We present a rigorous construction and uniqueness proof of the matrix Green's function for coupled radial Schrödinger equations with symmetric coupling potentials. The Green's matrix $\mathbf{G}(R,R^{\prime })$ is built from two fundamental sets of $N$ linearly independent solutions, regular and outgoing, of the coupled radial equations. We prove that the associated Wronskian matrix is diagonal with elements $W_n=-k_n$ and independent of the radial coordinate, and demonstrate through the symplectic structure of the $2N$-dimensional phase space that the resulting construction is the unique Green's matrix satisfying the defining equation with correct boundary conditions, continuity at the source point, and the prescribed derivative discontinuity. The construction applies to any system of coupled radial Schrödinger equations with symmetric coupling potentials and open channels, including coupled-channels problems arising in nuclear, atomic, and molecular scattering. As an illustrative application, we show how the Green's matrix enters the nonlocal dynamical polarization potential within the continuum-discretized coupled-channels framework, where retaining the off-diagonal elements captures multistep excitation pathways beyond the weak-coupling approximation.

Purely baryonic weak decays of heavy baryons are investigated within the framework of the Skyrme model. These decays belong to a new class of unobserved decay channels, which would help us to test the standard model, particularly potential sources of $\mathit{CP}$ violation in the baryonic sector. By interpreting the heavy baryon as a bound state of a heavy meson and a baryon (Skyrmion), a direct calculation of the decay process ${\mathrm{\Lambda }}_b\to p\overline{p}n$ is performed. The resulting branching fraction is of $O\left({10}^{-6}\right)$, in agreement with previous estimates.

We develop a novel model utilizing the forward $K^{*}$ production reaction off the nucleon, $\pi N\to K^{*}MB$, induced by a high-momentum $\pi$ beam, as a tool to study low-lying $Y^{*}$ resonances below and just above the $\overline{K}N$ threshold. Because conventional $K^{-}p$ scattering experiments face difficulties in directly accessing this kinematic region, the proposed reaction offers a valuable complementary approach for $Y^{*}$ spectroscopy. The constructed model is based on the one-meson exchange mechanism, which is known to dominate forward-angle production at high energies, and the half-off-shell scattering amplitudes from the ANL-Osaka dynamical coupled-channels models (Model A and Model B). We predict various observables, including differential cross sections and angular distributions. Our results demonstrate significant enhancements in the sub-threshold region of the invariant mass spectra. Notably, we show that overlapping resonances, such as a potential new $3/2^{+} \mathrm{\Sigma }$ state and the well-established $\mathrm{\Sigma }\left(1385\right)3/2^{+}$, can constitute a single peak in the $\pi \mathrm{\Lambda }$ mass spectrum, indicating that the existence of previously unconfirmed subthreshold states cannot be ruled out by analyzing only the existing mass spectrum data. Furthermore, we find that angular distributions provide strong discriminatory power to disentangle such overlapping states through partial-wave interference effects, while the $t^{\prime }$ and ${\varphi }_M^{*}$ dependencies provide crucial constraints on the high-energy production mechanisms. Our predictions for these highly sensitive observables can facilitate high-statistics measurements, which are accessible at modern hadron facilities such as J-PARC, to unravel the $S=-1 Y^{*}$ mass spectrum.

