In this work, we have studied the $2\nu \beta \beta$ decay of ${}^{76}\mathrm{Ge}$ and ${}^{96}\mathrm{Zr}$ isotopes utilizing large-scale shell-model calculations. The GWBXG effective interaction has been employed in the calculation of $2\nu \beta \beta$-decay nuclear matrix elements (NMEs). We have tested the effective interaction by comparing the predicted spectroscopic properties, such as energy spectra and transition probabilities, with the available experimental data. The variation of cumulative NMEs with respect to the $1^{+}$ state energies of the intermediate nucleus is also studied, corresponding to $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}, 0_{\mathrm{g}.\mathrm{s}.}^{+}\to 0_2^{+}$, and $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+}$ transitions between the parent and grand-daughter nuclei. The effective values of axial-vector coupling strength ($g_A^{\mathrm{eff}}$) are calculated using the predicted NMEs and experimental half-lives for $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ transitions. The extracted half-lives for $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 0_2^{+}$ and $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+}$ transitions using the shell-model predicted NMEs are consistent with the recent experimental data. The comparison of the shell-model predicted NMEs with previous NMEs available in the literature is discussed. Also, the computed branching ratios for the $2\nu \beta \beta$ decay of ${}^{76}\mathrm{Ge}$ and both the $2\nu \beta \beta$ and single-$\beta$ decay of ${}^{96}\mathrm{Zr}$ are reported corresponding to the calculated $g_A^{\mathrm{eff}}$ values.

Inspired by various studies on extracting the density distributions of nuclei from their collisions at ultrarelativistic energies, in the present work we investigate the possibility of extracting the neutron-skin thickness $\mathrm{\Delta }{r}_{np}$ in nuclei by their collisions at intermediate energies. We have analyzed the free neutron-to-proton yield ratio $n/p$ as a candidate probe at both midrapidities and forward rapidities in peripheral and central ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions based on an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, and found that the resulting $n/p$ yield ratio is more sensitive to the symmetry potential in the collision dynamics than to the initial $\mathrm{\Delta }{r}_{np}$ in colliding nuclei in most cases. The largest effect on the $n/p$ yield ratio from the initial $\mathrm{\Delta }{r}_{np}$ is observed for nucleons at large transverse or longitudinal momenta in central collisions at the collision energy of a few GeV/nucleon.

We report the systematic measurement of protons and light nuclei production in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=3\mathrm{GeV}$ by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The transverse momentum $\left(p_T\right)$ spectra of protons $\left(p\right)$, deuterons $\left(d\right)$, tritons $\left(t\right)$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ have been measured from midrapidity to target rapidity for different collision centralities. We present the rapidity and centrality dependence of particle yields $(dN/dy)$, average transverse momentum $(\langle p_T\rangle )$, yield ratios $(d/p,$ $t/p,{}^3\mathrm{He}/p,$ ${}^4\mathrm{He}/p)$, as well as the coalescence parameters $(B_2,$ $B_3)$. The $4\pi$ yields for various particles are determined by utilizing the measured rapidity distributions, $dN/dy$. Furthermore, we present the energy, centrality, and rapidity dependence of the compound yield ratios $(N_p\times N_t/N_d^2)$ and compare them with various model calculations. The physics implications of these results on the production mechanism of light nuclei and the QCD phase structure are discussed.

The background index (BI) is an important quantity to project and calculate the half-life sensitivity of neutrinoless double-$\beta$ decay $\left(0\nu \beta \beta \right)$ experiments. An analysis framework is presented to calculate the BI using the specific activities, masses, and simulated efficiencies of an experiments components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a BI distribution from the specific activity, mass, and efficiency distributions. This method is applied to the Majorana Demonstrator, which deployed arrays of high-purity Ge detectors enriched in ${}^{76}\mathrm{Ge}$ to search for $0\nu \beta \beta$. The original assay-based projection is requantified in the new framework, using the as-built geometry of the Demonstrator and additional assay information. While 47% higher than the original projection, the resulting BI of $[8.95\pm 0.36]\times {10}^{-4}\text{cts/(keV}\text{kg}\text{yr)}$ from the ${}^{232}\mathrm{Th}$ and ${}^{238}\mathrm{U}$ decay chains does not account for the higher-than-expected BI observed by the Demonstrator. This method enables us to demonstrate the statistical incompatibility between the Demonstrator's observed background and the assay results.

