We study uncertainties in the equation of state of neutron stars using conformal prediction as a distribution-free and model-agnostic method that provides coverage guarantees. In particular, we apply the Conformalized Quantile Regression (CQR) method to posterior samples calculated from Bayesian inference, creating reliable uncertainty bands without assuming a specific form of the underlying distribution. We first construct CQR bands using a polytropic equation of state and the Tolman-Oppenheimer-Volkoff equations. We then apply CQR as a postprocessing step to the posterior distribution of neutron star mass-radius relations provided by the NMMA Collaboration and to quantum Monte Carlo calculations of pure neutron matter. In all cases, empirical coverage studies confirm the robustness of the method.

We investigate proton-neutron ($pn$) pairing correlations within a generalized Hartree-Fock-Bogoliubov (HFB) framework using the Gogny D1S energy density functional. When $pn$ mixing is allowed, large single-particle bases trigger numerical instabilities in Gogny D1S due to its zero-range density-dependent term contribution to the $pn$ pairing field, whereas stable solutions are obtained with the Hamiltonian-based Brink-Boecker B1 interaction. Constrained HFB calculations in reduced spaces show that self-consistent minima with Gogny D1S systematically correspond to vanishing $pn$ pairing with total energy rising rapidly as $pn$ pairing correlations are introduced. Furthermore, particle-number restored calculations significantly flatten these HFB energy curves, inducing $pn$ mixing across the collective coordinates within the variation after particle-number projection framework. These results provide key insights into the limitations and behavior of Gogny functionals under generalized HFB conditions, offering guidance for future functional re-parametrizations and beyond-mean-field studies.

Shell model calculations for the neutron-rich $N=126{}^{206}\mathrm{Hg}\text{−}{}^{197}\mathrm{Lu} (Z=80-71)$ isotones were performed with two different parametrizations. The one refined to explain the isomerism in ${}^{204}\mathrm{Pt}$ was found to be the only one able to reproduce the more recent data on ${}^{203}\mathrm{Ir}$ and, in general, to give a better reproduction of the nuclei in this region. For more exotic nuclei approaching the $r$-process path, this refined parametrization predicts the existence of isomeric states with spin-parities $5^{-}$ and ${10}^{+}$ in the even-mass isotones and $19/2^{+}$ in the odd-mass isotones. Also, it predicts ground-state spin-parities of $3/2^{+}$ for ${}^{201}\mathrm{Re}$ and $11/2^{-}$ for ${}^{199}\mathrm{Ta}$ and ${}^{197}\mathrm{Lu}$, with low-energy long-lived isomers present. The remaining deficiencies of the interaction are related to the properties of the $\pi d_{5/2}$ orbital and are influenced by octupole collectivity. The presented predictions provide guidance and can be tested in the near future at radioactive-beam facilities.

The evolution of octupole deformation with rotation and the interleaved positive- and negative-parity bands in the pear-shaped nucleus ${}^{148}\mathrm{Ba}$ are investigated using the three-dimensional lattice cranking relativistic density functional theory, combined with a well-established shell-model-like approach to treat pairing correlations. The experimental $I\text{−}\omega$ relations for the yrast band are well reproduced. Potential energy surface calculations in the $({\beta }_{20},{\beta }_{30})$ plane reveal that the ground state of ${}^{148}\mathrm{Ba}$ possesses an axially symmetric yet reflection-asymmetric shape. Although the octupole deformation gradually decreases with increasing rotational frequency, the average value remains ${\beta }_{30}=0.12$ as the rotational frequency rises to 0.30 MeV, indicating the robustness of octupole shape against nuclear rotation. The evolution of the octupole-deformation proton driving pair $(d_{5/2},h_{11/2})$ and neutron driving pair $(f_{7/2},i_{13/2})$ with rotation is discussed by analyzing the components of single-particle levels in ${}^{148}\mathrm{Ba}$.

