model (GLDM) for describing the $2p$ radioactivity half-lives, this work performs a systematic study within the GLDM framework using distinct proximity energies. It is found that the proximity energy can counterbalance the Coulomb repulsion, lowering the barrier height and simultaneously shifting its peak to larger radial separations. Consequently, the specific proximity energy employed governs both the height and shape of the interaction barrier, thereby dictating the penetration probability, and ultimately, the $2p$ radioactivity half-life. Among all considered proximity energy formalisms, the Prox. 77-Set 13 yields the smallest standard deviation when reproducing experimental data for known true $2p$ emitters, representing an improvement over the original proximity potential. The spectroscopic factor of $2p$ radioactivity $S_{2p}$ is found to be essential for reducing systematic deviations. Using the GLDM with Prox. 77-Set 13, we predict $2p$ radioactivity half-lives for candidate nuclei. The predictions agree well with those from other established models and validate the newly proposed Geiger-Nuttall law for $2p$ radioactivity. This work would provide reference for future experimental investigations of $2p$ radioactivity in proton-rich nuclei.

The dependence of the $E2$ matrix elements on isospin projection $T_z$ is linked to the conservation of the isospin symmetry. To study this conjecture, we calculated the $B(E2:2^{+}\to 0^{+})$ rates for the even-even $T=1$ mirror nuclei with 42 $\le A \le$ 98 within nuclear density functional theory, employing the generalized Bohr Hamiltonian, and carrying out angular momentum projection. We demonstrated that collective effects are crucial for describing experimental data near the $N=Z$ line without invoking explicit beyond-Coulomb isospin symmetry-breaking corrections. We also determined the $B(E2\downarrow )$ values for odd-odd $T_z=0$ nuclei ${}^{70}\mathrm{Br}$ and ${}^{78}\mathrm{Y}$ in doubly blocked configurations. We discussed the requirements for accurately describing isobaric analog states and emphasized how current theoretical results should be interpreted within the study of isospin symmetry across isospin triplets.

Background: The low-energy enhancement observed in the deexcitation $\gamma$-ray strength functions, attributed to magnetic dipole ($M1$) radiations, has spurred theoretical efforts to improve on its description. Among the most widely used approaches are the quasiparticle random-phase approximation (QRPA) and its extensions. However, these methods often struggle to reproduce the correct behavior of the $M1$ strength at the lowest $\gamma$ energies. An alternative framework, the projected generator coordinate method (PGCM), offers significant advantages over QRPA by restoring broken symmetries and incorporating both vibrational and rotational dynamics within a unified description. Due to these features, PGCM has been proposed as a promising tool to study the low-energy $M1$ strength function in atomic nuclei. However, comprehensive investigations employing this method are lacking.

Purpose: The PGCM is developed and tested in its description of $1^{+}$ excited states in even-even nuclei, along with the $M1$ transitions connecting them to the $0^{+}$ ground state.

Methods: The PGCM is presently used within the frame of $sd$-shell valence space calculations based on the USDB shell-model interaction to benchmark its performance against the solutions obtained via exact diagonalization, i.e., results from the latter are considered as “exact” reference results in the present study. The reliability of two different sets of generator coordinates in the PGCM calculations is gauged using ${}^{24}\mathrm{Mg}$ as a test case.

Results: Energies and $M1$ transition strengths of the lowest excited $1^{+}$ states extracted from the PGCM calculation reproduce well the exact results for both sets of collective coordinates. Eventually, PGCM accurately models the exact level density and cumulative $B\left(M1\right)$ strength up to about 20-MeV excitation energy in all considered nuclei.

Conclusions: The ability of the PGCM to reproduce results from exact diagonalization in the $sd$ valence space is demonstrated for $1^{+}$ states and $M1$ transitions. Future work will need to assess whether the proposed method can be applied systematically and extended to large-scale calculations while maintaining a reasonable computational cost.

Nuclear excitation assisted by lasers holds broad application prospects in precision metrology and nuclear energy, such as nuclear batteries and nuclear clocks. In the present work, the nuclear excitation via inelastic electron scattering (NEIES) mechanism in ${}^{235}\mathrm{U}$ is investigated by combining the Dirac-Hartree-Fock-Slater method for theoretical calculations with 2D3V particle-in-cell (PIC) simulations for numerical modeling. The excitation cross sections of ${}^{235}\mathrm{U}$ from the ground state to excited states is evaluated, and an efficient indirect excitation scheme for generating ${}^{235}\mathrm{U}$ isomers is proposed by first exciting the nuclei from ground-state to high-energy excited states and then decaying to the isomeric state. The calculations show that laser-tuned multichannel NEIES can boost isomeric state accumulation efficiency by 11 orders of magnitude over direct excitation. Additionally, PIC simulations reveal that laser polarization significantly alters high-energy electron distributions. At identical intensity, $p$-polarized lasers generate seven times more electrons with energies sufficient for exciting ${}^{235}\mathrm{U}$ to the second excited state (and beyond to the fourth state) compared to $s$ polarization. This work offers a practical and feasible way for efficient isomeric state generation, supporting experimental tests of laser-assisted nuclear excitation.

