To investigate the impact of the finite nucleon size effects (FNS) and the short-range correction (SRC) on the Fermi, Gamow-Teller, and tensor matrix elements of the neutrinoless double-beta ($0\nu \beta \beta$) decay, calculations are performed within the SD-pair shell model framework for ${}^{128}\mathrm{Te}, {}^{130}\mathrm{Te}$, and ${}^{134}\mathrm{Xe}$. The results reveal that both FNS and SRC effectively reduce the magnitude of each type of matrix element in the decay process. Furthermore, when the model space is expanded from the 50–82 shell to the 50–126 shell, the magnitudes of all matrix elements increase significantly, consistent with the findings of the shell model. Additionally, the suppressing effect of higher-order contributions appears to be independent of model space truncation.

The oscillator parameters in nuclei are reevaluated using three different methods. The first employs a conventional approach, utilizing updated experimental charge-radius data and neutron skin thicknesses obtained from self-consistent mean-field calculations as constraints. The occupations of unique-parity intruder states, induced by the spin-orbit coupling, are properly accounted for using the level ordering generated with a realistic potential. However, the results from this method show no significant difference from those obtained in the prior work [Nucl. Phys. A 781, 350 (2007)]. In the second method, we explicitly introduce Coulomb and symmetry terms to the oscillator Hamiltonian. Within a specific form of these additional terms, their contributions can be absorbed, leading to a formal definition of an isospin-invariant and an isospin-dependent oscillator parameter. The oscillator parameter for protons corresponds exactly to those extracted from the charge-radius systematics in the first method, while the one for neutrons differs considerably from that obtained via neutron skin thickness. The isospin-invariant parameter does not have a traditional correspondence because its evaluation requires subtraction of Coulomb and symmetry contributions. This distinction could be impactful to the shell model where the configuration space is extremely limited, especially if isospin-nonconserving forces are incorporated. The final method involves direct adjustment of the oscillator functions to maximize the overlap with Hartree-Fock eigenfunctions using the effective Skyrme interaction. Despite larger uncertainties, reflecting substantial orbital- and Skyrme-parametrization dependences, the results of this approach agree fairly well with those extracted from the charge-radius systematics.

Preliminary data from the Beam-Energy Scan II measurements by the STAR Collaboration at the Relativistic Heavy Ion Collider suggest a dip in the fourth-to-second-order cumulant ratio when plotted vs beam energy. At the same energy range where the structure appears, a transition from hadrons to quarks is expected, the deconfinement transition. In this paper, the role of quark deconfinement in establishing fluctuaitions in the early stages of the collision is considered. Two models are compared: one with stopping occurring on a baryon-by-baryon basis, and a second where stopping proceeds through quark degrees of freedom. In the latter model, the fluctuation of baryon number is significantly reduced and this signal is found to survive recombination into hadrons and the subsequent diffusion. The transformation from baryon to quark stopping thus produces a dip in the fourth-to-second-order cumulant ratio when plotted vs beam energy, consistent with observations.

The newly published data on spin density matrix elements from the GlueX Collaboration, along with the previously released differential cross-section data from the CLAS Collaboration and the other two experiments for the $\gamma p\to {\rho }^{0}p$ reaction, are systematically investigated using an effective Lagrangian approach within the tree-level Born approximation. The model combines contributions from $t$-channel meson exchanges ($\pi , \eta$, and $f_2$), $s$-channel nucleon ($N$) and nucleon resonance ($N^{*}$) exchanges, $u$-channel $N$ exchange, and a generalized contact term to construct the scattering amplitudes. Regge propagators are employed for $t$-channel amplitudes to incorporate the contributions from mesons with various spins lying on the same trajectories. The analysis shows that the background contributions, dominated by the $f_2$-trajectory exchange, provide a satisfactory description of the data in the high-energy and forward-angle regions. The inclusion of specific nucleon resonances, such as $N\left(2100\right)1/2^{+}, N\left(2060\right)5/2^{-}$, or $\mathrm{\Delta }\left(2000\right)5/2^{+}$, significantly improves the description of the differential cross-section data at near-perpendicular scattering angles in the low-energy region. Predictions of photon beam and target nucleon asymmetries are provided, offering valuable insights to discriminate reaction mechanisms when corresponding data become available in the future.