In our earlier work [A. C. Wang et al., Phys. Rev. C 98, 045209 (2018)], we analyzed the differential cross-section data from the CLAS Collaboration for the reactions $\gamma p\to K^{*+}{\mathrm{\Sigma }}^0$ and $\gamma p\to K^{*0}{\mathrm{\Sigma }}^{+}$ using an effective Lagrangian approach. We found that a satisfactory description of the data required the inclusion of the $s$-channel $\mathrm{\Delta }\left(1905\right)5/2^{+}$ resonance, in addition to $t$-channel exchanges of $K, \kappa$, and $K^{*}, s$-channel contributions from nucleon ($N$) and $\mathrm{\Delta }, u$-channel exchanges of $\mathrm{\Lambda }, \mathrm{\Sigma }$, and ${\mathrm{\Sigma }}^{*}$, and a generalized contact term. In the present work, we extend our analysis to incorporate the data on spin density matrix elements from the LEPS Collaboration for the $\gamma p\to K^{*0}{\mathrm{\Sigma }}^{+}$ reaction at photon energies $E_{\gamma }=1.85–2.96\mathrm{GeV}$. Our goal is to impose more stringent constraints on the theoretical model and obtain a more reliable understanding of the reaction mechanisms. We obtain two fits that describe the experimental data equally well. In both fits, the $\mathrm{\Delta }\left(1905\right)5/2^{+}$ resonance plays an important role. However, the contribution from $t$-channel $\kappa$ exchange is significant in one fit but negligible in the other. This finding contradicts earlier claims in the literature that the LEPS parity spin asymmetry $P_{\sigma }$ data support a dominant role of $\kappa$ exchange in $\gamma p\to K^{*0}{\mathrm{\Sigma }}^{+}$. We also present predictions for $P_{\sigma }$ at $E_{\gamma }=8.5$ GeV, which may help clarify whether $\kappa$ exchange is indeed dominant in this reaction.

Understanding the thermal structure of the outer crust of accreting neutron stars is important for interpreting astronomical x-ray observations. Ground-state to ground-state $\beta$-decay transitions of neutron-rich nuclei comprising the crust enable Urca neutrino cooling processes that affect this thermal structure. Here we constrain the ground-state to ground-state transition strengths for the decays of ${}^{57}\mathrm{Sc}, {}^{57}\mathrm{Ti}$, and ${}^{59}\mathrm{Ti}$ based on experimental data. The data were obtained by combining total absorption $\gamma$-spectroscopy data from the SuN detection system with $\beta$-delayed neutron emission data from the NERO detection system at Michigan State University's National Superconducting Cyclotron Laboratory. We find $logft=5.8_{-0.2}^{+0.3}$ and $logft=5.{34}_{-0.24}^{+0.08}$ for the decays of ${}^{57}\mathrm{Ti}$ and ${}^{59}\mathrm{Ti}$, respectively, and find no evidence for ground-state feeding in the decay of ${}^{57}\mathrm{Sc}$. The results indicate weaker transitions than predicted by theory and indicated by previous measurements, resulting in reduced efficiency of neutrino cooling in accreted neutron star crusts in systems that exhibit x-ray superbursts.

Despite its nucleon numbers not coinciding with the traditional nuclear magic numbers, the structure of ${}^{54}\mathrm{Ca}$ shows signatures of a doubly closed shell nucleus. This article details the structures of neutron-excited states up to beyond the two-neutron emission threshold populated by the ${}^{55}\mathrm{Ca}(p,pn$) reaction at $\sim 200$ MeV/nucleon. Level energies and population cross sections were determined through $\gamma$-ray spectroscopy and invariant-mass spectroscopy of ${}^{54}\mathrm{Ca}$. Large-scale shell model calculations with protons and neutrons allowed to occupy the $sd\text{−}pf\text{−}sdg$ orbitals were performed to predict energy levels and spectroscopic factors. Distorted wave impulse approximation calculations provided single-particle knockout cross sections and momentum distributions of the reaction products. The theoretical calculations reproduce the data well. Both theory and experiment are suggestive of a well-preserved shell structure at high excitation energy. Also, inelastic scattering of ${}^{54}\mathrm{Ca}$, carried out within the same experiment, validates previously proposed level schemes.

