This paper presents a high-precision Nyström quadrature-discretization method for the coordinate-space Lippmann-Schwinger equation. While the direct application of the Nyström approach is hampered by the derivative jump in the free Green's function, a robust subtraction and smoothing procedure is introduced to regularize this discontinuity. Tested on $p$- and $d$-wave scattering for two model potentials, this regularization is shown to be essential for numerical stability, yielding 8-digit accuracy for the partial-wave $S$ matrices with a relatively small set of quadrature points. Because full Nyström matrices can become computationally prohibitive for large-scale applications, there exists a need for contracting this high-fidelity information into a more compact representation. Petrov-Galerkin approaches appear appropriate for this purpose. Among many possibilities, the Bateman approximation, Schwinger variational method and Newton variational method appear especially promising. Bateman method for the resolvent is of interest because an interesting connection exists between Nyström and Bateman methods. Numerical results confirm that the Bateman procedure successfully reduces the information content of large-scale Nyström calculations into a compact form with reasonable accuracy, while the Schwinger and Newton variational methods exhibit even higher efficiency in this reduction task. This compression of high-fidelity Nyström information into a minimal basis resembles the data-contraction techniques prevalent in modern machine learning and emulation.

While chiral perturbation theory for mesons is characterized by a momentum expansion in $Q/{\mathrm{\Lambda }}_{\chi }$ with ${\mathrm{\Lambda }}_{\chi }\approx 1\mathrm{GeV}$, existing formulations of effective theory for nucleon-nucleon scattering deviate from data at $Q\approx 300\mathrm{MeV}$ or lower. We offer heuristic evidence that unsuspected nonanalytic structure exists in the complex momentum plane obstructing the effective field theory expansion in the spin-triplet channels, associated with the peak of the angular-momentum barrier whose energy in low partial waves satisfies $k=\sqrt{ME}\approx 300\mathrm{MeV}$. With this motivation, we construct a meromorphic function of $k^2$ we call the $C$-matrix, for which the radius of convergence of its Taylor expansion in $k^2$ is equivalent to that of the momentum expansion of the effective field theory. Thus the range of validity of the effective theory is directly related to the pole structure of the $C$-matrix. We uncover that pole structure and confirm that it is the source of the obstruction. The systematic inclusion of dimer fields as propagating degrees of freedom in the effective theory to account for those poles results in cutoff insensitive fits at order $Q^0$ to most of the lower partial-wave phase shifts up to the pion production threshold, using only the one pion exchange part of the long-range nucleon-nucleon interaction. Our theory should be applicable to the singular potentials regularly found in atomic physics as well.

The possible antimagnetic rotation in the $N=46$ odd-$A$ isotones ${}^{83}\mathrm{Rb}$ and ${}^{85}\mathrm{Y}$ is investigated using the cranked shell model combined with a particle-number-conserving method. For the positive-parity yrast bands in the two isotones, the angular-momentum alignments are reproduced well. The configurations of high-spin part in both bands are determined as $\pi g_{9/2}\otimes \nu g_{9/2}^{-4}$, by analyzing the occupation probability of each cranked Nilsson orbital near the Fermi surface. The calculated $B\left(E2\right)$ values are small and decrease with the increasing rotational frequency, in agreement with the experiments; meanwhile, the two-shears-like mechanism is exhibited clearly. Therefore, the high-spin parts of the two bands, built on $\pi g_{9/2}\otimes \nu g_{9/2}^{-4}$ configuration, match the criteria of antimagnetic rotation, which is the first time that the antimagnetic rotation is revealed for odd-$A$ nuclei in the $A\approx 80$ mass region.

A configuration-interaction time-dependent density functional theory (CI-TDDFT) for nuclear dynamics is developed. In this framework, the correlated nuclear many-body wave function is expanded in terms of time-dependent many-particle configurations built from a common set of orthonormal single-particle states. The equations of motion for both the expansion coefficients and the single-particle states are derived self-consistently using the Dirac-Frenkel time-dependent variational principle. This formulation extends conventional time-dependent density functional theory (TDDFT) by incorporating configuration mixing and beyond-mean-field correlations, while preserving energy and particle-number conservation. As an illustrative application, the method is implemented using the relativistic point-coupling functional PC-PK1 in the particle-hole channel and a monopole pairing interaction in the particle-particle channel and is applied to the study of isoscalar giant monopole resonance in ${}^{58}\mathrm{Ni}$ and ${}^{60}\mathrm{Ni}$. Numerical tests show that both the total energy and particle number are conserved, with relative deviations within $4\times {10}^{-4}$ during the time evolution. Compared with conventional TDDFT, CI-TDDFT yields broader strength distributions for giant monopole resonances while keeping the main peak positions close to those from TDDFT. This broadening is associated with configuration mixing in the valence space and suggests a coupling of the monopole oscillation to additional collective degrees of freedom. These results demonstrate the potential of CI-TDDFT as a quantum, microscopic beyond-mean-field framework for nuclear dynamics.