This work applies a reduced basis method to study the continuum physics of a finite quantum system—either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [Zhang, Phys. Rev. Lett. 135, 242501 (2025)], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

Data for near-barrier ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ inelastic scattering to the 2.60-MeV $3_1^{-}$ level of ${}^{208}\mathrm{Pb}$ have proved difficult to fit within the distorted-wave Born approximation (DWBA) or coupled-channel (CC) formalisms employing collective model form factors. In particular, the data for incident energies in the vicinity of the so-called threshold anomaly proved impossible to describe without introducing an unphysically large quadrupole reorientation term into CC calculations, even when allowing the nuclear deformation lengths to vary with the incident energy. In this work a satisfactory description of the elastic and inelastic scattering for a range of energies close to the Coulomb barrier was obtained with fixed coupling strengths derived from the results of a recent Coulomb excitation measurement. The description of the data was insensitive to the inclusion of the small quadrupole reorientation term for the $3_1^{-}$ level consistent with the strength derived from the Coulomb excitation measurement. Coupled-channel calculations employing the same coupling scheme and coupling strengths were able to describe well near-barrier $\alpha +{}^{208}\mathrm{Pb}$ elastic and inelastic scattering data. Simultaneous minimization of ${\chi }^2$ for elastic and inelastic scattering was crucial to obtaining a good description of the ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ data with either DWBA or CC calculations.

Determining the transport properties of quark-gluon plasma is one of the most important aspects of relativistic heavy ion collision studies. Field-theoretical calculations of transport coefficients such as the shear and bulk viscosities require Kubo formulas, which in turn require real-time correlation functions of stress-energy tensors. Consequently, knowing the analytic structure of these correlation functions is essential in any such studies. Using the energy-conservation laws and the results from gravity-hydrodynamics analysis, we determine the low-frequency and low-wavenumber analytic structures of all stress-energy correlation functions in the rest frame of the medium. By comparing with the diffusion and sound spectra from the second-order and third-order relativistic hydrodynamics, various new Kubo formulas are derived in the limit where the zero-frequency limit is taken first. We also show that the meaning of the Kubo formulas for relaxation times can change when higher-order terms are added to the hydrodynamics. A subtle issue of taking the zero frequency and zero wave0number limits when using skeleton diagrams is addressed as well.

We compute the density dependence of in-medium pion properties, such as mass, wave function renormalization, and decay constant in the correlation function approach, and how they change under the influence of isospin-asymmetric nuclear matter. To this end, we use in-medium chiral perturbation theory to compute the relevant Feynman diagrams up to two-loop diagrams. Our results show that the isospin asymmetry of the nuclear matter splits these quantities into three separate values, corresponding to the three pions. Consequently, the tendency of each in-medium pion mass, wave function renormalization, and decay constant is dependent on the density and the neutron-to-proton ratio ${\rho }_n/{\rho }_p$ of nuclear matter. We also derive an in-medium Gell-Mann–Oakes–Renner relation which is valid for isospin-asymmetric nuclear matter and investigate to what extent it holds within our calculations.

The main observables of the rare two-proton emission process—half-life, total energy of the decay, as well as energy and angular correlations between the emitted protons—have been measured for ${}^{48}\mathrm{Ni}$ and ${}^{45}\mathrm{Fe}$ in a recent experiment performed at the GANIL/LISE3 facility. The results, together with previous experimental work, are compared for the first time with calculations performed in the recently developed Gamow coupled-channel (GCC) framework and with three-body predictions from the literature. The comparison with the ${}^{48}\mathrm{Ni}$ and the ${}^{45}\mathrm{Fe}$ two-proton angular distributions with the GCC calculations confirms the adopted strength of the proton-proton interaction for both nuclei, and the predominance of emission at small angles. A comparison with three-body model angular distributions indicates the shell closure of the $f_{7/2}$ orbital for ${}^{48}\mathrm{Ni}$ and a substantial occupancy of the $p$ orbital for ${}^{45}\mathrm{Fe}$. Discrepancies between experimental data and theoretical predictions arise when studying the other observables: half-lives, total energy of the decay, and energy correlations, showing the complexity of the description of the two-proton emission process.

We present a measurement of elemental fragmentation cross sections (EFCSs) for ${}^{32-38}\mathrm{S}$ on a carbon target at approximately 200 MeV/nucleon. Our measurement, together with existing data, reveals a universal trend toward unity in the odd-even staggering (OES) magnitude of the EFCSs with increasing projectile isospin and consistency in its strength variation across different isotopic chains. This is well reproduced by the isospin-dependent quantum molecular dynamics model coupled with the GEMINI evaporation model (IQMD+GEMINI). The magnitude of OES exhibits a dependence on the excitation energy distribution (EED) of prefragments in the collision phase, providing a potential method for evaluating the EED using high-precision EFCS data.