The $\beta$ decays of ${}^{87}\mathrm{Br}$, ${}^{88}\mathrm{Br}$, and ${}^{87}\mathrm{Kr}$ were measured with the Modular Total Absorption Spectrometer (MTAS) at Oak Ridge National Laboratory's Holifield Radioactive Ion Beam Facility (HRIBF). Both bromine isotopes are $\beta$-delayed neutron emitters that have large cumulative fission yields and were identified as top-priority cases for total absorption study by the Nuclear Energy Agency in 2007. Our investigations corroborate that the decay schemes of ${}^{87}\mathrm{Br}$ and ${}^{88}\mathrm{Br}$ suffer from the so-called pandemonium effect. Unique MTAS properties enable direct neutron measurements. We present MTAS-derived $\beta$-delayed neutron spectra, $\beta$-delayed neutron emission probabilities of $P_n({}^{87}\mathrm{Br})$ $=2.36\left(24\right)\%$, and $P_n({}^{88}\mathrm{Br})$ $=6.4\left(6\right)\%$, and the $\beta$-delayed neutron transitions intensity of 4(2)% to the first excited ${}^{87}\mathrm{Kr}$ state, populated in the $\beta$-neutron decay of ${}^{88}\mathrm{Br}$. Incorporating new data into calculations of the electromagnetic decay heat component emitted during thermal neutron fission of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ improves agreement with experimental data up to approximately 80 s after fission. The estimation of the nuclear reactor ${\overline{\nu }}_e$ flux results in changes of up to 1% in the expected ${\overline{\nu }}_e$ interactions with the detector material for ${}^{235}\mathrm{U}$, ${}^{238}\mathrm{U}$, ${}^{239}\mathrm{Pu}$, and ${}^{241}\mathrm{Pu}$.

The determination of the nuclear spectral function from the measured cross section of the electron-nucleus scattering process $e+A\to e^{\prime }+p+(A-1)$ is discussed and illustrated for the case of a carbon target. The theoretical model based on the local density approximation, previously employed to derive the spectral function from a combination of accurate theoretical calculations and experimental data, has been developed further by including additional information obtained from measurements performed with high missing energy resolution. The implications for the analysis of $\gamma$-ray emission associated with nuclear deexcitation are considered.

We study the evolution of critical fluctuations in an expanding system within a hadronic transport approach. The initialization of the system with critical fluctuations is achieved by coupling the ideal hadron resonance gas cumulants to the ones from the three-dimensional Ising model and generating the net and total particle number distribution from the principle of maximum entropy. These distributions are then evolved using realistic hadronic interactions. We systematically investigate the evolution of the critical fluctuations initialized at various temperatures and chemical potentials along a freeze-out line. We find that resonance regeneration and isospin randomization processes have the strongest influence on the evolution of the fluctuations. Additionally, the sets of particles coupled to the critical mode are modified to assess the strength of the propagation of correlations through interactions. We find that in the scaling region of the critical point correlations are propagated through the whole collisional history and are still present after the kinetic freeze-out of the matter if the coupling strength is large enough.

The charmed ${\mathrm{\Lambda }}_c^{+}$ hypernuclei were investigated within the framework of the density-dependent relativistic mean-field (DDRMF) theory. Starting from the empirical hyperon potential in symmetric nuclear matter, obtained through microscopic first-principle calculations, two sets of ${\mathrm{\Lambda }}_{c}N$ effective interactions were derived by fitting the potentials at a certain density either with minimal model uncertainty (Fermi momentum $k_{F,n}=1.05{\mathrm{fm}}^{-1}$) or nearby the saturation point ($k_{F,n}=1.35{\mathrm{fm}}^{-1}$). These DDRMF models were then used to explore the ${\mathrm{\Lambda }}_{c}N$ effective interaction uncertainties on the description of hypernuclear bulk and single-particle properties. A systematic investigation was conducted on the existence of bound ${\mathrm{\Lambda }}_c^{+}$ hypernuclei. The dominant factors affecting the existence and stability of hypernuclei were analyzed from the perspective of the ${\mathrm{\Lambda }}_c^{+}$ potential. It was found that the hyperon potential is influenced not only by the Coulomb repulsion, but by an extra contribution from the rearrangement terms due to the density dependence of the meson-baryon coupling strengths. Therefore, the rearrangement term significantly impacts the stability description for light hypernuclei, while for heavier hypernuclei the contribution from Coulomb repulsion becomes increasingly significant and eventually dominant. The discussion then focuses on the bulk and single-particle properties of charmed hypernuclei using these models. It is shown that different treatments of nuclear medium effects could lead to discrepancies in the theoretical description of hypernuclear structures, even when different models yield similar hyperon potentials within nuclear matter, indicating that constraints on the ${\mathrm{\Lambda }}_{c}N$ interaction at finite densities are crucial for the study of ${\mathrm{\Lambda }}_c^{+}$ hypernuclear structures.