Within the framework of Lanzhou quantum molecular dynamics transport model, the cluster dynamics and double differential cross sections in the spallation reactions have been systematically investigated. The cluster yields are contributed from the preequilibrium emission in the cascade collisions and from the statistical decay via the hot fragments, in which the surface coalescence and GEMINI statistical decay are used for the cluster production. The spallation reactions of proton, deuteron, triton, ${}^3\mathrm{He}$, and $\alpha$ on ${}^{208}\mathrm{Pb}, {}^{209}\mathrm{Bi}$, and ${}^{232}\mathrm{Th}$ are systematically investigated. It is demonstrated that the energetic clusters are mainly contributed from the preequilibrium emission, in particular, at the kinetic energies above 30 MeV. The more bound nucleus is available for the production in the spallation reactions, i.e., the larger yields for $\alpha$ in comparison with ${}^3\mathrm{He}$. The kinetic energy tail of cluster production is enhanced with increasing beam energy. The low-energy clusters are mainly produced from the decay of hot fragments and correlated with the energy deposition of incident nuclides. The experimental double differential cross sections are well reproduced within the combined approach.

We perform a theoretical study of intermediate-energy quasifree one-proton knockout reactions on proton targets. Single-particle wave functions constrained by the experimental proton separation energies are employed to calculate longitudinal momentum distributions, one-proton removal cross sections, and full momentum-space profiles for ${}^{26}\mathrm{P}, {}^{27}\mathrm{S}$, and ${}^{31}\mathrm{Ar}$ nuclei. To establish robust criteria to identify proton halos, the analysis is extended beyond the traditional momentum-width approach by investigating the spatial extension of the valence proton through root-mean-square radii and the probability that the proton resides outside the core nucleus, $P(r>R_{\mathrm{core}})$. We also examine Coulomb-barrier systematics, mirror-nucleus comparisons, realistic spectroscopic mixtures, finite experimental momentum resolution, and uncertainties associated with the proton separation energy. Our calculations indicate that proton-halo structure cannot be identified reliably from a single observable. A consistent interpretation emerges only when momentum distributions, spatial observables, Coulomb effects, and many-body structure are considered simultaneously. Within the present model, ${}^{26}\mathrm{P}$ exhibits the strongest proton-halo signatures, while ${}^{27}\mathrm{S}$ retains pronounced halolike features despite its larger Coulomb barrier. The more strongly confined ${}^{31}\mathrm{Ar}$ provides a useful comparison and illustrates the progressive suppression of halo observables with increasing binding and core charge.

This study validates and generalizes the intermediate-energy α-induced reaction model originally developed in [Phys. Rev. C 112, 024616 (2025)]. We measured double-differential cross sections for five emission channels ($p, d, t, {}^3\mathrm{He}$ and α) using C and Co targets at 230 MeV/u. By optimizing the transition impact parameter $b_{\mathrm{tr}}$ for each target, it was found to be expressed as $1.2R-3a$, where $R$ is the nuclear radius and $a$ is the diffuseness parameter, reflecting the nuclear-size dependence. The model, employing this universal formulation, successfully reproduced the new experimental data. Furthermore, using the parameters determined from the 230 MeV/u data, the model was tested against existing data at different incident energies up to 800 MeV/u; remarkably, it demonstrated high predictive accuracy without any additional parameter adjustments.

The excited states of ${}^{209}\mathrm{Po}$ have been investigated via the ${}^{208}\mathrm{Pb}(\alpha ,3n){}^{209}\mathrm{Po}$ reaction, at a beam energy of 40 MeV delivered by the K-130 cyclotron at the Variable Energy Cyclotron Centre, Kolkata. The deexcited $\gamma$ rays were detected with the Compton-suppressed clover high-purity germanium detectors of the Indian National Gamma Array setup. The level scheme has been significantly extended by identification and placement of 63 new $\gamma$-ray transitions. The spin-parity assignments of the different levels have been carried out on the basis of directional correlation of oriented states and polarization asymmetry measurements. Additionally, the possible presence of an isomeric state at a spin of $23/2^{+}$ has been indicated. Large-scale shell model calculations have been performed, with the inclusion of excitations of neutrons across the $N=126$ core, and compared with the experimental results.

