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We propose a theoretical method to calculate the bound-state $\beta$-decay half-lives of highly-ionized atoms, which is based on the combination of the Takahashi-Yokoi model and our recently-developed projected shell model that can take into account both allowed and first-forbidden transitions of nuclear $\beta$ decay. Three examples that are of much experimental interests, $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$ are taken for calculations. The ground and low-lying states of related nuclei are described reasonably. The bound-state $\beta$-decay half-lives of $^{163}$Dy$^{66+}$ and $^{187}$Re$^{75+}$ are described within a factor of two and four by our calculations without and with the quenching factors in allowed and first-forbidden transitions. The bound-state $\beta$-decay half-life of the last $s$-process branching point $^{205}$Tl$^{81+}$ is predicted to be 58 and 305 days for cases without and with the quenching factors in calculations. The presented method provides a theoretical way to calculate systematically the bound-state $\beta$-decay half-lives of nuclei from light to heavy ones including odd-mass and even-mass cases for the first time.

We explore the potential manifestation of a hexaquark, the H particle, as a constituent within neutron stars. The H particle, characterized by a quark composition of $uuddss$, is constructed using the framework of Chromomagnetic Interaction (CMI). Specifically, we contemplate the flavor-singlet state H with $J^P=0^+$. Our computations indicate that the three-flavor hexaquark state, the H particle, possesses a lower mass of $2212.7~\rm{MeV}$ in comparison to the $d^*(2380)$, implying greater stability than the two-flavor $d^*(2380)$. The analysis involving the H particle is carried out using the relativistic mean-field (RMF) model. We investigate the influence of H particle couplings, a key factor in determining the system stability, and focus on the potential existence of H particle within neutron stars. We find that H particle could potentially endure as a stable constituent within neutron stars, and lead to a reduction of the maximum mass.

This paper presents a phenomenological study on the angle between the Standard and the Winner-Take-All (WTA) jet axes ($\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$) in high-energy nuclear collisions. The $p$+$p$ baseline is provided by the Pythia8 event generator. The in-medium jet propagation is simulated by the linear Boltzmann transport (LBT) model, which considers both the elastic and inelastic jet-medium interactions. Our theoretical results calculated by the LBT model show that the $\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$ distribution in Pb+Pb at $\sqrt{s}=5.02$ TeV is narrower than that in $p$+$p$, which agrees well with the recent ALICE measurements. The narrowing of $\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$ seems to violate the $p_T$-broadening nature of the jet quenching effect, usually explained by the influence of "selection bias". However, the physical details still need to be fully understood. Utilizing a matching-jet method to track the jet evolution in the QGP to remove the selection bias in the Monte Carlo simulations, we observe that the $\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$ distribution becomes broader due to the jet-medium interactions. At the same time, by rescaling the quark/gluon-jet fractions in Pb+Pb collisions to be the same as that in $p$+$p$, we find that the fraction change may not significantly influence the modification pattern of jet $\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$. On the other hand, the selected jet sample in A+A collisions has a significantly narrower initial $\Delta R_{{\rm axis}}^{{\rm WTA-Std}}$ distribution than the $p$+$p$ baseline, and such a biased comparison between $p$+$p$ and A+A conceals the actual jet-broadening effect in the experimental measurements. The investigations presented in this paper will deepen our understanding of the relationship between the actual intra-jet modifications in the QGP and the experimental observations.

We propose a theoretical method to calculate the stellar $\beta$-decay rates of nuclei in stellar environments with high temperature and density, based on the projected shell model, where contributions from both allowed and first-forbidden transitions are taken into account. As the first example, the stellar $\beta$-decay rate of one of the last $s$-process branching-point nuclei, $^{204}$Tl, is calculated and studied, where all related transitions are first-forbidden transitions. For the terrestrial case, the ground-state to ground-state transition is unique first-forbidden transition, which is described reasonably by our calculations. At the typical $s$-process temperature ($T\approx 0.3$ GK), non-unique first-forbidden transitions from thermally populated excited states of the parent nucleus are involved, the effective rate from our calculations is much lower than the one from the widely used data tables by Takahashi and Yokoi. Effect of the quenching factors for nuclear matrix elements in first-forbidden transitions on the stellar $\beta$-decay rates is discussed as well.

The first-forbidden transition of nuclear $\beta$ decay is expected to play crucial roles in many aspects in nuclear physics, nuclear astrophysics and particle physics such as the stellar $\beta$-decay rates and the reactor anti-neutrino spectra. In this work we develop the projected shell model (PSM) for description of first-forbidden transition of nuclear $\beta$ decay for the first time. Detailed theoretical framework and logics are provided, and 35 dominant first-forbidden transitions that are expected to be important for the reactor anti-neutrino spectra problems are calculated and compared systematically with the data to test the new development of the PSM. The corresponding experimental Log$f_0 t$ values are described reasonably, and the quenching factors of nuclear matrix elements are found to affect the Log$f_0 t$ values as well as the related shape factors, which may be helpful for better understanding of the reactor anti-neutrino spectra problems.