In the framework of relativistic-mean-field (RMF) models, we investigate the properties of light and heavy $\mathrm{\Lambda }$ hyperclusters emersed in nuclear matter at various densities $n_{\mathrm{gas}}$ and proton fractions $Y_p$. In particular, the (hyper)clusters are fixed by solving the Dirac equations imposing the Dirichlet-Neumann boundary condition, while the nuclear matter take constant densities and is treated with Thomas-Fermi approximation. The binding energies of (hyper)clusters decrease with the density of nuclear matter $n_{\mathrm{gas}}$, which eventually become unbound and melt in the presence of nuclear medium, i.e., Mott transition. For light clusters with proton numbers $N_p<4$, with the addition of $\mathrm{\Lambda }$ hyperons, the binding energies per baryon for $\mathrm{\Lambda }$ hyperclusters become smaller and decrease faster with $n_{\mathrm{gas}}$ due to the weaker $N\text{−}\mathrm{\Lambda }$ attraction. For heavy clusters with $N_p\ge 4$, on the contrary, the addition of $\mathrm{\Lambda }$ hyperons increases the stability of (hyper)clusters so that the Mott transition density becomes larger as nucleons occupying higher energy states while $\mathrm{\Lambda }$ hyperons remain in the $1s_{1/2}$ orbital. The isovector effects on (hyper)clusters in nuclear medium are also identified, where the binding energies for (hyper)clusters with $N_p>N_n$ ($N_p<N_n$) increase (decrease) with $Y_p$. For those predicted by nonlinear relativistic density functionals, light (hyper)clusters are destabilized drastically as $n_{\mathrm{gas}}$ increases, while the binding energies of heavier (hyper)clusters vary smoothly with $n_{\mathrm{gas}}$. The binding energy shifts of various (hyper)clusters due to the impact of nuclear medium are fitted to an analytical formula, which could be employed to examine the evolutions of (hyper)clusters in both heavy-ion collisions and neutron stars.

We present a new method for constructing the total angular momentum of many-nucleon states. We find that the restrictions imposed by the fermion antisymmetry on the total state are fully absorbed into the single-$j$ space when the broken rotational symmetry of the product state is restored by angular momentum projection. For different $j$ shells, any total angular momentum that obeys the selection rule is allowed, just as for nonidentical particles. The method based on this reorganization is conceptually different from the traditional $J$ and $m$ schemes and may help to improve the efficiency of angular momentum coupling in nuclear many-body calculations.

We present a systematic survey of even-even nuclei with $Z>50$ to identify where a very large prolate configuration driven by the second intruder orbit emerges. Within the energy density functional theory framework, we find in representative cases a pronounced prolate minimum at quadrupole deformation ${\beta }_2\approx$ 0.3–0.4. A characteristic feature of these minima is a local enhancement of the hexadecapole (${\beta }_4$) component relative to nearby deformations, which is a clear fingerprint of the ${\beta }_2\text{−}{\beta }_4$ coupling expected for the second intruder orbit. Representative comparisons among three Skyrme interactions show a similar appearance of the highly deformed minimum and a local enhancement of ${\beta }_4$ at the prolate minimum, indicating qualitative robustness with respect to the interaction. The resulting maps highlight specific heavy nuclei where highly deformed ground states are anticipated.

In the framework of dinuclear system model, we analyze the effects of barrier distribution on the synthesis of superheavy nuclei. The capture cross sections and evaporation residual cross sections for the production of superheavy nuclei with $Z=112–118$ are calculated within two barrier distributions, and a comparison with experimental data is given. Our calculations demonstrate the effects of two barrier distributions on production cross sections mainly at a lower incident energy, corresponding to the 2n and 3n evaporation channel. Both barrier distributions exhibit minimal impact on the optimal incident energy across each exit channel. The uncertainties caused by two barrier distributions are estimated for the production of unknown superheavy nuclei with $Z=119$ and $Z=120$.