We present a theoretical framework for understanding α-clustering in even-even self-conjugate ($N=Z$) nuclei through a deformed harmonic oscillator approach that incorporates schematic nuclear interactions. The work introduces three enhancements to conventional single-particle gap analyses: (1) a generalized four-nucleon stability criterion $\mathrm{\Delta }{E}_{\text{clus}}^{\left(4\right)}=min(4\mathrm{\Delta }E,-E_{\text{pair}}+2\mathrm{\Delta }E,-2E_{\text{pair}})$ that accounts for the correlated nature of alpha clusters, (2) the incorporation of a schematic spin-orbit interaction $\mathrm{\Delta }{E}_{\mathrm{SO}}=-\kappa \hslash {\omega }_0[\mathbf{l}·\mathbf{s}]$ that breaks degeneracies, and (3) a BCS-inspired pairing correction $E_{\text{pair}}=(-{\mathrm{\Delta }}_0^2/G)exp[-1/\left(G\rho \left(E_F\right)\right)]$ that modifies cluster stability near the Fermi surface. Using this framework we compute cluster stability maps for a complete set of self-conjugate nuclei from ${}^4\mathrm{He}$ to ${}^{64}\mathrm{Ge}$, documenting the evolution of α-cluster correlations across the nuclear chart. The results indicate that while the overall magnitude of cluster stability decreases with increasing mass number due to growing level density, localized regions of enhanced stability persist at specific deformations that correspond to experimentally observed cluster configurations. The spin-orbit interaction selectively suppresses certain configurations while preserving the most robust ones, offering a possible explanation as to why some harmonic oscillator predictions are not observed experimentally. Pairing effects become increasingly important in heavier systems ($A>40$), sometimes enhancing stability at large deformations through superfluid-type correlations. This systematic study provides a qualitative bridge between simple harmonic oscillator insights and realistic mean-field predictions, offering a useful exploratory framework for interpreting cluster structures in self-conjugate nuclei.

The excited states of ${}^{95}\mathrm{Nb}$ have been investigated using the heavy-ion fusion-evaporation reaction ${}^{82}\mathrm{Se}$(${}^{18}\mathrm{O},p4n){}^{95}\mathrm{Nb}$ at the beam energies of 82 and 88 MeV. Particle-$\gamma \text{−}\gamma$ and $\gamma \text{−}\gamma$ coincidence measurements using CsI and HPGe arrays are employed to gain selectivity to Nb isotopic products. The level scheme of ${}^{95}\mathrm{Nb}$ was extended up to $E\approx 12$ MeV and $I^{\pi }=(53/2^{-})$ with 32 new $\gamma$-ray transitions. The suggested positive parity sequence of earlier publication is modified to negative parity; a previously unobserved new decay sequence has been assigned as positive parity. The coupling of the odd proton occupying the $g_{9/2}$ orbital to the levels in the even-even ${}^{94}\mathrm{Zr}$ core can account for the low-lying excited states of ${}^{95}\mathrm{Nb}$. The observed experimental states are compared with theoretical shell-model calculations.

I develop a theoretical framework to describe quasiparticle resonance states within the Hartree-Fock-Bogoliubov (HFB) theory by integrating the complex-scaled Jost function method with the Autonne-Takagi factorization. The HFB completeness relation is derived from the analytical properties of the Green's function using contour integration in the complex energy plane, where the complex scaling method is shown to be essential for explicitly separating resonance pole contributions from the continuum background. To uniquely define and normalize the resonant wave functions (Gamow states), the Autonne-Takagi factorization is applied to the rank-1 residue matrix of the flux-adjusted $S$-matrix at the pole energy. This scheme determines the absolute scale and phase of the eigenfunctions without relying on artificial adjustments or phenomenological basis sets. Numerical analysis confirms that physical observables and the defined wave functions remain invariant under the rotation of the scaling angle $\theta$. Furthermore, the $T$-matrix residues calculated via the Mittag-Leffler expansion are shown to be in exact numerical agreement with those obtained from the microscopic integrals of the Takagi-normalized Gamow states. My analysis of the scattering profiles reveals that hole-type quasiparticle resonances can be understood as a manifestation of the Fano process originating from the interference between the discrete poles and the background continuum. The proposed normalization scheme provides a foundation for evaluating the collectivity of various excitation modes in open quantum many-body systems.