We propose a projected shell model (PSM) for description of stellar weak-interaction rates between even-even and odd-odd nuclei with extended configuration space where up to six-quasiparticle (qp) configurations are included, and the stellar weak-interaction rates for eight $rp$-process waiting-point (WP) nuclei, $^{64}$Ge, $^{68}$Se, $^{72}$Kr, $^{76}$Sr, $^{80}$Zr, $^{84}$Mo, $^{88}$Ru and $^{92}$Pd, are calculated and analyzed for the first time within the model. Higher-order qp configurations are found to affect the underlying Gamow-Teller strength distributions and the corresponding stellar weak-interaction rates. Under $rp$-process environments with high temperatures and densities, on one hand, thermal population of excited states of parent nuclei tends to decrease the stellar $\beta^+$ decay rates. On the other hand, the possibility of electron capture (EC) tends to provide increasing contribution to the rates with temperature and density. The effective half-lives of WP nuclei under the $rp$-process peak condition are predicted to be reduced as compared with the terrestrial case, especially for $^{64}$Ge and $^{68}$Se.

Nuclear $\beta$ spectrum and the corresponding (anti-)neutrino spectrum play important roles in many aspects of nuclear astrophysics, particle physics, nuclear industry and nuclear data. In this work we propose a projected shell model (PSM) to calculate the level energies as well as the reduced one-body transition density (ROBTD) by the Pfaffian algorithm for nuclear $\beta$ decays. The calculated level energies and ROBTD are inputed to the Beta Spectrum Generator (BSG) code to study the high precision $\beta$ spectrum of allowed one-to-one transitions. When experimental level energies are adopted, the calculated $\beta$ spectrum by ROBTD of the PSM deviates from the one by the extreme simple particle evaluation of the BSG by up to $10\%$, reflecting the importance of nuclear many-body correlations. When calculated level energies are adopted, the calculated $\beta$ spectrum shows sensitive dependence on the reliability of calculated level energies. The developed method for ROBTD by the PSM will also be useful for study of the first-forbidden transitions, the isovector spin monopole resonance etc. in a straightforward way.

Scaling analyses have been successfully applied to study the inclusive electron scattering $(\textit{e}, \textit{e}^{\prime})$ over the past few decades. In this paper, we utilize the $\psi^{\prime}$ scaling function in momentum space to analyze the $(\textit{e}, \textit{e}^{\prime})$ cross sections, where the nucleon momentum distributions are derived from self-consistent mean-field calculations. By further introducing the energy and momentum conservation in the scaling analysis, an improved $\psi^{\prime}$ scaling function is proposed to investigate the high-momentum part of the momentum distributions. Using the proposed scaling function, we systematically explore the effects of the nucleon-nucleon short-range correlation ($\textit{NN}$-SRC) on the $(\textit{e}, \textit{e}^{\prime})$ cross sections. From the experimental $(\textit{e}, \textit{e}^{\prime})$ data, the \textitNN-SRC strength is further extracted within the framework of the improved $\psi^{\prime}$ scaling function. The studies in this paper offer a new method to investigate the nucleon momentum distributions and the $\textit{NN}$-SRC effects in nuclei.

Using $(1.0087\pm0.0044)\times10^{10}$ $J/\psi$ events collected with the BESIII detector at the BEPCII storage ring, the process $\Xi^{0}n\rightarrow\Xi^{-}p$ is studied, where the $\Xi^0$ baryon is produced in the process $J/\psi\rightarrow\Xi^0\bar{\Xi}^0$ and the neutron is a component of the $^9\rm{Be}$, $^{12}\rm{C}$ and $^{197}\rm{Au}$ nuclei in the beam pipe. A clear signal is observed with a statistical significance of $7.1\sigma$. The cross section of the reaction $\Xi^0+{^9\rm{Be}}\rightarrow\Xi^-+p+{^8\rm{Be}}$ is determined to be $\sigma(\Xi^0+{^9\rm{Be}}\rightarrow\Xi^-+p+{^8\rm{Be}})=(22.1\pm5.3_{\rm{stat}}\pm4.5_{\rm{sys}})$ mb at the $\Xi^0$ momentum of $0.818$ GeV/$c$, where the first uncertainty is statistical and the second is systematic. No significant $H$-dibaryon signal is observed in the $\Xi^-p$ final state. This is the first study of hyperon-nucleon interactions in electron-positron collisions and opens up a new direction for such research.