The nonlocality of the imaginary part of the microscopic optical potential is investigated for neutron elastic scattering on ${}^{16}\mathrm{O}, {}^{40}\mathrm{Ca}, {}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ at incident energies up to 30 MeV. The potential is derived within the particle-vibration coupling framework using fully self-consistent Skyrme-Hartree-Fock plus random-phase approximation (RPA) calculations with the SLy5 interaction, without ad hoc adjustable parameters. By fitting the nonlocality coordinate dependence of the absorptive potential $W(R,s)\equiv \mathrm{Im}\mathrm{\Delta }\mathrm{\Sigma }$, where $\mathrm{\Delta }\mathrm{\Sigma }$ is the dynamical part of the nucleon self-energy, to a Gaussian form at representative volume and surface radial positions, we extract the radius- and energy-dependent nonlocality function $\beta (R,E)$, whose values range from 1.01 to 2.03 fm, with a clear dependence on radial position, incident energy, and target mass. These results demonstrate that, for the absorptive part of the optical potential, a single universal constant such as the Perey-Buck value $\beta =0.85\mathrm{fm}$ cannot capture the radial, energy, and target-mass dependence of the nonlocality, and that nucleus-dependent, energy-dependent, and radially resolved descriptions of the absorptive potential $W$ are required for precision nuclear reaction calculations.

Background: The role of hexadecapole deformation (${\beta }_4$) in sub-barrier fusion has been studied for the ${}^{16}\mathrm{O}+{}^{174,176}\mathrm{Yb}$ reactions; however, the extracted ${\beta }_4$ values are model dependent and carry systematic uncertainties that remain unresolved.

Purpose: We extend fusion cross-section measurements to the ${}^{16}\mathrm{O}+{}^{170,172}\mathrm{Yb}$ reactions to investigate isotopic dependence of fusion excitation functions and to clarify the role of higher-order static deformations across the complete ${}^{16}\mathrm{O}+{}^{170,172,174,176}\mathrm{Yb}$ isotopic chain.

Method: Evaporation residue (ER) cross sections for ${}^{16}\mathrm{O}+{}^{170,172}\mathrm{Yb}$ were measured from 12% below to 35% above the Coulomb barrier using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. The data are analyzed within the coupled-channels and statistical model frameworks.

Results: A strong sub-barrier fusion enhancement is observed relative to one-dimensional barrier penetration model (1D-BPM) predictions. Coupled-channels calculations incorporating quadrupole and hexadecapole deformations of the target nuclei reproduce the measured fusion excitation functions for both reactions. Statistical model calculations with a single fission-barrier scaling factor $k_f=1.10$ reproduce the ER and fission cross sections simultaneously, over the entire measured energy range. The single-Gaussian barrier-distribution analysis shows that ${}^{16}\mathrm{O}+{}^{174}\mathrm{Yb}$ exhibits the largest sub-barrier enhancement among the ${}^{170,172,174,176}\mathrm{Yb}$ nuclei.

Conclusions: Coupled-channels calculations including both quadrupole ${\beta }_2$ and hexadecapole ${\beta }_4$ deformations of the target nuclei successfully reproduce the measured fusion excitation functions for ${}^{16}\mathrm{O}+{}^{170,172}\mathrm{Yb}$. Our analysis brings out the role of ${\beta }_4$ across the entire range of Yb nuclei. The reproduction of ER and fission excitation functions with $k_f=1.10$ rules out noncompound nuclear fission (NCNF) contributions for both systems. The pronounced sub-barrier enhancement in ${}^{16}\mathrm{O}+{}^{174}\mathrm{Yb}$ is attributed to the midshell character of ${}^{174}\mathrm{Yb}$ ($N$ = 104), where nuclear collectivity is maximal.

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a nonzero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring/sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of $4.90$.

We investigate the crust-core transition in neutron stars using both thermodynamic and dynamical descriptions of the instability. In the thermodynamic approach, the transition is identified through the vanishing of a generalized incompressibility coefficient signaling the onset of a bulk spinodal instability. In contrast, the dynamical approach based on the relativistic random-phase approximation (RPA) incorporates Coulomb screening and finite-size effects that determine the instability at finite wavelength. Using a family of covariant energy density functionals spanning a broad range of symmetry-energy slopes, we show that the dynamical treatment systematically predicts lower transition densities and pressures compared to the thermodynamic approach. We further demonstrate that the RPA instability develops at a characteristic length scale set by the competition among bulk, Coulomb, and surface effects. Most importantly, we show that these differences propagate directly into neutron-star observables. Because the thermodynamic approach predicts larger transition pressures, it generates thicker crusts and significantly larger crustal fractions of the stellar moment of inertia than the dynamical-RPA framework—with important implications for the interpretation of pulsar glitches and other crust-sensitive neutron-star observables.

