In recent years, machine learning (ML) techniques have emerged as powerful tools for studying many-body complex systems, and encompassing phase transitions in various domains of physics. This mini review provides a concise yet comprehensive examination of the advancements achieved in applying ML to investigate phase transitions, with a primary focus on those involved in nuclear matter studies.

A two-stage cascade magnetic compression scheme based on field reversed configuration plasma is proposed. The temperature and density of plasma before and after magnetic compression are analyzed. In addition, the suppression of the two-fluid effect and the finite Larmor radius effect on the tilting mode and the rotating mode of major magnetic hydrodynamic instability is studied, and finally, the key physical and engineering parameters of the deuterium–deuterium fusion pulse device are introduced. Further analysis shows that the fusion neutrons can be produced at an energy flux of more than 2 MW/m$^{2}$ per year, which meets the material testing requirements for the fusion demonstration reactor (DEMO). If the recovery of magnetic field energy is taken into account, net energy outputs may be achieved, indicating that the scheme has a potential application prospect as a deuterium–deuterium pulse fusion energy.

Valuable information on dynamics of expanding fluids can be inferred from the response of such systems to perturbations in their initial geometry. We apply this technique in high-energy $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr collisions to scrutinize the expansion dynamics of the quark-gluon plasma, where the initial geometry perturbations are sourced by the differences in deformations and radial profiles between $^{96}$Ru and $^{96}$Zr, and the collective response is captured by the change in anisotropic flow $V_n$ between the two collision systems. Using a transport model, we analyze how the nonlinear coupling between lower-order flow harmonics $V_2$ and $V_3$ to the higher-order flow harmonics $V_4$ and $V_5$, expected to scale as $V_{4\mathrm{NL}}=\chi_4 V_2^2$ and $V_{5\mathrm{NL}}=\chi_5 V_2V_3$, gets modified as one moves from $^{96}$Ru+$^{96}$Ru to $^{96}$Zr+$^{96}$Zr systems. We find that these scaling relations are valid to high precision: variations of order 20% in $V_{4\mathrm{NL}}$ and $V_{5\mathrm{NL}}$ due to differences in quadrupole deformation, octupole deformation, and nuclear skin modify $\chi_{4}$ and $\chi_5$ by about 1–2%. Percent-level deviations are however larger than the expected experimental uncertainties and could be measured. Therefore, collisions of isobars with different nuclear structures are a unique tool to isolate subtle nonlinear effects in the expansion of the quark-gluon plasma that would be otherwise impossible to access in a single collision system.

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 PYTHIA8, and the energy loss of fast parton traversing in a hot/dense quantum-chromodynamic medium is simulated with the linear Boltzmann transport model. We predict the normalized distributions of the groomed jet radius $\theta_{\rm g}$ and momentum splitting fraction $z_{\rm g}$ with the dynamical grooming algorithm in Pb+Pb collisions at $\sqrt{s_{\scriptscriptstyle{\rm NN}}}$ = 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 $z_{\rm g}$ in $z_{\mathrm{cut}} = 0.1$, $\beta = 0$ soft drop case are close to unity, those in $a=0.1$ dynamical grooming case show enhancement at small $z_{\rm g}$, and Pb+Pb/p+p with respect to $\theta_{\rm g}$ 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 $\langle z_{\rm g} \rangle_{\rm jets}$ and averaged groomed jet radius $\langle \theta_{\rm g} \rangle_{\rm jets}$ in p+p and A+A for both grooming cases in three $p^{\rm ch~jet}_{\scriptscriptstyle{\rm T}}$ intervals, and find that the originally generated well balanced groomed jets will become more momentum imbalanced and jet size less narrowed due to jet quenching, and weaker medium modification of $z_{\rm g}$ and $\theta_{\rm g}$ in the $a =0.1$ dynamical grooming case than in the soft drop counterparts.

We studied the fission properties of neutron-rich nuclei $^{278, 286}$Cf around the end point of $r$-process by microscopic self-consistent approaches. The fission barriers and potential energy surfaces are obtained by constrained static Skyrme Hartree–Fock-BCS calculations. Fission fragments are studied by dynamical time-dependent Hartree–Fock+BCS calculations. Results show that $^{286}$Cf has an octupole deformation at ground state, which can increase the fission barrier height by 1.1 MeV and enhance significantly the spontaneous fission half-life. To search possible fission channels, dynamical calculations with a broad coverage of initial deformations result in two slightly asymmetric peaks around $A=128$ and 150 for $^{278}$Cf, and $A=133$ and 153 for $^{286}$Cf. Very asymmetric fission channels as given by semi-empirical models are not found in our results.

A time-of-flight polarized neutron imaging setup was realized by integrating an in situ pumped polarized $^3$He spin filter and energy dispersive neutron camera on the neutron technique development beamline (BL-20) of the China Spallation Neutron Source (CSNS). Test experiments were performed with a solenoid with aluminum wire as a sample. These demonstrated that polarized radiography with a field of view in diameter 2.0 cm at different wavelengths can be obtained. The wavelength-dependent polarization was used to distinguish the neutron polarization behavior for different positions inside and outside the solenoid. The results of this work show the possibility of applying the technique at CSNS and marks a milestone for future polarized neutron imaging developments.

In 2012, we investigated the possible molecular states composed of two charmed mesons [Phys. Rev. D 88 (2013) 114008; 2012 arXiv:1211.5007 [hep-ph]]. The $D^*D$ system with the quantum numbers of $I(J^P)=0(1^+)$ was found to be a good candidate of the loosely bound molecular state. This state is very close to the $D^*D$ threshold with a binding energy around 0.47 MeV. This prediction was confirmed by the new LHCb observation of $T_{\rm cc}^+$ [see Franz Muheim's talk at the European Physical Society conference on high energy physics 2021].