One-proton emission is a direct probe of nuclear structure near the proton drip line and plays a critical role in understanding exotic decay modes and nucleosynthesis processes. In this study, we investigate the half-lives of one-proton emitters for $71\le Z\le 83$ odd-$Z$ nuclei by employing the WKB approximation with nuclear potentials obtained from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and, for comparison, the relativistic continuum Hartree-Bogoliubov theory. We first compare the calculated half-lives with available experimental data. The inclusion of quadrupole deformation via the DRHBc hardly contributes to improving the predictions of half-lives for the deformed nuclei. We find that all the studied nuclei exhibit ground states with $|{\beta }_{2,\mathrm{DRHBc}}|<0.15$, and within this limited deformation range the spectroscopic factor provides the dominant contribution to the half-life, compared to the decay width. In particular, for nuclei exhibiting shape coexistence in DRHBc, such as ${}^{170}\mathrm{Au}$, where the half-life varies significantly with the quadrupole deformation through its effect on the spectroscopic factor, we expect shape coexistence to exert a substantial influence on the variation of half-lives. Finally, we discuss the half-lives in consideration of shape coexistence. Our results indicate that the calculated half-life is governed not by the total-energy difference between coexisting minima but rather by the spectroscopic factor influenced by the deformation.

Studies of the isoscalar giant monopole resonance (ISGMR) across the chart of nuclides provide insight into the incompressibility of nuclear matter near saturation density, $K_{\infty }$. Such studies had revealed a discrepancy between theoretical approaches: quasiparticle random-phase approximation (QRPA) derived from Skyrme interactions reproduce the strength distributions of the ISGMR in the “doubly-closed-shell” nuclei ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$, but their descriptions of strength distributions in open-shell medium-heavy nuclei suggest higher centroid energies should be experimentally observed. The latter nuclei required a smaller $K_{\infty }$ and were thus deemed “softer.” The present work serves to add to this “softness” discourse by extracting ISGMR strength distributions for ${}^{104,106,108,110}\mathrm{Pd}$ via 386-MeV inelastic $\alpha$ scattering. The extracted giant resonance strength distributions are consistent with expectations in this isotopic range. Additional quasiparticle vibration coupling (QPVC) effects are included with the QRPA approach and compared to aforementioned ISGMR strength distributions.

Islands of inversion occur when the nuclear ground state is dominated by intruder configurations, specifically particle-hole excitations across shell gaps, rather than by the naive spherical shell-model expectation of filled shell configurations. Using the realistic and rigorous no-core shell model, we are able to confirm that deformation drives these intruder states in the light halo nuclides ${}^{11}\mathrm{Li}$ and ${}^{29}\mathrm{F}$. In small model spaces, these deformed intruders lie high in energy with respect to spherical normal states; as the model space size increases, the intruders energetically approach, albeit slowly, the normal states. This provides further strong evidence of the connection between shape deformation or coexistence and islands of inversion, as well as demonstrating the computational challenges in rigorously modeling this phenomenon. Our results also suggest halo states can be strongly deformed and/or strongly mixed with normal spherical states.

We have employed Bayesian inference to extract the centroid energies and widths from the isovector giant dipole resonance (IVGDR) data for the IVGDR built on the ground states of nuclei. These IVGDR properties were modeled by explicitly incorporating the structural effects like isospin asymmetry, nuclear deformation, and shell correction. The resulting parametrizations reproduce the IVGDR systematics with remarkable precision for both spherical and axially deformed nuclei. Subsequently, the extracted IVGDR parameters were used to constrain the coefficients of the nuclear symmetry energy, which are found to be in good agreement with recent measurements of nuclear dipole polarizability. Furthermore, these symmetry-energy coefficients were employed to predict the dipole polarizability within different self-consistent mean-field models and to investigate its correlation with the neutron-skin thickness. The present findings provide valuable input for large-scale calculations of radiative capture processes relevant to nuclear astrophysics and for improving our understanding of astrophysical scenarios under extreme conditions.