For the last 60 years researchers have struggled to unambiguously identify the first excited state in ${}^9\mathrm{B}$. Many prior experimental and theoretical results provide conflicting answers on the expected energy that this level should possess. Within these lie a trend wherein two distinct values emerge as possible solutions to this long-standing question. This dual energy mystery has now been resolved following the identification of the $3/2^{-}$ ground-state ghost peak in the $R$-matrix spectrum of ${}^9\mathrm{B}$. Reevaluation of existing experimental data in the context of this new insight provides further proof of historical misidentification of a state at 0.8 MeV in ${}^9\mathrm{B}$.

This study explores the application of Kolmogorov-Arnold networks (KANs) in predicting nuclear binding energies, leveraging their ability to decompose complex multiparameter systems into simpler univariate functions. By utilizing data from the Atomic Mass Evaluation (AME2020) and incorporating features such as atomic number, neutron number, and shell effects, KANs achieved a significant lower root mean square error (0.26 MeV), surpassing traditional models. The symbolic regression analysis yielded simplified analytical expressions for binding energies, aligning with classical models like the liquid drop model and the Bethe-Weizsäcker formula. These results highlight KANs' potential in enhancing the interpretability and understanding of nuclear phenomena, paving the way for future applications in nuclear physics and beyond.

We investigate the intriguing phenomenon of beta decay of a free neutron in a non-plane-wave (structured) state. Our analysis covers three types of states: unpolarized vortex (Bessel) neutrons that possess nonzero orbital angular momentum (OAM), Laguerre-Gaussian wave packets, and spin-correlated OAM (spin-orbit) states characterized by unique polarization patterns. These states are of particular interest as they have recently been generated in neutron optics experiments and have promising applications in studies of quantum magnetic materials. The spectral-angular distributions (SAD) of the emitted electrons and protons are examined. We show that the high sensitivity of the protons' SAD to the structure of the neutron wave packet can be used as a tool to extract the distinctive features of the non-plane-wave neutron states. Furthermore, we demonstrate that the angular distribution of the emitted particles serves as a reflection of the spatial symmetries inherent to the neutron wave packet.

The angular distribution of products in multinucleon transfer (MNT) reactions is a significant topic of interest in both experimental and theoretical studies. By considering fluctuations and nucleon transfer effects based on the classical deflection function, a method is developed that integrates the dinuclear system (DNS) model for calculating angular distributions in MNT reactions. The angular distributions of projectile-like fragments (PLFs) and target-like fragments (TLFs) of the reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ are obtained, with results demonstrating good agreement with experimental data. To further investigate the effects of nucleon transfer, the performance of the method across the regions of $68<Z<82, 92<Z<103$, and $Z>103$ is discussed. Additionally, the double differential cross section of the reaction ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ is explored, along with the angular distribution of primary and final products with proton numbers greater than 103. The proposed method and the calculated results contribute to a deeper understanding of the mechanisms underlying angular distributions in MNT reactions.

A comprehensive test of level density models for explaining the decay of excited compound nuclei ${}^{54}\mathrm{Mn}$, ${}^{56}\mathrm{Fe}$, ${}^{58}\mathrm{Co}$, ${}^{60}\mathrm{Ni}$, ${}^{61}\mathrm{Ni}$, and ${}^{63}\mathrm{Cu}$ in the energy range of 28–36 MeV was performed. The compound nuclei of interest in the desired ranges were populated using ${}^6\mathrm{Li}$ based transfer reactions. The proton decay spectrum for each excitation energy bin was measured. The measured proton spectrum was reproduced using statistical model calculations with different level density models. A variance minimized approach was employed for analyzing the prediction capability of different level density models. This approach was converged to the Gogny Hartree-Fock-Bogoliubov (HFB) microscopic level density model, which is considered the most accurate model for the desired nuclei.