This work presents the first theoretical investigation of the medium modification of jet broadening as an event-shape observable in multijet final states due to jet quenching in high-energy nuclear collisions. The partonic spectrum of $pp$ collisions with next-to-leading order (NLO) accuracy at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV is provided by the POWHEG$+$PYTHIA8 event generator, while the linear Boltzmann transport (LBT) model is utilized to investigate the energy loss of fast partons as they traverse through the hot and dense QCD medium. We present the jet broadening distributions in multijet final states for both $pp$ and PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, then observe an enhancement at the small jet broadening region and suppression at the large jet broadening region in PbPb collisions relative to that in $pp$. This suggests that medium modification with parton energy loss in the QGP leads to a more concentrated energy flow in all observed multijet events in PbPb reactions. We also demonstrate that the intertwining of two effects, the jet number reduction and the restructured contribution, results in the novel behavior of nuclear modification of the jet broadening observable in PbPb collisions.

A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is to measure the $\mathcal{O}(10)$ MeV neutrinos produced by a Galactic core-collapse supernova if one should occur during the lifetime of the experiment. The liquid-argon-based detectors planned for DUNE are expected to be uniquely sensitive to the $\nu_e$ component of the supernova flux, enabling a wide variety of physics and astrophysics measurements. A key requirement for a correct interpretation of these measurements is a good understanding of the energy-dependent total cross section $\sigma(E_\nu)$ for charged-current $\nu_e$ absorption on argon. In the context of a simulated extraction of supernova $\nu_e$ spectral parameters from a toy analysis, we investigate the impact of $\sigma(E_\nu)$ modeling uncertainties on DUNE's supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on $\sigma(E_\nu)$ must be substantially reduced before the $\nu_e$ flux parameters can be extracted reliably: in the absence of external constraints, a measurement of the integrated neutrino luminosity with less than 10\% bias with DUNE requires $\sigma(E_\nu)$ to be known to about 5%. The neutrino spectral shape parameters can be known to better than 10% for a 20% uncertainty on the cross-section scale, although they will be sensitive to uncertainties on the shape of $\sigma(E_\nu)$. A direct measurement of low-energy $\nu_e$-argon scattering would be invaluable for improving the theoretical precision to the needed level.

In recent years, machine learning has emerged as a powerful computational tool and novel problem-solving perspective for physics, offering new avenues for studying strongly interacting QCD matter properties under extreme conditions. This review article aims to provide an overview of the current state of this intersection of fields, focusing on the application of machine learning to theoretical studies in high energy nuclear physics. It covers diverse aspects, including heavy ion collisions, lattice field theory, and neutron stars, and discuss how machine learning can be used to explore and facilitate the physics goals of understanding QCD matter. The review also provides a commonality overview from a methodology perspective, from data-driven perspective to physics-driven perspective. We conclude by discussing the challenges and future prospects of machine learning applications in high energy nuclear physics, also underscoring the importance of incorporating physics priors into the purely data-driven learning toolbox. This review highlights the critical role of machine learning as a valuable computational paradigm for advancing physics exploration in high energy nuclear physics.

We investigate the medium modifications of momentum splitting fraction and groomed jet radius with both dynamical grooming and soft drop algorithms in heavy-ion collisions. In the calculation, the partonic spectrum of initial hard scattering in p+p collisions is provided by the event generator PYTHIA 8, and the energy loss of fast parton traversing in a hot/dense QCD medium is simulated with the Linear Boltzmann Transport (LBT) model. We predict the normalized distributions of the groomed jet radius $\theta_g$ and momentum splitting fraction $z_g$ with the dynamical grooming algorithm in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, then compare these quantities in dynamical grooming at $a=0.1$, with that in soft drop at $z_{\mathrm{cut}} = 0.1$ and $\beta = 0$. It is found that the normalized distribution ratios Pb+Pb/p+p with respect to $z_g$ in $z_{\mathrm{cut}} = 0.1$, $\beta = 0$ soft drop case are close to unity and those in $a=0.1$ dynamical grooming case show enhancement at small $z_g$, and Pb+Pb/p+p with respect to $\theta_g$ in the dynamical grooming case demonstrate weaker modification than those in the soft drop counterparts. We further calculate the groomed jet number averaged momentum splitting fraction $\rm \langle z_g \rangle_{jets}$ and averaged groomed jet radius $\rm \langle \theta_g \rangle_{jets}$ in p+p and A+A for both grooming cases in three $p^{\rm ch, jet}_{\rm T}$ intervals, and find that the originally generated well balanced groomed jets will become more momentum imbalanced and less jet size narrowing due to jet quenching, and weaker medium modification of $z_g$ and $\theta_g$ in $a =0.1$ dynamical grooming case than in the soft drop counterparts.

Motivated by recent experimental LHC measurements on the forward inclusive jet productions and based on our previous calculations on forward hadron productions, we calculate single inclusive jet cross-section in $pA$ collisions at forward rapidity within the color glass condensate framework up to the next-to-leading-order. Moreover, with the application of jet algorithm and proper subtraction of the rapidity and collinear divergences, we further demonstrate that the resulting next-to-leading-order hard coefficients are finite. In addition, in order to deal with the large logarithms that can potentially spoil the convergence of the perturbative expansion and improve the reliability of the numerical predictions, we introduce the collinear jet function and the threshold jet function and resum these large logarithms hidden in the hard coefficients.