The electric conductivity, ${\sigma }_{\mathrm{el}}$, is a fundamental transport coefficient of QCD matter that can be related to the zero-energy limit of the electromagnetic (EM) spectral function at vanishing three-momentum in the medium. The EM spectral function is also the central quantity to describe the thermal emission rates and pertinent spectra of photon and dilepton radiation in heavy-ion collisions. Employing a model for dilepton rates that combines hadronic many-body theory with nonperturbative QGP emission constrained by lattice QCD which describes existing dilepton measurements in heavy-ion collisions, I investigate the sensitivity of low-mass dilepton spectra in Pb-Pb collisions at the CERN Large Hadron Collider (LHC) to ${\sigma }_{\mathrm{el}}$. In particular, I separately evaluate the contributions from QGP and hadronic emission, and identify signatures that can help to extract ${\sigma }_{\mathrm{el}}$ from high-precision experimental data expected to be attainable with future detector systems at the LHC.

Highly precise measurements of the ${}^{99}\mathrm{Tc}\beta$ spectrum were performed in two laboratories using metallic magnetic calorimeters. Independent sample preparations, evaluation methods, and analyses yielded consistent results and the spectrum could be measured down to less than $1\mathrm{k}\mathrm{e}\mathrm{V}$. Consistent $\beta$ spectra were also obtained via cross evaluations of the experimental data sets. An additional independent measurement with silicon detectors in a $4\pi$ configuration confirms the spectrum shape above $25\mathrm{k}\mathrm{e}\mathrm{V}$. Detailed theoretical calculations were performed using the nuclear shell model and including atomic effects. The spectrum shape was found to be sensitive to the effective value of the axial-vector coupling constant. Combining measurements and predictions, we extracted $Q_{\beta }=295.82\left(16\right)\mathrm{k}\mathrm{e}\mathrm{V}$, $g_V^{\text{eff}}=0.376\left(5\right)$, and $g_A^{\text{eff}}=0.574\left(36\right)$, which seems to solve an inconsistency of the quenched coupling constants between first and higher forbidden nonunique transitions. Furthermore, we derived the mean energy of the $\beta$ spectrum, ${\overline{E}}_{\beta }=98.51\left(23\right)\mathrm{k}\mathrm{e}\mathrm{V}$, $logf=-0.47660\left(22\right)$, and $logft=12.3478\left(23\right)$.

Negative components are observed in the representation $d^2\left(\sigma E\right)/d{E}^2$ in heavy-ion fusions related to recent studies of noticeable oscillations in the high-energy region of the fusion excitation functions. A modified multi-Gaussian model has been developed, which includes contributions for both positive and negative components in the $d^2\left(\sigma E\right)/d{E}^2$ representation. The model reproduces the heavy-ion fusion excitation functions very well, including oscillations. The property of these negative components in the $d^2\left(\sigma E\right)/d{E}^2$ spectrum and the reaction mechanism of fusion at energies above the Coulomb barrier are investigated. The model also reproduces well light heavy-ion fusion reactions between ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ at high energy; results imply that the compound nucleus channel effect may have an important contribution at the high energy region for all fusion systems.

A universal function for heavy-ion fusion cross sections, $Y=\sqrt{\pi }X\mathit{erfc}(-X)+exp(-X^2)$ is proposed. By scaling both the cross section $\sigma \left(E\right)$ and the energy $E$, heavy-ion fusion cross section data are found to follow closely a universal function over the whole energy range. The scaling is developed from either a simple, empirical single-Gaussian barrier distribution model for the representation $d^2\left(\sigma E\right)/d{E}^2$, or the modified Siwek-Wilczynski model. The cross section expressions of these models are analytical, and can be easily used for all heavy-ion fusion excitation functions. Thus a bench marking of heavy-ion fusion excitation functions has been achieved. A general discussion regarding the universal function is given.

The resonance region of ${}^{11}\mathrm{B}$ covering excitation energies from 8.4 to 13.6 MeV was investigated with the $(d,p)$ reaction performed on an enriched ${}^{10}\mathrm{B}$ target at the Florida State University Super-Enge Split-Pole Spectrograph of the John D. Fox Superconducting Linear Accelerator Laboratory. Complementary measurements were performed with a target enriched in ${}^{11}\mathrm{B}$ to identify possible ${}^{12}\mathrm{B}$ contaminants in the $(d,p)$ reaction. Four strongly populated ${}^{11}\mathrm{B}$ states were observed above the $\alpha$-decay threshold. Angular distributions were measured and compared to distorted wave Born approximation (DWBA) calculations to extract angular momentum transfers and ${}^{10}\mathrm{B}\left(3^{+}\right)+n$ spectroscopic factors. The recently observed and heavily discussed resonance at 11.4 MeV in ${}^{11}\mathrm{B}$ was not observed in this work. This result is consistent with the interpretation that it is predominantly a ${}^{10}\mathrm{Be}\left(0^{+}\right)+p$ resonance with a possible additional ${}^7\mathrm{Li}+\alpha$ contribution. The predicted ${}^{10}\mathrm{B}\left(3^{+}\right)+n$ resonance at 11.6 MeV, analogous to the 11.4-MeV proton resonance, was not observed either. Upper limits for the ${}^{10}\mathrm{B}\left(3^{+}\right)+n$ spectroscopic factors of the 11.4- and 11.6-MeV states were determined. In addition, supporting configuration interaction shell model calculations with the effective WBP interaction are presented.