Heavy-ion-fusion reactions at near-barrier energies take place in two steps. In the first, the system overcomes the potential barrier. In the second, the collision partners merge to form a single body, losing their identities. Most theoretical models ignore the latter, assuming that barrier transmission guarantees fusion. However, it is well known that this assumption is not valid in collisions of very heavy systems. In that case, the collision partners may fuse or emerge from the inner region of the barrier, roughly keeping their original properties. The present paper investigates the influence of the second stage of the collision on the fusion cross section. For this aim, we compare the fusion data of many systems in different mass regions. To eliminate the influence of the height and radius of the Coulomb barrier, the data used in our comparisons are reduced by the classical fusion function method. We find that the evolution of the system is determined by the effective fissility parameter. Barrier transmission guarantees fusion for light and medium-heavy systems where the value of this parameter is less than 25. A different situation is encountered above this limit. The projectile may be captured by the target, or the collision partners may reseparate with their original identities or differ by exchanging a few nucleons. As a result, the capture cross section is suppressed compared to the predictions of the barrier penetration models.

We compute baryon and electric charge deposition in high-energy heavy-ion collisions using the color glass condensate effective field theory, where at leading order, charge is deposited through multiple scatterings of valence quarks with a saturated gluon target. A simplified phenomenological formula is derived to describe charge deposition, from which the parametrical dependence with collisional energy and geometry can be extracted. We present an approximate analytical prediction of the so-called baryon stopping parameter ${\alpha }_B$, which shows excellent agreement with the state-of-the art extractions of ${\alpha }_B$ from experimental data. These results are further validated using the McDipper framework, by computing charge deposition at midrapidity across a range of collision energies $(\sqrt{s_{NN}}=62.4–5020\mathrm{GeV})$.

Can relativistic heavy-ion collisions only probe the global shape of colliding nuclei, or their detailed internal structure as well? Taking ${}^{20}\mathrm{Ne}$ as an example, we attempt to directly probe its internal $\alpha$-cluster structure, by comparing experimentally measured observables in collisions at relativistic energies from density distributions of ${}^{20}\mathrm{Ne}$ with and without $\alpha$-cluster structure. Since the two density distributions give the same nucleus size and deformation, they lead to similar midrapidity observables. However, the $\alpha$-cluster structure may considerably reduce the free spectator nucleon yield and enhance the spectator light nuclei yield, as a result of more compact initial phase-space distribution of nucleons inside $\alpha$ clusters. We propose to measure the scaled yield ratio of free spectator neutrons to charged particles with mass-to-charge ratio $A/Z=3$, 3/2, and 2 in ultracentral ${}^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions, which is found to be reduced by about $25\%$ at $\sqrt{s_{NN}}=7$ TeV and about 20% at $\sqrt{s_{NN}}=200$ GeV with $\alpha$-cluster structure in ${}^{20}\mathrm{Ne}$. This scaled yield ratio thus serves as a robust and direct probe of the existence of $\alpha$-cluster structure in ${}^{20}\mathrm{Ne}$ free from the uncertainty of midrapidity dynamics.

The attractor, which is supposed to be one of the possible answers for the early applicability of hydrodynamics in the evolution with different initial conditions, has attracted great attention to the fast decreasing of degrees of freedom in heavy ion collisions. We find attractor behaviors for $1+1\mathrm{D}$ viscous hydrodynamics with general rapidity distribution based on Müller-Isreal-Stewart theory. Meanwhile, we also observe that a rapid expansion in the fluid velocity is essential for a rapid early time attractor.