Observations from high-multiplicity proton-lead ($p$-Pb) collisions indicate that small systems may exhibit collective behavior in both heavy and light hadrons. This work investigates the roles of initial- and final-state interactions in shaping the nuclear modification factor and elliptic flow of $D$ mesons measured in $p$-Pb collisions. Initial-state effects, including the Cronin and shadowing effects, are considered in the heavy-quark initial conditions, while final-state interactions are simulated through Langevin evolution combined with the coalescence model of hadronization. Different initial geometries attributed to fluctuations in the medium's energy density are parametrized and translated into the momentum anisotropies of both light and heavy quarks. The corresponding $R_{p\mathrm{Pb}}$ and $v_2$ of $D$ mesons in 8.16 TeV $p$-Pb collisions are calculated under different assumptions for the final-state interactions. Assuming that the initial-state effects only modify the transverse-momentum spectra without altering the azimuthal distribution of heavy quarks, the measured $R_{p\mathrm{Pb}}$ of $D$ mesons can be qualitatively reproduced by the combined influence of initial- and final-state effects. However, the observed $v_2$ cannot be accounted for by final-state interactions alone. These results suggest that additional contributions to azimuthal anisotropies of heavy quarks originating from initial-state effects are required to explain the experimentally observed $v_2$.

We investigate how higher-order symmetry-energy coefficients of the equation of state (EOS) describing $npe\mu$ core matter impact key neutron star (NS) properties at its crust inner edge, its moment of inertia and corresponding crustal fraction, threshold conditions for direct Urca process, adiabatic index, and related structure observables. Our analysis employs a comprehensive set of CDM3Y-IVF1 equations of state, derived from the M3Y-Paris nucleon-nucleon interaction within a nonrelativistic Hartree-Fock framework, covering a wide range of nuclear matter isoscalar stiffness from soft ($K_0=150$ MeV) to extremely stiff (330 MeV) regimes. Our analysis reveals that the stiffer EOS characterized by higher isoscalar incompressibility ($K_0$) and fourth-order symmetry-energy skewness ($Q_4$) coefficients, coupled with diminished negative values of isoscalar $Q_0$ and $H_0$, and isovector $K_4, K_{\tau 4}, I_{2,4}$, and $G_2$ coefficients, systematically increase the estimated core-crust transition pressure, density, and charged-particle ($p,e,\mu$) fractions, and their threshold values for direct Urca process, as well as the total NS moment of inertia and its crustal fraction, and the central adiabatic index. Simultaneously, they yield less central fraction of $p, e$, and $\mu$, and reduced fractional crust thickness and moment of inertia for the maximum NS mass supported by a certain EOS. Conversely, enhanced values of the isoscalar kurtosis $I_0$ and $G_0$ symmetry coefficients, and of the higher-order $Q_2, H_2, K_6$, and $K_{\tau 6}$ coefficients, combined with diminished negative contributions from $K_2$ and $K_{\tau 2}$, produce systematically opposite effects on the mentioned NS quantities, reversing their trends with $K_0$.

We investigate an anomalous collective motion in atomic nuclei observed in recent experiments, characterized by three distinct signatures: (1) an excitation energy ratio $R_{4/2}>2$, (2) sizable electric-quadrupole transition strengths $B\left(E2\right)$ in low-lying states, and (3) a suppressed ratio $B_{4/2}\equiv B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})<1$. This pattern challenges the prevailing understanding of nuclear theory because it contradicts all established collective models as well as microscopic models in nuclear physics. Using the full configuration-interaction shell model combined with the two-body random ensemble, we show that such an anomalous rotational mode emerges naturally in a small fraction of random many-body systems, providing critical insights into the connection between triaxiality and the emergent collectivity. The anomaly can arise from strong mixing between the $4^{+}$ states in the ground-state band and the triaxiality-induced $\gamma$ band in the SU(3) dynamical symmetry. These findings underscore the necessity of incorporating triaxial degrees of freedom in descriptions of nuclear collectivity and the critical role of the residual two-body interactions in inducing the rare collective mode with mixed nature.

The possible bound state of the ${}_{c\overline{c}}{}^9\mathrm{Be}$, a charmonium-nucleus system, is investigated. The analysis is carried out within a three-cluster model, where its binary subsystems are represented as $c\overline{c}\text{+}\alpha$ and $\alpha +\alpha$. The hyperspherical harmonics method is employed to facilitate a convenient description of this three-cluster configuration. The calculations are done by employing the effective $c\overline{c}\text{−}\alpha$ potentials. These potentials were derived recently based on state-of-the-art lattice QCD calculations by HAL collaboration, which provided interactions for the spin-3/2 $J/\psi N$, spin-1/2 $J/\psi N$, spin-1/2 ${\eta }_{c}N$, and spin-averaged $J/\psi N$ interactions, all obtained with nearly physical pion masses. The Coulomb interaction was also incorporated into the current calculations. It is determined that, despite neither the ${}_{c\overline{c}}{}^5\mathrm{He}$ nor the ${}^8\mathrm{Be}$ binary subsystems being bound, a bound state of the $c\overline{c}\text{−}\alpha \alpha$ nuclear system could potentially exist. The maximum central binding energy is found to be approximately 1.71 MeV, based on the spin-1/2 $J/\psi N$ interaction, while a minimum value of about 0.56 MeV is obtained from calculations involving the spin-1/2 ${\eta }_{c}N$ interaction.