The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and efficient algorithm for the Wigner $d$ function based on the Jacobi polynomials. We compare our method with the conventional Wigner method and the Tajima Fourier method through some testing calculations, and demonstrate that our algorithm can always give stable results with similar high-precision as the Fourier method, and in some cases (for special sets of $j, m, k$ and $\theta$) ours are even more accurate. Moreover, our method is self-contained and less memory consuming. A related testing code and subroutines are provided as Supplemental Material in the present paper.

The production of $\pi^0$, $\eta$, and $\phi$ in the most central (0%-5%) Xe+Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV is investigated in the framework of the perturbative QCD (pQCD) improved parton model at an accuracy of next-to-leading order (NLO). The jet quenching effect is effectively incorporated by medium-modified fragmentation functions via the higher-twist approach. Predictions of the nuclear modification factors of $\pi^0$, $\eta$, and $\phi$ as functions of the transverse momentum $p_{\rm T}$ are made with the jet transport parameter $\hat{q}_0$, which is extracted from the available experimental data of charged hadrons provided by ALICE and CMS. The particle ratios $\eta/\pi^0,\ \phi/\pi^0$ as functions of $p_{\rm T}$ in Xe+Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV as well as in 0%-5% Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are also presented. The numerical simulations of the scaled ratios of charged hadron production in the Xe+Xe 5.44 TeV system over those in the Pb+Pb 5.02 TeV system give a good description of the CMS data, and the scaled ratios of $\pi^0$, $\eta$, and $\phi$ production coincide with the curve of charged hadron production.

Reconstructing hadron spectral functions through Euclidean correlation functions are of the important missions in lattice QCD calculations. However, in a Källen--Lehmann(KL) spectral representation, the reconstruction is observed to be ill-posed in practice. It is usually ascribed to the fewer observation points compared to the number of points in the spectral function. In this paper, by solving the eigenvalue problem of continuous KL convolution, we show analytically that the ill-posedness of the inversion is fundamental and it exists even for continuous correlation functions. We discussed how to introduce regulators to alleviate the predicament, in which include the Artificial Neural Networks(ANNs) representations recently proposed by the Authors in~[Phys. Rev. D 106 (2022) L051502]. The uniqueness of solutions using ANNs representations is manifested analytically and validated numerically. Reconstructed spectral functions using different regularization schemes are also demonstrated, together with their eigen-mode decomposition. We observe that components with large eigenvalues can be reliably reconstructed by all methods, whereas those with low eigenvalues need to be constrained by regulators.

The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. In this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of $\sim$1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations. We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future Electron-Ion Collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy Quantum Chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in $pp$ and $pA$ collisions, especially in the high $p_T$ region, and obtain reliable descriptions of all existing data measured at RHIC and the LHC across all $p_T$ regions. Consequently, this technique can pave the way for the precision studies of the CGC next-to-leading-order predictions by confronting them with a large amount of precise data.

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasi-particle configurations. Detailed derivation based on [Mizusaki et al., Phys. Lett. B 715, 219 (2012)] and [Hu et al., Phys. Lett. B 734, 162 (2014)] is provided, and potential applications in generator coordinate method with chiral interactions, as well as in study of nuclear matrix elements in neutrinoless double beta decay are discussed.

Capture of electrons by nuclei is an important process in stellar environments where excited nuclear states are thermally populated. However, accurate treatment for excited configurations in electron capture (EC) rates has been an unsolved problem for medium-heavy and heavy nuclei. In this work, we take the $^{93}$Nb $\rightarrow$ $^{93}$Zr EC rates as the example to introduce the Projected-Shell-Model (PSM) in which excited configurations are explicitly included as multi-quasiparticle states. Applying the prevalent assumption that the parent nucleus always stays in its ground state in stellar conditions, we critically compare the obtained PSM results with the recently-measured Gamow-Teller transition data, and with the previous calculations by the conventional shell model and the quasiparticle random-phase approximation. We discuss important ingredients that are required in theoretical models used for stellar EC calculations, and demonstrate effects of the explicit inclusion of excited nuclear states in EC rate calculations, especially when both electron density and environment temperature are high.

In this proceeding, the deep Convolutional Neural Networks (CNNs) are deployed to recognize the order of QCD phase transition and predict the dynamical parameters in Langevin processes. To overcome the intrinsic randomness existed in a stochastic process, we treat the final spectra as image-type inputs which preserve sufficient spatiotemporal correlations. As a practical example, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a $1+1$-dimensional Langevin equation for $\sigma$ field. The well-trained CNNs accurately classify the first-order phase transition and crossover from $\sigma$ field configurations with fluctuations, in which the noise does not impair the performance of the recognition. In reconstructing the dynamics, we demonstrate it is robust to extract the damping coefficients $\eta$ from the intricate field configurations.