The four nucleons in ${}^8\mathrm{Li}$ outside the $\alpha$ particle ($\alpha ={}^4\mathrm{He}$) can be divided into pairs of one neutron ($n$) and three nucleons in the triton ($t={}^3\mathrm{H}$), or two in the deuteron ($d={}^2\mathrm{H}$) and two neutrons in a dineutron (${}^{2}n$). The corresponding three-body structures, $\alpha +t+n$ or $\alpha +d+{}^{2}n$, are suggested to describe the bulk part of the low-energy ($<10\mathrm{MeV}$) states of ${}^8\mathrm{Li}$. Several breakup thresholds influence the structures and possible decays. We calculate the three-body structures of the various $J^{\pi }$ states where different clustering appears, e.g., ${}^7\mathrm{Li}^{*}+n$, ${}^6\mathrm{Li}^{*}+{}^{2}n$, ${}^6\mathrm{He}^{*}+d$. The experimental ${}^8\mathrm{Li}$ spectrum can be reproduced with fine tuning by a three-body potential parameter. Three unobserved $0^{+}$ states and an excited $2^{+}$ state are found. All states appear as bound states or resonances. The lowest or highest energies have cluster structures, $\alpha +t+n$ or $\alpha +d+{}^{2}n$, respectively. We give calculated energy and width (if possible), geometry, and partial wave decomposition for all states.

Event-by-event mean transverse momentum fluctuations ($\langle p_{\mathrm{T}}\rangle$) serve as a sensitive probe of initial state overlap geometry and energy density fluctuations in relativistic heavy-ion collisions. We present a systematic investigation of $\langle p_{\mathrm{T}}\rangle$ fluctuations in Au + Au collisions at $\sqrt{{\mathrm{s}}_{\mathrm{NN}}}=3.0-19.6\mathrm{GeV}$, examining their centrality and energy dependence with the framework of an improved multiphase transport model. The centrality dependence of the $p_{\mathrm{T}}$ cumulants up to fourth order deviates significantly from simple powering-law scaling. Scaled cumulants are performed, with variances aligning well with the trends observed in the experimental data. Employing a two-subevent method, short-range correlations are slightly suppressed compared to the standard approach. Furthermore, baryons exhibit more pronounced $\langle p_{\mathrm{T}}\rangle$ fluctuations than mesons, potentially attributable to the effect of radial flow. These results provide referenced insight into the role of initial state fluctuations across different energies in heavy-ion collisions.

Background: Measurements of the polarization observables $\mathrm{\Sigma },\mathbf{P},\mathbf{T},{\mathbf{O}}_{\mathbf{x}},{\mathbf{O}}_{\mathbf{z}}$ for the reaction $\vec{\gamma }p\to K_S^0{\mathrm{\Sigma }}^{+}$ using a linearly polarized photon beam of energy 1.1 to 2.1 GeV are reported.

Purpose: The measured data provide information on a channel that has not been studied extensively, but is required for a full coupled-channel analysis in the nucleon resonance region.

Method: Observables have been simultaneously extracted using likelihood sampling with a Markov-Chain Monte Carlo process.

Results: Angular distributions in bins of photon energy $E_{\gamma }$ are produced for each polarization observable. $\mathbf{T},{\mathbf{O}}_{\mathbf{x}}$, and ${\mathbf{O}}_{\mathbf{z}}$ are first time measurements of these observables in this reaction. The extraction of $\mathrm{\Sigma }$ extends the energy range beyond a previous measurement. The measurement of $\mathbf{P}$, the recoil polarization, is consistent with previous measurements.

Conclusions: The measured data are shown to be significant enough to affect the estimation of the nucleon resonance parameters when fitted within a coupled-channels model.

Background: The CNO cycle powers core H burning, in stars with $M>1.2M_{\odot }$, and shell H burning, during the advanced evolutionary phases. Therefore, the uncertainties affecting the reaction rates of proton captures on C, N, and O isotopes limit our understanding of stellar evolution and nucleosynthesis.

Purpose: We aim to develop a general and self-consistent tool for the calculation of nuclear reaction rates and their uncertainties, starting from available experimental data. As a longer term plan, we intend to use this tool to revise the proton-capture reactions of the CNO cycle for which new experimental data are or will be available in the next future.

Method: The general procedure consists of $R$-matrix cross section calculations based on available measurements of the relevant nuclear parameters (energies, widths, strengths of known resonances, interference patterns, etc.), coupled to a Monte Carlo procedure to evaluate the global reaction rate error.