Photoneutron double-differential cross sections in the giant dipole resonance (GDR) region were calculated to investigate the underlying nuclear reaction mechanisms with particular emphasis on the role of the direct process. Contributions from direct, pre-equilibrium, and compound processes were all taken into account. Wilkinson's resonance direct (RD) theory, based on the independent particle model, was applied to describe high-energy neutron emission from the direct process. The angular distribution of neutrons emitted via the RD mechanism was formulated using the Agodi and Courant formalism, which was incorporated into the RD framework. Neutron emission from the pre-equilibrium and compound processes was calculated using the two-component exciton model and the Hauser–Feshbach formalism, respectively. The calculated results were compared with experimental data obtained at NewSUBARU using 16.6-MeV quasi-monochromatic linearly polarized photon beams. Good agreement between calculations and measurements was observed for Pb, Au, and Sn, confirming the validity of the proposed model. Furthermore, the angular anisotropies of photoneutrons emitted from these elements were investigated, revealing considerable contributions from the RD process at high neutron energies. This study provides a deeper understanding of photoneutron emission mechanisms in the GDR energy region.

The observed fluid behavior of the matter produced in heavy ion and $pp$ collisions implies that the strings stretched between the constituents of the projectile and target should have a hard core giving rise to a repulsion between them. It is shown that in these collisions there are two critical string densities, one corresponding to the well-studied percolation of strings and another to the percolation of the hard core of the strings. These two critical densities are related to two critical temperatures, one $T\approx 160$ MeV would correspond to the restoration of chiral symmetry and partial deconfinement and a second transition $T\approx 220$ MeV form the fluid behavior of quantum chromodynamics matter strongly interacting to a quasi free gas of quarks and gluons. This argument is supported by the recently published results on the sudden increase in the degrees of freedom above the deconfinement temperature in $pp$ and $A\text{−}A$ collisions [Mishra et al., Nucl. Phys. A 1046, 122865 (2024)].

We developed a theoretical approach to elastic electron scattering on nuclei that includes a two-photon-exchange mechanism responsible for parity-conserving single-spin beam asymmetries. The two-photon-exchange amplitude at small scattering angles is treated in a diffractive framework similar to that used for pion-nucleus elastic scattering, and the approach is applied to the nuclei ${}_6^{12}\mathrm{C},{}_{20}^{40}\mathrm{Ca}$, and ${}_{82}^{208}\mathrm{Pb}$. The predicted kinematic features of the beam polarization asymmetries for different nuclei may reconcile Jefferson Lab's experimental results at finite scattering angles with a forward limit given by an optical theorem, potentially resolving the so-called “PREX puzzle” for ${}_{82}{}^{208}\mathrm{Pb}$.

Energy-integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show that the relevant integrals are the moments of the responses, and integrals weighted with $1/{(a+\omega )}^n$ with $n\le 2$. These can be directly obtained from the Euclidean response, avoiding the need for inversion of the Laplace transform. As a proof of concept, we study the procedure with toy-model responses for the quasielastic peak. We show that the different contributions can be straightforwardly organized in terms of relative importance, and how flux-averaged cross sections can be obtained. Using a realistic model for the response and numerical uncertainty, we show that it is feasible to obtain the required integrals from the Euclidean response, with large uncertainties only for the third moment. Due to kinematic restrictions, the integrals contain contributions from the unphysical region for neutrino scattering, coming from high-momentum nucleons. We show that (in the absence of two-body currents) robust corrections for this contamination are obtained from the single-nucleon momentum distribution. These results present an opportunity to compute certain neutrino cross sections with ab initio methods with controlled uncertainties.

The impact of the density dependence of symmetry energy and effective mass on the properties of the liquid-gas phase transition in hot asymmetric nuclear matter is investigated in the relativistic mean field model using Hornick-Tolos-Zacchi-Christian-Schaffner (HTZCS) parameter sets. The HTZCS parameter sets adhere to recent constraints on the symmetry energy $J$ and the slope parameter $L$ for pure neutron matter. The density dependence of the symmetry energy is governed by the slope parameter $L$. In the present study, two values of effective mass $m^{*}/m=0.65$ and 0.75 with fixed values of $L=50$ and 60 MeV for $J=32$ MeV were used. The present study indicates that compared to the effective mass, the density dependence of symmetry energy exerts a significant influence on various aspects of the liquid-gas phase, including the boundaries and area of the liquid-gas coexistence region, the maximum isospin asymmetry, and the critical values of pressure and isospin asymmetry. The critical pressure and the area of the phase-coexistence region systematically increase with the softening of the symmetry energy. The critical temperature of hot asymmetric nuclear matter, which marks the boundary between the single-phase region and two-phase regions, is influenced by the symmetry energy. Nevertheless, the critical temperature of hot asymmetric nuclear matter consistently exhibits a pattern of higher (lower) values up to a certain isospin asymmetry ($\alpha$) value for $m^{*}/m=0.65\left(0.75\right)$, then shifts to lower (higher) values for $m^{*}/m=0.65\left(0.75\right)$ for both $L=50$ and 60 MeV.

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.