The search of chiral magnetic effect (CME) in heavy-ion collisions has attracted long-term attentions. Multiple observables have been proposed but all suffer from obstacles due to large background contaminations. In this Letter, we construct an observable-independent CME-meter based on a deep convolutional neural network. After trained over data set generated by a multiphase transport model, the CME-meter shows high accuracy in recognizing the CME-featured charge separation from the final-state pion spectra. It also exhibits remarkable robustness to diverse conditions including different collision energies, centralities, and elliptic flow backgrounds. In a transfer learning manner, the CME-meter is validated in isobaric collision systems, showing good transferability among different colliding systems. Based on variational approaches, we utilize the DeepDream method to derive the most responsive CME-spectra that demonstrates the physical contents the machine learns.

It is non-trivial to recognize phase transitions and track dynamics inside a stochastic process because of its intrinsic stochasticity. In this paper, we employ the deep learning method to classify the phase orders and predict the damping coefficient of fluctuating systems under Langevin's description. As a concrete set-up, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a $1+1$-dimensional Langevin equation for $\sigma$ field. In a supervised learning manner, the Convolutional Neural Networks(CNNs) accurately classify the first-order phase transition and crossover based on $\sigma$ field configurations with fluctuations. Noise in the stochastic process does not significantly hinder the performance of the well-trained neural network for phase order recognition. For mixed dynamics with diverse dynamical parameters, we further devise and train the machine to predict the damping coefficients $\eta$ in a broad range. The results show that it is robust to extract the dynamics from the bumpy field configurations.

The excited-state structure of atomic nuclei can modify nuclear processes in stellar environments. In this work, we study the influence of nuclear excitations on Urca cooling (repeated back-and-forth beta decay and electron capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars. We provide for the first time an expression for Urca process neutrino luminosity which accounts for excited states of both members of an Urca pair. We use our new formula with state-of-the-art nuclear structure inputs to compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear inputs consist of the latest experimental data supplemented with calculations using the projected shell model. We show that, in contrast with previous results that only consider the ground states of both nuclei in the pair, our calculated neutrino luminosities for different Urca pairs vary sensitively with the environment temperature and can be radically different from those obtained in the one transition approximation.

$\alpha$-decay always has enormous impetuses to the development of physics and chemistry, in particular due to its indispensable role in the research of new elements. Although it has been observed in laboratories for more than a century, it remains a difficult problem to calculate accurately the formation probability $S_\alpha$ microscopically. To this end, we establish a new model, i.e., multistep model, and the corresponding formation probability $S_\alpha$ values of some typical $\alpha$-emitters are calculated without adjustable parameters. The experimental half-lives, in particular their irregular behavior around a shell closure, are remarkably well reproduced by half-life laws combined with these $S_\alpha$. In our strategy, the cluster formation is a gradual process in heavy nuclei, different from the situation that cluster pre-exists in light nuclei. The present study may pave the way to a fully understanding of $\alpha$-decay from the perspective of nuclear structure.

We report a study of the processes of $e^+e^-\to K^+ (D_s^- D^{*0} + D^{*-}_s D^0)$ based on $e^+e^-$ annihilation samples collected with the BESIII detector operating at BEPCII at five center-of-mass energies ranging from 4.628 to 4.698 GeV with a total integrated luminosity of 3.7 fb$^{-1}$. An excess over the known contributions of the conventional charmed mesons is observed near the $D_s^- D^{*0}$ and $D^{*-}_s D^0$ mass thresholds in the $K^{+}$ recoil-mass spectrum for events collected at $\sqrt{s}=4.681$ GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as $(3982.5^{+1.8}_{-2.6}\pm2.1)$ MeV/$c^2$ and $(12.8^{+5.3}_{-4.4}\pm3.0)$ MeV, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be 5.3 $\sigma$ over the contributions only from the conventional charmed mesons. This is the first candidate of the charged hidden-charm tetraquark with strangeness, decaying into $D_s^- D^{*0}$ and $D^{*-}_s D^0$. However, the properties of the excess need further exploration with more statistics.

Based on rare fluctuations in strong interactions, we argue that there is a strong physical resemblance between the high multiplicity events in photo-nuclear collisions and those in $pA$ collisions, in which interesting long range collective phenomena are discovered. This indicates that the collectivity can also be studied in certain kinematic region of the upcoming Electron-Ion Collider (EIC) where the incoming virtual photon has a sufficiently long lifetime. Using a model in the Color Glass Condensate formalism, we first show that the initial state interactions can explain the recent ATLAS azimuthal correlation results measured in the photo-nuclear collisions, and then we provide quantitative predictions for the long range correlations in $eA$ collisions in the EIC regime. With the unprecedented precision and the ability to change the size of the collisional system, the high luminosity EIC will open a new window to explore the physical mechanism responsible for the collective phenomenon.