We propose vortex nucleon scattering as an angular-momentum-resolved probe of nucleon-nucleon partial waves. Using the standard $LSJ$ partial-wave $S$ matrix as input, we show that an on-axis vortex incident state with a fixed orbital angular-momentum projection $m_L=\ell$ imposes the direct selection rule $L\ge \left|\ell \right|$ on the initial nucleon-nucleon partial waves. As a result, the entrance $S$-wave component is excluded for $\ell =1$, while both the initial $S$ and $P$ waves are excluded for $\ell =2$. The underlying phase shifts are not modified. Instead, the vortex external state changes how the ordinary partial waves are projected into the scattering amplitude. We further analyze off-axis scattering, where the displacement of the target from the vortex axis introduces Bessel-function weights and partially relaxes the on-axis selection rule. These results suggest that vortex nucleons can provide a new experimental handle on the partial-wave content of the strong nucleon-nucleon interaction.

Machine-learning approaches can improve nuclear mass modeling, but the most accurate strategies often depend on a theoretical mass baseline or hand-crafted physics features. We test whether a modular architecture encoding selected nuclear-structure priors improves baseline-free direct prediction and yields informative branch diagnostics. The Cooperative Neural Network (CoNN) implements this approach through four form-constrained branches: a smooth macroscopic network, discrete embeddings, a two-dimensional regional grid, and a parity-aware network. It extracts complementary patterns from $(Z,N)$ through these branches and sums their outputs to predict binding energies without a theoretical mass-model baseline. Thus, the model retains physics priors while reducing its reliance on engineered input features. On AME2020, CoNN reaches a root-mean-square deviation (RMSD) of 0.269 MeV for 3558 nuclei, compared with 0.836 MeV for a parameter-matched unstructured multilayer perceptron (MLP). It also gives RMSDs of 0.419 MeV on a held-out interpolation subset and 0.728 MeV on 122 nuclei newly measured since AME2016. The learned branch outputs show recognizable physical patterns, including embedding shell-kink signatures at major magic numbers and odd-even staggering along isotopic chains. These results identify architecture-level priors as a practical route to baseline-free mass prediction, with learned components that help diagnose both nuclear-structure patterns and extrapolation limits.

Nuclear $\beta$-decay energies $Q_{\beta }$ are investigated using the machine learning algorithm LightGBM. By comparing different combinations of physically informed input features, the optimal feature set for predicting $Q_{\beta }$ was obtained. The mean absolute error reached 0.1447 MeV and demonstrated strong interpolation capability in the region of $A>50$. To address the black-box problem, feature analysis is performed using the interpretable Shapley Additive Explanations algorithm tool to determine the impact of different input features on $Q_{\beta }$. Among these features, ${[\left(N\text{−}Z\right)/A]}^2$ is identified as the most significant factor. Unlike traditional symmetry energy terms which rank last, the ${[\left(N\text{−}Z\right)/A]}^2$ term ranks first and improves accuracy. This finding provides that the isospin chemical potential plays a more critical role in the $Q_{\beta }$ process.