Modern nuclear data evaluation increasingly requires not only accurate scattering calculations but also efficient methods for uncertainty quantification and parameter optimization, tasks that benefit from differentiable solvers amenable to gradient-based algorithms. I present a neural network emulator based on bidirectional liquid neural networks that provides a differentiable mapping from the optical potential to scattering wave functions. The key innovation enabling generalization across the parameter space is the use of phase-space coordinates $\rho =kr$ that normalize the oscillation wavelength regardless of projectile energy, allowing a single network to span 1 to 200 MeV. Trained on Numerov solutions for 12 target nuclei (${}^{12}\mathrm{C}$ to ${}^{208}\mathrm{Pb}$), both protons and neutrons, and partial waves up to $l=30$, the network achieves an overall relative error of 0.6%. The predicted wave functions yield accurate $S$-matrix elements and elastic scattering cross sections, reproducing diffraction patterns spanning four orders of magnitude. Importantly, the model generalizes successfully to nuclei not included in training (${}^{24}\mathrm{Mg}, {}^{63}\mathrm{Cu}$, and ${}^{184}\mathrm{W}$) with comparable accuracy, demonstrating that it has captured the smooth functional dependence encoded in the Koning-Delaroche (KD02) parametrization rather than memorizing specific targets. The differentiable nature of the trained model is the key prerequisite for gradient-based optimization of optical model parameters and uncertainty quantification, which I identify as the principal direction for future work.

We report the observation of two nuclear recoil peaks induced by neutron capture on aluminum in a cryogenic ${\mathrm{Al}}_2{\mathrm{O}}_3$ detector developed by the Nucleus collaboration for the detection of reactor neutrinos via coherent elastic neutrino-nucleus ($\mathrm{CE}\nu \mathrm{NS}$) process. Data collected at the Technical University of Munich in 2024 with a ${}^{252}\mathrm{Cf}$ source reveal a main recoil line at 1145 eV from single-$\gamma$ de-excitation of ${}^{28}\mathrm{Al}$ and a newly observed structure near 575 eV originating from several two-$\gamma$ cascades. The latter constitutes the first direct measurement of a nuclear recoil line induced by multi-$\gamma$ cascades. It is predicted by our simulations when the recoiling nucleus has time to stop before the emission of the next $\gamma$ ray in the cascade. These results demonstrate the potential performance of the Crab (Calibration Recoil for Accurate Bolometry) method for in situ nuclear recoil calibration and highlight the importance of accurately modeling recoil stopping and nuclear de-excitation times in cryogenic detectors of $\mathrm{CE}\nu \mathrm{NS}$ and dark-matter interactions.

The nuclear matrix elements (NMEs) of the neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay in the candidate nuclei relevant to the current and next-generation experimental searches are crucial for extracting beyond-standard-model parameters from the experimental half-life measurements. However, the recently recognized short-range operator with an unknown coupling, required by the renormalizability of the leading-order $nn\to ppee$ amplitudes within the framework of chiral effective field theory (EFT), has introduced significant uncertainties into the NMEs. In this Letter, the $0\nu \beta \beta$-decay NMEs of ${}^{48}\mathrm{Ca}, {}^{76}\mathrm{Ge}, {}^{82}\mathrm{Se}, {}^{100}\mathrm{Mo}$, and ${}^{136}\mathrm{Xe}$ are calculated using, for the first time, the decay operator derived from the relativistic chiral EFT and the relativistic many-body wave functions obtained from the state-of-the-art relativistic configuration-interaction density functional theory. The resulting NMEs are free from the uncertainties typically introduced by leading-order short-range operators, as the relativistic chiral decay operator naturally ensures the renormalizability of the $nn\to ppee$ amplitudes at leading order, obviating the need for a short-range term. The present NMEs are then compared with those obtained using the nonrelativistic chiral decay operators, which includes both long- and short-range terms, and the short-range uncertainties are analyzed comprehensively. This study significantly reduces a key source of uncertainty in the evaluation of $0\nu \beta \beta$-decay NMEs. The reported NMEs without contamination of the leading-order short-range uncertainties are important for assessing the sensitivity to the inverted neutrino-mass hierarchy in next-generation experiments.

