The charge-dependent nucleon-nucleon $\left(NN\right)$ interaction plays a crucial role in understanding the nuclear structure and reaction problems. In this work, we explore the charge-dependent $NN$ interaction in covariant chiral effective field theory. By incorporating the isospin-breaking contributions, we derive the charge-dependent covariant chiral $NN$ potential up to next-to-next-to-leading order. The calculated $np$ and $pp$ phase shifts are in satisfactory agreement with the PWA93 partial wave analysis. Our results contribute to a deeper understanding of isospin-breaking effects in nuclear forces and provide a solid foundation for future studies of nuclear structure and reactions within the covariant framework.

The lowest states of the ${}^{52,54}\mathrm{Cr}$ isotopes are investigated for the presence of the shape coexistence phenomenon. The ground state deformation is extracted using the covariant density functional theory with a density-dependent point-coupling X parametrization, while the properties of the excited states are described involving the Bohr-Mottelson collective Hamiltonian with a sixth order anharmonic oscillator. A coexistence between near-spherical and well-deformed shapes is found in ${}^{52}\mathrm{Cr}$, and shape fluctuations of the ground state in ${}^{54}\mathrm{Cr}$. Moreover, the presence of coexisting shapes in ${}^{52}\mathrm{Cr}$ indicates that the $4^{+}$ state at 2768 keV would fit better the ground band than the $4^{+}$ state at 2370 keV. This latter assumption, in turn, implies that ${}^{52}\mathrm{Cr}$ could be a good candidate for the manifestation of the so-called $B_{4/2}$ anomaly.

A detailed investigation of the structural evolution of mercury (Hg) isotopes with mass numbers $A=174$–266 is carried out within the Skyrme Hartree-Fock-Bogoliubov (SHFB) framework using the UNEDF2 energy density functional. The study encompasses both bulk nuclear properties, such as binding energies, two-neutron separation energies, potential energy surfaces, root-mean-square radii, nuclear deformation parameters, and single-particle energy levels, as well as isospin-sensitive observables relevant to neutron-rich systems. To explore the isospin dependence, the coherent density fluctuation model (CDFM) is employed, using SHFB results as input to extract the symmetry energy and its volume and surface components. These quantities are particularly crucial for understanding the behavior of nuclei near the neutron drip line. The results reproduce the established shell closures at neutron numbers $N$ = 82 and 126 across both bulk and isospin-dependent observables. In addition, several calculated observables exhibit features consistent with a possible shell or subshell closure around $N$ = 184, although its presence remains model dependent and less robust than the traditional magic numbers. These findings suggest enhanced stability in extremely neutron-rich Hg isotopes and motivate further theoretical and experimental investigations in this region. The consistency between SHFB and CDFM predictions highlights the robustness of the combined theoretical framework in capturing both microscopic and macroscopic aspects of nuclear structure. The present work contributes to a deeper understanding of shell evolution, the role of the symmetry energy, and the stability of heavy isotopes far from the valley of stability.

The most stringent laboratory-based experimental limits on the existence of submegaelectronvolt sterile neutrinos are currently set by decay spectroscopy of radioactive ${}^7\mathrm{Be}$ embedded into superconducting sensors. The systematic uncertainties are dominated by the modeling of the electron shakeup and shakeoff spectra that are not based on state-of-the-art atomic theory and do not include electron correlations or relativistic effects. We have used the multiconfiguration Dirac-Fock formalism to obtain correlated wave functions ab initio and compute all single and double shake processes in the electron capture decay of atomic ${}^7\mathrm{Be}$. The simulations can explain some but not all of the observed spectral features, likely because the wave functions are modified by the Ta sensor material that the ${}^7\mathrm{Be}$ is embedded into. The new models also show that the $L/K$ electron capture ratio of ${}^7\mathrm{Be}$ in Ta has previously been slightly underestimated revising the previous value of 0.070(7) to a new value of 0.0756(20).

The inelastic scattering of ${}^{12}\mathrm{C}$ from ${}^{208}\mathrm{Pb}$ at an incident energy of 98 MeV exhibits a curious anomaly. While the shape of the angular distribution for populating the 4.086-MeV $2_1^{+}$ level of ${}^{208}\mathrm{Pb}$ is well reproduced by distorted wave Born approximation (DWBA) calculations, a coupling strength approximately double that of the accepted value is required. The inelastic scattering of a 270-MeV ${}^3\mathrm{He}$ beam from a ${}^{208}\mathrm{Pb}$ target exhibits similar behavior. This minor mystery has remained unsolved for the past 50 years. A solution is suggested based on the high level density of ${}^{208}\mathrm{Pb}$ in the region of 4-MeV excitation energy and the possibility that the measured $2_1^{+}$ angular distributions contain contributions from a number of unresolved levels, in particular the 4.324-MeV $4_1^{+}$. The coupling strengths for these levels, required as input for DWBA calculations, were obtained from an analysis of existing high-resolution ${}^{208}\mathrm{Pb}$($p,p^{\prime }$) scattering data, while the $2_1^{+}$ coupling strength was fixed by the adopted value of the $B\left(E2\right)$. Using these strengths a consistent description of a wide range of light-ion scattering data is obtained, in addition to the “anomalous” ${}^{12}\mathrm{C}$ and ${}^3\mathrm{He}$ data. While the individual contributions of the levels other than the $2_1^{+}$ and $4_1^{+}$ are negligible, their sum makes a significant contribution to the total angular distribution.