Background: The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the ${}^{16}\mathrm{O}$ nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, $2^{+}$) and (7.12 MeV, $1^{-}$), that dominate the behavior of the low-energy $S$ factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy.

Purpose: The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy $S$ factor, especially at the key astrophysical energy of $300\mathrm{keV}$.

Method: The $S$ factors are calculated within the framework of the $R$-matrix method using the azure2 code.

Results: Our total $S$ factor takes into account the $E1$ and $E2$ transitions to the ground state of ${}^{16}\mathrm{O}$ including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of ${}^{16}\mathrm{O}$ through four subthreshold states: $0_2^{+},3^{-},2^{+}$, and $1^{-}$. To evaluate the impact of subthreshold ANCs on the low-energy $S$ factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev et al., Eur. Phys. J. A 59, 162 (2023)]. The set with low ANC values was employed by deBoer et al. [Rev. Mod. Phys. 89, 035007 (2017)]. A detailed comparison of the $S$ factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this $S$ factor.

Conclusion: The contribution to the total $E1$ and $E2S$ factors from the corresponding subthreshold resonances at $300\mathrm{keV}$ are $(71–74)\%$ and $(102–103)\%$, respectively. The correlation of the uncertainties of the subthreshold ANCs with the $E1$ and $E2S\left(300\mathrm{keV}\right)$ factors is found. The $E1$ transition of the subthreshold resonance $1^{-}$ does not depend on the ground-state ANC but interferes constructively with a broad $(9.585\mathrm{MeV};1^{-})$ resonance giving (for the present subthreshold ANC) an additional $26\%$ contribution to the total $E1S\left(300\mathrm{keV}\right)$ factor. Interference of the $E2$ transition through the subthreshold resonance $2^{+}$ with direct capture is almost negligible for small ground-state ANC of $58{\mathrm{fm}}^{-1/2}$. However, its interference with direct capture for higher ground-state ANC of $337{\mathrm{fm}}^{-1/2}$ is significant and destructive, contributing $-27\%$. The low-energy $S_{E2}\left(300\mathrm{keV}\right)$ factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase.

The $\alpha$ decay to deformed doubly magic superheavy nucleus ${}^{270}\mathrm{Hs}$ is of particular interest for microscopic multidimensional $\alpha$-decay theory, which has not been observed in experiment so far. Here we present a coupled-channels calculation of the fine structure of $\alpha$ decay to rotational states of superheavy nuclei surrounding ${}^{270}\mathrm{Hs}$. The deformations and the decay energies $Q_{\alpha }$ of the unknown superheavy nuclei are sourced from sophisticated nuclear mass models. The rotational excitation energies are described by the rotor model while the nuclear moments of inertia are estimated by the cranking approximation. The $\alpha$-decay fine structure for the emitters in the vicinity of ${}^{270}\mathrm{Hs}$ is predicted and the impact of the deformed shell closure on decay half-lives and branching ratios is analyzed in detail.

We investigate nuclear shape coexistence for a wide range of even-even nuclides. By varying general pair condensates, which include Slater determinants as a limit but also allow for arbitrary pairing channels, we frequently find multiple coexisting minima and often more than two. This is consistent with recent experimental results. In order to measure general pairwise correlations beyond a simple Slater determinant, we introduce a novel entropy-like measure, which is smallest midshell and largest near shell closures; this is consistent with a picture of pairing-like behavior dominating near closed shells and deformation midshell. After surveying nuclides spanning from the $sd$ shell to nuclides between magic numbers 50 and 82, we focus on the six lightest nuclei with shape coexistence. Angular-momentum projected variational pair condensate (PVPC) calculations identify band structures, including two newly proposed coexisting bands in ${}^{26}\mathrm{Si}$/Mg and ${}^{24}\mathrm{Si}$/Ne. The PVPC results agree well with data, providing robust experimental support for the pervasiveness of coexistence in these light nuclei.

We present a method for measurement analyses based on probabilistic deep neural networks that provide several advantages over conventional analyses with phenomenological models. These include predicting physical quantities directly from data, the rapid generation of statistically robust uncertainties, and the ability to bypass some parameters that may induce ambiguities and complications in data analysis. As deep learning methods make predictions through “black boxes,” the uncertainty quantification is typically challenging. We use a probabilistic framework that provides thorough uncertainty quantification and is straightforward to follow in practice. With the network architecture based on the Transformer, we demonstrate the current method for predicting nuclear resonance parameters from scattering data using the phenomenological $\mathit{R}$-matrix model.