The present work aimed at the synthesis of the hitherto unknown ${}^{231}\mathrm{Am}$ and known ${}^{229}\mathrm{Am}$ isotopes via the $4n$ evaporation channels of the fusion reactions of ${}^{48}\mathrm{Ca}+{}^{187}\mathrm{Re}$ and ${}^{48}\mathrm{Ca}+{}^{185}\mathrm{Re}$, respectively. The new isotope ${}^{231}\mathrm{Am}$, with a half-life of ${47}_{-19}^{+85}\mathrm{s}$, was identified on the basis of five observed $\alpha$-decay chains. It emits $\alpha$ particles with an energy of 7.11(2) MeV. An upper limit of 0.66 was estimated for the electron-capture decay branch of ${}^{231}\mathrm{Am}$. No $\alpha$-decay chain from ${}^{229}\mathrm{Am}$ was observed, corresponding to a cross-section level of 0.03 nb for the detection of a single event. The $\alpha$-decay properties of ${}^{231}\mathrm{Am}$ are discussed in the framework of the Geiger-Nuttall empirical relation.

Based on the empirical coupled-channel model for calculating the capture cross section and the statistical model for calculating the survival probability, we apply the dinuclear system model for investigating the synthesis of superheavy element 116. The theoretical results can systematically reproduce the experimental data of the reactions ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$, ${}^{50}\mathrm{Ti}+{}^{242}\mathrm{Pu}$, ${}^{50}\mathrm{Ti}+{}^{244}\mathrm{Pu}$, and ${}^{54}\mathrm{Cr}+{}^{238}\mathrm{U}$. Simultaneously, the reactions ${}^{45}\mathrm{Sc}+{}^{243}\mathrm{Am}$, ${}^{51}\mathrm{V}+{}^{237}\mathrm{Np}$, ${}^{55}\mathrm{Mn}+{}^{231}\mathrm{Pa}$, and ${}^{58}\mathrm{Fe}+{}^{232}\mathrm{Th}$ are investigated. The results show that the calculated maximal evaporation-residue cross section is about 0.25 pb.

We propose an improved dinuclear system (DNS) model to describe both capture and noncapture transfer reactions within a unified framework. The main improvements in this work include the introduction of noncapture transfer processes and dynamic deformation mechanisms. The multinucleon transfer (MNT) reactions of ${}^{58,64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ are used to test the improved model. The results show that the improved DNS model can successfully calculate the observables including mass distributions, total kinetic energy–mass distributions, and isotopic cross sections from both capture and noncapture transfer processes. These results indicate that the present DNS model is an effective tool for efficiently calculating product cross sections and investigating energy dissipation mechanisms in MNT reactions.

Background: The experiment of ${}^{180}\mathrm{Hg}$ fission revealed a possible “new asymmetric fission mode” in the preactinide region, posing challenges to current fission theory. Similarity in shell effects is observed between fission and quasifission, providing the possibility for widely exploring the topography of a fission potential-energy surface (PES).

Purpose: We aim to investigate the shell effects in the quasifission toward ${}^{180}\mathrm{Hg}$ and to explore their connection with the ${}^{180}\mathrm{Hg}$ fission.

Method: ${}^{68}\mathrm{Zn}+{}^{112}\mathrm{Sn}$, ${}^{74}\mathrm{Se}+{}^{106}\mathrm{Pd}$, ${}^{80}\mathrm{Kr}+{}^{100}\mathrm{Ru}$, and ${}^{84}\mathrm{Kr}+{}^{96}\mathrm{Ru}$ central collisions at different energies and projectile orientations are calculated using the Skyrme time-dependent Hartree-Fock approach. The static fission properties are calculated with the constrained Hartree-Fock-Bogoliubov method and compared with the quasifission results.