Within the framework of Soft Collinear Effective Theory, we present calculations of semi-inclusive jet functions and fragmenting jet functions at next-to-leading order (NLO) for both quark- and gluon-initiated jets, for jet algorithms of $J_{E_T}^{(I)}$ and $J_{E_T}^{(II)}$ where one maximizes a suitable jet function. We demonstrate the consistency of the obtained results with the standard perturbative QCD calculations for $J_{E_T}^{(I)}$ algorithm, while the results for fragmenting jet functions with the $J_{E_T}^{(II)}$ algorithm are new. The renormalization group (RG) equation for both semi-inclusive jet functions and fragmenting jet functions are derived and shown to follow the time-like DGLAP evolution equations, independent of specific jet algorithms. The RG equation can be used to resum single logarithms of the jet size parameter $\beta$ for highly collimated jets in these algorithms where $\beta \gg 1$.

Using a model based on the Color Glass Condensate framework and the dilute-dense factorization, we systematically study the azimuthal angular correlations between a heavy flavor meson and a light reference particle in proton-nucleus collisions. The obtained second harmonic coefficients (also known as the elliptic flows) for $J/\psi$ and $D^0$ agree with recent experimental data from the LHC. We also provide predictions for the elliptic flows of $\Upsilon$ and $B$ meson, which can be measured in the near future at the LHC. This work can shed light on the physics origin of the collectivity phenomenon in the collisions of small systems.

We investigate the influence of rotation on the dynamical chiral symmetry breaking in strongly interacting matter. We develop a self-consistent Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous chiral condensate and the possible chiral vortex state in rotating finite-size matter in four-fermion interacting theories. We show that for sufficiently rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex state, a type of topological defect in analogy to superfluids and superconductors. The vortex state exhibits pion condensation, providing a new mechanism to realize pseudoscalar condensation in strongly interacting matter.

The rotation induced inhomogeneous problem is non-trivial and inevitable. In this paper a generic framework is developed to investigate the inhomogeneous condensate in a system of fermions under the presence of rotation. It is a self-consistent method basing on a set of relativistic BdG equations solved with typical iteration algorithm. Taking the chiral condensate for example we study rotational effects numerically and discover two inhomogeneous effects, the local rotational suppression effect and centrifugal effect. They may have significant impacts on the phase structure of various kinds of matter. Several systems in different physics branches have been discussed in the paper.

The observations combined with theory of neutron star (NS) cooling play a crucial role in achieving the intriguing information of the stellar interior, such as the equation of state (EOS), composition and superfluidity of dense matter. The traditional NS cooling theory is based on the assumption that the stellar structure does not change with time. The validity of such a static description has not yet been confirmed. We generalize the theory to a dynamic treatment; that is, continuous change of the NS structure (rearrangement of the stellar density distribution with the total baryon number fixed) as the decrease of temperature during the thermal evolution, is taken into account. It is found that the practical thermal energy used for the cooling is slightly lower than that is estimated in static situation, and hence the cooling of NSs is accelerated correspondingly but the effect is rather weak. Therefore, the static treatment is a good approximation in the calculations of NS cooling.

We use a reference state based on symmetry-restored states from deformed mean-field or generator-coordinate-method (GCM) calculations in conjunction with the in-medium similarity-renormalization group (IMSRG) to compute spectra and matrix elements for neutrinoless double-beta ($0\nu\beta\beta$) decay. Because the decay involves ground states from two nuclei, we use evolved operators from the IMSRG in one nucleus in a subsequent GCM calculation in the other. We benchmark the resulting IMSRG+GCM method against complete shell-model diagonalization for both the energies of low-lying states in $^{48}$Ca and $^{48}$Ti and the $0\nu\beta\beta$ matrix element for the decay of $^{48}$Ca, all in a single valence shell. Our approach produces better spectra than either the IMSRG with a spherical-mean-field reference or GCM calculations with unevolved operators. For the $0\nu\beta\beta$ matrix element the improvement is slight, but we expect more significant effects in full ab-initio calculations.

We examine the leading effects of two-body weak currents from chiral effective field theory on the matrix elements governing neutrinoless double-beta decay. In the closure approximation these effects are generated by the product of a one-body current with a two-body current, yielding both two- and three-body operators. When the three-body operators are considered without approximation, they quench matrix elements by about 10%, less than suggested by prior work, which neglected portions of the operators. The two-body operators, when treated in the standard way, can produce much larger quenching. In a consistent effective field theory, however, these large effects become divergent and must be renormalized by a contact operator, the coefficient of which we cannot determine at present.