Recent advances in experiments have enabled the measurement of $\gamma$ decay from giant and pygmy resonances to low-lying states, establishing this technique as a unique probe for nuclear structure. However, a microscopic description of $\gamma$ decay to low-lying states in superfluid nuclei is still lacking. We develop the Skyrme quasiparticle vibration (QPVC) model to calculate $\gamma$-decay widths between vibrational states. This model treats initial and final states as quasiparticle random-phase-approximation (QRPA) phonons and includes all the second-order diagrams for the interaction between the quasiparticles and the phonons, while consistently accounting for the polarization processes. The same Skyrme functional is employed for the ground state and the interaction vertices. As a timely application, the $\gamma$-decay width from the giant dipole resonance (GDR) to the $2_1^{+}$ state in ${}^{140}\mathrm{Ce}$ is calculated, which has recently been measured at the High Intensity $\gamma$-ray Source ($\mathrm{HI}\gamma \mathrm{S}$). For the 4 Skyrme functionals we used, the total width of the collective dipole states in GDR region is 250–420 eV and the corresponding branching ratio is 0.87–1.18%. The polarization effect, extracted microscopically, agrees in trend with the macroscopic Bohr-Mottelson formula.

Recent experimental results in high-multiplicity proton-proton ($\mathit{pp}$) collisions have suggested the possible emergence of collective behavior and medium-like effects previously considered characteristic of heavy-ion collisions. Resonance production provides a sensitive probe of such effects, as resonance yields and transverse-momentum distributions can be modified by hadronic interactions occurring between chemical and kinetic freeze-out. In this study, these effects are investigated using the EPOS4 event generator, in which hadronic final-state interactions are modeled through the ultrarelativistic quantum molecular dynamics (UrQMD) transport approach. By comparing calculations performed with and without UrQMD, the impact of hadronic interactions on resonance production is evaluated. In addition, the UrQMD contributions are separated into regeneration and rescattering, enabling a detailed investigation of both resonance production enhancement and the loss of reconstructible resonance signals. The analysis is performed for various mesonic and baryonic resonances with different lifetimes in $\mathit{pp}$ collisions at energies available at the Large Hadron Collider and is extended to $p\mathrm{O}$, OO, and Pb-Pb collisions to study the system-size dependence of hadronic-phase effects. The results show that resonance production is governed by the competition between regeneration and rescattering, whose relative importance depends strongly on the resonance species, transverse momentum, and collision system. While rescattering suppresses reconstructible short-lived resonance signals, regeneration can significantly enhance the yields of several resonance species, particularly baryonic resonances. These findings demonstrate that hadronic interactions can play an important role even in small collision systems and highlight the need to measure resonances with different lifetimes and quantum numbers to constrain the dynamics and lifetime of the hadronic phase across collision systems.

Excited states of semimagic ${}^{50}\mathrm{Ti}$ were studied up to the neutron-separation energy via the $(d,p)$ and $(d,p\gamma )$ reactions. In total, 82 excited states were identified based on the measurement of angular distributions with the Super-Enge Split-Pole Spectrograph at Florida State University. From the experimental data, sum rules related to vacancies were calculated for the $2p_{3/2}$, $2p_{1/2}$, $1f_{5/2}$, $1g_{9/2}$, and $2d_{5/2}$ neutron single-particle orbitals and compared with predictions obtained with the time-dependent continuum shell model, the quasiparticle-phonon model, and the relativistic equation of motion theory. A comparison for the $(d,p)$ data obtained for ${}^{51}\mathrm{Ti}$ and ${}^{50}\mathrm{Ti}$ is also presented, focusing on differences in the single-particle strength fragmentation in even-$A$ and odd-$A$ nuclei.

The CREX and PREX-II measurements of the neutron-skin thickness of ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ challenge standard nuclear energy-density functional (EDF) descriptions of nuclei and nuclear matter. It is shown that the apparent tension arises from an implicit constraint in current EDF parametrizations that ties the density dependence of the functional at the dilute nuclear surface to that of uniform matter near saturation. Relaxing this surface-bulk coupling and independently constraining the dilute-density sector, while preserving realistic saturation properties and the high-density equation of state, yields EDFs that simultaneously reproduce the neutron skins of both nuclei, their electric dipole polarizabilities, and neutron-star mass-radius relations. The established correlation between the neutron-skin thickness and the symmetry-energy slope parameter $L$ at saturation is retained but becomes substantially broader. The results show that current neutron-skin data do not require extreme values of $L$ and highlight an underconstrained degree of freedom associated with low-density nuclear matter.

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multicomponent matrix form. A relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density)—a long-standing problem in relativistic hydrodynamics.