Results: A first application of this method to ${}^{17}\mathrm{O}(p,\gamma ){}^{18}\mathrm{F}$ and ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$, the reactions that determine the ${}^{17}\mathrm{O}$ destruction in stellar interiors where the CNO cycle is active, is presented. These two reactions also allow us to test the multichannel and multilevel capabilities of the $R$-matrix method. In the temperature range of hydrostatic H burning ($T<100$ MK), we confirm that the median rates are up to a factor of 2 higher than those suggested in reaction rate libraries commonly used in stellar model calculations. In this temperature range, the ${}^{17}\mathrm{O}$ destruction mainly proceeds through the ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$ channel, whose rate is known within $\pm 20\%$ (95% C.L.).

Conclusions: Based on current stellar models of red giant stars, we show that this uncertainty produces a 10% variation on the predicted ${}^{16}\mathrm{O}/{}^{17}\mathrm{O}$ abundance ratio. Other uncertainties, such as those affecting the ${}^{17}\mathrm{O}$ production rate, i.e., the ${}^{16}\mathrm{O}(p,\gamma ){}^{17}\mathrm{F}$ reaction, have a stronger impact on this theoretical prediction, a fact that motivates further experimental investigations of the ${}^{17}\mathrm{O}$ production channel.

The reaction rates have been calculated for the $n+p+d\to d+d\mathrm{and}n+p+n+p\to d+d$ capture reactions using the Faddeev-Yakubovskii chain-of-partition momentum-space integral equations. Using time reversal invariance, the amplitudes for the capture reactions were related to the $d+d\to n+p+d$ and $d+d\to n+p+n+p$ breakup amplitudes. The capture rates were then determined using this amplitude relationship, together with precalculated breakup amplitudes as input. The $n+p+d\to d+d$ single-capture reaction rates were determined for the $S=2\mathrm{spin}\text{and}L=0$ angular-momentum state for energies $E\le 4.17\mathrm{MeV}$. At the energy $E=3.29\mathrm{MeV}$, the reaction rate increased as a function of the initial neutron-proton relative momentum $\kappa \le 0.16{\mathrm{fm}}^{-1}$. The capture reaction rate also increased as a function of energy, especially with higher neutron-proton momentum. The $S=2/L=0$ reaction rates for the $n+p+n+p\to d+d$ double capture were calculated as a function of the initial neutron-proton relative momentum $\kappa \le 0.072\mathrm{f}{\mathrm{m}}^{-1}$ and as a function of energy E $\le$ 5.48 MeV. The calculations indicated a strong increase of the capture rate with increasing neutron-proton relative momentum and with decreasing energy. A comparison of the double and single capture rates found the double capture to be much stronger. The muon-catalyzed capture rates were used to determine the energy contribution and deuteron production for input to the $dd\mu$ and $dt\mu$ fusion calculations. While all capture times were less than the muon lifetime and increased fusion deuterons, the double capture was fast enough to allow multicapture cycling. The capture rates were also calculated for inertial-confinement fusion (ICF). In the ICF case of deuteron-triton fusion $\left[\to {}^4\mathrm{He}\left(3.5\mathrm{MeV}\right)+n\left(14.1\mathrm{MeV}\right)\right]$, at the fusion-born neutron-deuteron breakup peak, the fusion neutron produces $\sim 0.10\mathrm{captures}$/s fusion. The deuteron-breakup fusion reduction, in both the muon-catalyzed and inertial-confinement fusion, is reduced by subsequent neutron-proton capture, which increases the fusion rate. The single and double capture rates were also used as input to the big bang nucleosynthesis model. Comparison of the radiative and catalytic capture rates indicated that the contribution of the catalytic single and double captures is very small compared to that of the radiative captures.

In light of the recently observed $8\times {10}^5$ barn thermal neutron absorption cross section of zirconium-88, this work investigates the rate (isomeric yield ratio) of metastable zirconium-89 production and resulting implications for ongoing measurements around zirconium-88 neutron absorption. The metastable state of zirconium-89 resides at 588 keV above the ground state with a half-life of 4.2 min. A $5\mu \mathrm{Ci}$ zirconium-88 sample was irradiated for 10 min in the core of a TRIGA Mark II nuclear research reactor and measured with a high purity germanium detector starting 3 min after irradiation. The isomeric yield ratio was measured to be $74.9\pm 0.6\%$.