In this paper, we study the production of isolated-photon plus a jet in $pp$ and $PbPb$ collisions, which can be used as an important probe to the jet transport property in quark gluon plasma created in heavy ion collisions. Normally, there are two types of observables associated with the production of isolated-photon plus a jet, namely, the azimuthal angular correlation and the transverse momentum imbalance. To understand both observables in the full kinematical region, we need to employ the perturbative QCD calculation, which takes into account the hard splitting of partons, together with the Sudakov resummation formalism, which resums soft gluon splittings. Furthermore, by introducing energy-loss into the system, we calculate the enhancement of the momentum imbalance distribution for $AA$ as compared to $pp$ collisions and make predictions for future unfolded experimental data. In addition, in order to extract the jet transport coefficient more precisely in our numerical calculation, we also distinguish quark jets from gluon jets, since they interact with quark gluon plasma with different strengths. This work provides a reliable theoretical tool for the calculation of the gamma-jet correlation, which can lead us to a more precise extraction of the jet transport coefficient in relativistic heavy-ion collisions.

The phase transition of nuclei to increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A equal 160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration along the yrast lines while increasing spin. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei as a function of spin. In addition, in order to get the insight into the rotational-like properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei using the total Routhian surfaces (TRS) model. The TRS plots indicate that the 165Yb and 157Dy isotopes have stable prolate shapes at low spin states. At higher rotational frequency (larger than 0.50 MeV), a distinct decrease in the quadrupole deformation is predicted by the calculations, and the isotopes becomes rigid in the gamma deformation.

We explore the features of the $U_A(1)$ and chiral symmetry breaking of the Nambu--Jona-Lasinio model without the Kobayashi-Maskawa-'t Hooft determinant term in the presence of a parallel electromagnetic field. We show that the electromagnetic chiral anomaly can induce both finite neutral pion condensate and isospin-singlet pseudo-scalar $\eta$ condensate and thus modifies the chiral symmetry breaking pattern. In order to characterize the strength of the $U_A(1)$ symmetry breaking, we evaluate the susceptibility associated with the $U_A(1)$ charge. The result shows that the susceptibility contributed from the chiral anomaly is consistent with the behavior of the corresponding $\eta$ condensate. The spectra of the mesonic excitations are also studied.

In this work, we explore the competition between magnetic catalysis effect and chiral rotation effect in a general parallel electromagnetic field within the effective Nambu--Jona-Lasinio model. For a given electric field $E$ at zero temperature, the mass gap shows three different features with respect to an increasing magnetic field $B$: increasing monotonically, decreasing after increasing and decreasing monotonically. By making use of strong magnetic field approximation, we illuminate that this is due to the competition between catalysis effect and chiral rotation effect induced both by the magnetic field, and a critical electric field $\sqrt{eE_c}=86.4~{\rm MeV}$ is found beyond which the mass gap will eventually decrease at large $B$. As only large magnetic field is relevant for the derivation, the critical electric field does not depend on the temperature $T$ or chemical potential $\mu$.

The Wigner Isobaric Multiplet Mass Equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question for the origin of the Nolen-Schiffer anomaly found in the Coulomb displacement energy of mirror nuclei. We find that the naturally-emerged CSB term in GIMME is largely responsible for explaining the Nolen-Schiffer anomaly.

The quadratic form of the isobaric multiplet mass equation (IMME), which was originally suggested by Wigner and has been generally regarded as valid, is seriously questioned by recent high-precision nuclear mass measurements. The usual resolution to this problem is to add empirically the cubic and quartic $T_z$-terms to characterize the deviations from the IMME, but finding the origin of these terms remains an unsolved difficulty. Based on a strategy beyond the Wigner's first-order perturbation, we derive explicitly the cubic and quartic $T_z$-terms. These terms are shown to be generated by the effective charge-symmetry breaking and charge-independent breaking interactions in nuclear medium combined with the Coulomb polarization effect. Calculations for the $sd$- and lower $fp$-shells explore a systematical emergence of the cubic $T_z$-term, suggesting a general deviation from the original IMME. Intriguingly, the magnitude of the deviation exhibits an oscillation-like behavior with mass number, modulated by the shell effect.

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qps. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the Projected Shell Model is expanded to include 6-qp states for both positive and negative parities. Taking $^{166}$Hf as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I \approx 34\hbar$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in $^{176}$Hf are analyzed as another example.

SPECT (Single-photon Emission Computerized Tomography) and PET (Positron Emission Tomography) are essential medical imaging tools, for which the sampling angle number, scan time should be chosen carefully to compromise between image quality and the radiopharmaceutical dose. In this study, the image quality of different acquisition protocol was evaluated via varied angle number and count number per angle with Monte Carlo simulation data. It was shown that when similar imaging counts were used, the factor of acquisition counts was more important than that of the sampling number in ECT (Emission Computerized Tomography). To further reduce the activity requirement and the scan duration, an iterative image reconstruction algorithm for limited-view and low-dose tomography based on compressed sensing theory has been developed. The total variation regulation was added in the reconstruction process to improve SNR (Signal to Noise Ratio) and reduce the artifacts caused by the limited angle sampling. Maximization of maximum likelihood of the estimated image and the measured data and minimization of the total variation of the image are alternative implemented. By using this advanced algorithm, the reconstruction process is able to achieve image quality matching or exceeding that of normal scan with only half of the injection radiopharmaceutical dose.