Results: Shell effects are found to hinder mass equilibration between the prefragments, enhancing the production of fragments near the $80/100$ mass split. By comparing the quasifission trajectories with the PES in the $(Q_{20},Q_{30})$ space, the role of the PES ridge in forming fragments is identified. The presence of the asymmetric valley causes the ${}^{68}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ quasifission to exhibit a prefragment mass equilibration process and scission-point configuration similar to those of ${}^{180}\mathrm{Hg}$ fission. The elongated light fragment is found to be a key factor in reproducing the experimental fission total kinetic energies. Meanwhile, a more pronounced proton shell gap is found in the ${}^{68}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ quasifission compared with other reactions.

Conclusions: By using quasifission dynamics as a probe of the fission pathway, the present calculations help clarify the specific influence of the PES topography and provide support for the dominance of proton shell effects and light fragment deformation in preactinide fission.

Parity-violating electron scattering provides a largely model-independent way of measuring neutron densities in nuclei that has important implications for the structure of nuclei and neutron stars. In this paper we calculate radiative corrections to the parity-violating asymmetry $A_{\mathrm{pv}}$ in electron-nucleus scattering including vertex and vacuum polarization contributions. We find large cancellations between the vertex corrections to the vector and axial-vector vertices. As a result, the total radiative correction in second Born approximation is dominated by vacuum polarization and is of order $-0.5\%$. Coulomb distortions have modest effects on radiative corrections for ${}^{12}\mathrm{C}$ and ${}^{48}\mathrm{Ca}$ nuclei. For ${}^{208}\mathrm{Pb}$, Coulomb distortions reduce the total radiative correction to only about 0.1%. Therefore, these corrections are not important for the interpretation of the PREX and MREX experiments on ${}^{208}\mathrm{Pb}$ and for the CREX experiment on ${}^{48}\mathrm{Ca}$. However, radiative corrections must be carefully included for a precision measurement of the weak charge of ${}^{12}\mathrm{C}$.

Three-nucleon force (3NF) plays an important role in understanding the structure of finite nuclei and the saturation properties of infinite nuclear matter. More specifically, 3NF should be necessary for each two-nucleon force (2NF) to obtain more accurate description of nuclear systems. 3NF derived from the chiral effective field theory has been successful in ab initio calculations of atomic nuclei. Most of established chiral nuclear forces have a nonlocal form in the momentum space. In this work, we construct a companion chiral 3NF specifically tailored to the new Idaho local position-space 2NF, and calculate binding energies and radii of nuclei up to ${}^{132}\mathrm{Sn}$. We find that a chiral 3NF with hybrid local and nonlocal regulators has advantages in improving the nuclear structure calculations of both binding energies and radii with the new Idaho 2NF. The two low-energy constants of 3NF are constrained by the ground-state energies of ${}^3\mathrm{H}$ and ${}^{16}\mathrm{O}$ as suggested in a recent work.

When training data are limited, data-driven models are especially vulnerable to optimization-related fluctuations from random initialization and to sampling-induced bias from insufficient training data. We address both challenges with transfer learning (TL): deep neural networks (DNNs) are first pretrained on $\alpha$-decay half-lives and then fine-tuned on a small cluster-decay dataset. The pretraining stage provides a physically informed initialization that stabilizes optimization, while transferred global-decay systematics regularize the fit and reduce sensitivity to training-set composition. Despite extreme data sparsity, the resulting models accurately predict cluster-decay half-lives for parent nuclei from ${}^{221}\mathrm{Fr}$ to ${}^{242}\mathrm{Cm}$. We further quantify how initialization and sample selection affect predictive accuracy and robustness, demonstrating that TL enables stable and reliable learning in the small-sample regime.