The electron spectra of the $\beta$ decays of ${}^{92}\mathrm{Rb}$ and ${}^{142}\mathrm{Cs}$, key contributors to the reactor antineutrino spectrum, were measured at the IGISOL facility using radioactive beams of high isotopic purity. The shapes of the measured $\beta$ spectra were compared with various $\beta$-shape models, including first-forbidden correction factors for $\mathrm{\Delta }{I}^{\pi }=0^{-}$ ground-state to ground-state transitions. Comparisons with previous experimental results are also provided. The shapes of the newly measured $\beta$ spectra are well reproduced employing feedings extracted from total absorption gamma spectroscopy measurements.

Background: Positron decays of proton-rich nuclides exhibit large $Q$ values, producing complex cascades which frequently involve various radiations, including protons and $\gamma$ rays. Often, only one of the two is measured in a single experiment, limiting the accuracy and completeness of the decay scheme. An example is ${}^{31}\mathrm{Cl}$, for which protons and $\gamma$ rays have been measured separately in detail but never with substantial sensitivity to proton-$\gamma$ coincidences.

Purpose: Provide detailed measurements of ${}^{31}\mathrm{Cl} \beta$-delayed proton decay including $\beta \text{−}p\text{−}\gamma$ sequences, extract spectroscopic information on ${}^{31}\mathrm{S}$ excited states as well as their ${\beta }^{+}$ feedings, and compare to shell-model calculations.

Methods: A fast fragmented beam of ${}^{31}\mathrm{Cl}$ provided by the National Superconducting Cyclotron Laboratory was deposited in the Gaseous Detector with Germanium Tagging (GADGET) system. GADGET's gas-filled Proton Detector was used to detect $\beta$-delayed protons, and the Segmented Germanium Array was used to detect $\beta$-delayed $\gamma$ rays.

Results: As many as 20 previously unobserved $\beta$-delayed proton transitions have been discovered in the present data, most of which populate excited states of ${}^{30}\mathrm{P}$. The first detailed ${}^{31}\mathrm{Cl}$($\beta p\gamma ){}^{30}\mathrm{P}$ decay scheme is presented, including updated $\beta$-delayed proton-decay energies and intensities, as well as several new ${}^{31}\mathrm{S}$ levels. Improved agreement is found with theoretical calculations of the Gamow-Teller strengths $B\left(\text{GT}\right)$ for ${}^{31}\mathrm{S}$ excitation energies $7.5<E_x<9.5$ MeV.

Conclusions: The present work demonstrates that the ability to detect $\beta$-delayed protons and $\gamma$ rays in coincidence is essential to construct accurate positron decay schemes for comparison to theoretical nuclear structure calculations. In some respects, this phenomenon for $\beta$-delayed protons resembles the pandemonium effect originally introduced for $\beta$-delayed $\gamma$ rays.

A microscopic energy term is introduced into the $\alpha$-decay energy correlation formula and further extended to half-life predictions, substantially improving the predictive accuracy of both quantities, particularly in regions near nuclear shell closures. For 96 reference-target pairs, the root-mean-square deviation (RMSD) of the predicted $\alpha$-decay energies decreases from 0.052 to 0.018 MeV upon inclusion of the correction. Building upon the Royer systematics, we develop an improved neighboring-nuclei $\alpha$-decay half-life law (the NR formula) by incorporating the microscopic energy term. For 170 even-even nuclei, the RMSD of predicted ${log}_{10}{T}_{1/2}$ values decreases from 0.324 to 0.186, representing a 43% improvement over the original Royer formula.

The electric dipole polarizability ${\alpha }_D$ and the neutron-skin thickness $\mathrm{\Delta }{R}_{np}$ of ${}^{208}\mathrm{Pb}$ are two powerful and clean probes for constraining the symmetry energy at subsaturation densities. Within the framework of the antisymmetrized molecular dynamics (AMD) model, the width of the strength function and its dynamical origins are understood, and the ${\alpha }_D$ and $\mathrm{\Delta }{R}_{np}$ data favor effective interaction parameter sets with $S_0\approx 32–34$ MeV and $L=64–87$ MeV. In addition, our calculations show that the sensitive densities of ${\alpha }_D$ and $\mathrm{\Delta }{R}_{np}$ range from $0.2{\rho }_0$ to $0.57{\rho }_0$, and the corresponding values of the symmetry energy at the lower and upper ends of this sensitive density region are $S\left(0.2{\rho }_0\right)=10.18\pm 1.10$ MeV and $S\left(0.57{\rho }_0\right)=22.31\pm 1.32$ MeV.

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.