The odd-even staggerings (OES) on nuclear binding energies are studied systematically within the covariant density functional (CDF) theories, specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and the relativistic Hartree-Bogoliubov (RHB) theories. Taking the finite-range Gogny force D1S as an effective pairing interaction, both CDF models can provide appropriate descriptions on the OESs of nuclear binding energies for C, O, Ca, Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N=50 and 82 isotones. However, due to the inconsistence between the non-relativistic pairing interaction and the relativistic effective Lagrangians, there exist some systematical discrepancies from the data, i.e., the underestimated OESs in light C and O isotopes and the overestimated ones in heavy region, respectively. Such discrepancies can be eliminated partially by introducing a $Z$- or $N$-dependent strength factor into the pairing force Gogny D1S. In addition, successful descriptions of the occupation numbers of Sn isotopes are achieved with the optimized Gogny pairing force. Furthermore, the analysis of the systematics of both pairing effects and nuclear binding energy indicate the requirement of an unified relativistic mechanism in both p-p and p-h channels to improve the quantitative precision of the theory.

Thermal fission energy is one of the basic parameters needed in the calculation of antineutrino flux for reactor neutrino experiments. It is useful to improve the precision of the thermal fission energy calculation for current and future reactor neutrino experiments, which are aimed at more precise determination of neutrino oscillation parameters. In this article, we give new values for thermal fission energies of some common thermal reactor fuel isotopes, with improvements on three aspects. One is more recent input data acquired from updated nuclear databases. the second one is a consideration of the production yields of fission fragments from both thermal and fast incident neutrons for each of the four main fuel isotopes. The last one is more carefully calculation of the average energy taken away by antineutrinos in thermal fission with the comparison of antineutrino spectrum from different models. The change in calculated antineutrino flux due to the new values of thermal fission energy is about 0.32%, and the uncertainties of the new values are about 50% smaller.

Tensor effects on the N=40 gap evolution of N=40 isotones are studied by employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the inclusion of the tensor component are compared with the experimental data. When the tensor force is included, both of the two different approaches are found to give the same trend and agree with the experimental one, which indicates the necessity of introducing the tensor force in the evolution of N=40 subshell and on the other hand the reliability of the methods. Furthermore, it is shown that the gap evolution is primarily determined by the corresponding tensor contributions from $\pi$ and $\rho$-tensor coupling in the relativistic framework.

The $\Lambda$ $\to$ $\Sigma^0$ transition magnetic moment is computed in the QCD sum rules approach. Three independent tensor structures are derived in the external field method using generalized interpolating fields. They are analyzed together with the $\Lambda$ and $\Sigma^0$ mass sum rules using a Monte-Carlo-based analysis, with attention to OPE convergence, ground-state dominance, and the role of the transitions in the intermediate states. Relations between sum rules for magnetic moments of $\Lambda$ and $\Sigma^0$ and sum rules for transition magnetic moment of $\Lambda$ $\to$ $\Sigma^0$ are also examined. Our best prediction for the transition magnetic moment is $\mu_{\Sigma^0\Lambda}= 1.60\pm 0.07\; \mu_N$. A comparison is made with other calculations in the literature.

We study the $\eta$NN coupling constant using the method of QCD sum rules starting from the vacuum-to-eta correlation function of the interpolating fields of two nucleons. The matrix element of this correlation has been taken with respect to nucleon spinors to avoid unwanted pole contribution. The SU(3)-flavor symmetry breaking effects have been accounted for via the $\eta$-mass, s-quark mass and eta decay constant to leading order. Out of the four sum rules obtained by taking the ratios of the two sum rules in conjunction with the two sum rules in nucleon mass, three are found to give mutually consistent results. We find the SU(3) breaking effects significant, as large as 50% of the SU(3) symmetric part.

A comprehensive study is made for the magnetic moments of octet baryons in the method of QCD sum rules. A complete set of QCD sum rules is derived using the external field method and generalized interpolating fields. For each member, three sum rules are constructed from three independent tensor structures. They are analyzed in conjunction with the corresponding mass sum rules. The performance of each of the sum rules is examined using the criteria of OPE convergence and ground-state dominance, along with the role of the transitions in intermediate states. Individual contributions from the u, d and s quarks are isolated and their implications in the underlying dynamics are explored. Valid sum rules are identified and their predictions are obtained. The results are compared with experiment and previous calculations.