Within the framework of quantum molecular dynamics transport model, the isospin and in-medium effects on the hyperon production in the reaction of $^{197}$Au + $^{197}$Au are investigated thoroughly. A repulsive hyperon-nucleon potential from the chiral effective field theory is implemented into the model, which is related to the hyperon momentum and baryon density. The correction on threshold energy of the elementary hyperon cross section is taken into account. It is found that the $\varSigma$ yields are suppressed in the domain of midrapidity and kinetic energy spectra with the potential. The hyperons are emitted in the reaction plane because of the strangeness exchange reaction and reabsorption process in the nuclear medium. The $\varSigma^{-}/\varSigma^{+}$ ratio depends on the stiffness of nuclear symmetry energy, in particular in the high-energy region (above 500 MeV).

Polarized $^{3}$He neutron spin filters (NSFs) can be used as a vital tool for neutron polarization production and analysis. The China Spallation Neutron Source (CSNS), as one of the major neutron facilities in China, has committed resources to the development of a polarized $^3$He NSF program to support its growing polarized neutron research. A spin-exchange optical pumping (SEOP)-based polarized $^{3}$He system and other necessary hardware for NSF transport has been recently developed. The performance of the system is benchmarked using an in-house developed cell named “Trident”. Neutron beam measurements yield a $^{3}$He polarization of 77% with over 200 h of on-beam relaxation time. Combining this newly developed SEOP system with the recently reported cell fabrication station, CSNS is now capable of the fully self-sustained production of $^{3}$He NSFs that shall support its future neutron polarization research.

The Nb$_{3}$Sn thin film cavity, having the potential to be operated at a higher temperature and higher gradient compared to the cavity made from bulk niobium, is one of the most promising key technologies for the next-generation radio-frequency superconducting accelerators. In our work, several 1.3 GHz single-cell TESLA-shaped Nb$_{3}$Sn thin film cavities, coated by the vapor diffusion method, were tested at Peking University and Institute of Modern Physics, Chinese Academy of Sciences. It was observed that the performance of the Nb$_{3}$Sn thin film cavities in the tests without the slow cooling down procedure and the effective magnetic field shielding was significantly improved by using a low temperature baking at 100 ℃ for 48 hours. Although the peak electric field of the cavity remained unchanged, the rapid drop of the unloaded $Q$ value ($Q_{0}$) with the increasing accelerating field ($Q$-slope) was effectively eliminated, resulting in an improvement of the $Q_{0}$ in the intermediate field region by $\sim $8 times. Furthermore, under better test conditions with the shielded magnetic field less than 5 mG and the slow cooling down procedure in the temperature range of 25–15 K, the $Q_{0}$ was still improved by about 20%. Our study shows that the low temperature baking can be an effective supplement to the effective post-treatment for the Nb$_{3}$Sn thin film cavity.

Recently, a relativistic chiral nucleon–nucleon interaction was formulated up to leading order, which provides a good description of the phase shifts of $J\leq1$ partial waves [Chin. Phys. C 42 (2018) 014103]. Nevertheless, a separable regulator function that is not manifestly covariant was used in solving the relativistic scattering equation. In the present work, we first explore a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging $^1\!S_0$ channel which features several low-energy scales. In addition to being self-consistent, we show that the resulting relativistic potential can describe quite well the unique features of the $^1\!S_0$ channel at leading order, in particular the pole position of the virtual bound state and the zero amplitude at the scattering momentum $\sim $340 MeV, indicating that the relativistic formulation may be more natural from the viewpoint of effective field theories.

A unified description of finite nuclei and equation of state of neutron stars presents both a major challenge and also opportunities for understanding nuclear interactions. Inspired by the Lee–Huang–Yang formula of hard-sphere gases, we develop effective nuclear interactions with an additional high-order density dependent term. While the original Skyrme force SLy4 is widely used in studies of neutron stars, there are not satisfactory global descriptions of finite nuclei. The refitted SLy4${'}$ force can improve descriptions of finite nuclei but slightly reduces the radius of neutron star of 1.4$M_{\odot}$ with $M_{\odot}$ being the solar mass. We find that the extended SLy4 force with a higher-order density dependence can properly describe properties of both finite nuclei and GW170817 binary neutron stars, including the mass-radius relation and the tidal deformability. This demonstrates the essential role of high-order density dependence at ultrahigh densities. Our work provides a unified and predictive model for neutron stars, as well as new insights for the future development of effective interactions.

At the China Spallation Neutron Source (CSNS), we have developed a custom gas-filling station, a glassblowing workshop, and a spin-exchange optical pumping (SEOP) system for producing high-quality $^3$He-based neutron spin filter (NSF) cells. The gas-filling station is capable of routinely filling $^3$He cells made from GE180 glass of various dimensions, to be used as neutron polarizers and analyzers on beamlines at the CSNS. Performance tests on cells fabricated at our gas-filling station are conducted via neutron transmission and nuclear-magnetic-resonance measurements, revealing nominal filling pressures, and a saturated $^3$He polarization in the region of 80%, with a lifetime of approximately 240 hours. These results demonstrate our ability to produce competitive NSF cells to meet the ever-increasing research needs of the polarized neutron research community.

The remaining uncertainties in relation to isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although neutron-skin thickness data or isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations among other parameters can also be built. Using combined data for both the neutron-skin thickness and the isovector giant dipole resonance helps to significantly constrain all isovector interaction parameters; as such, it serves as a useful methodology for future research.

A higher-twist modified parton evolution equation is used to evolve the initial valence quark distributions in pions, which are derived based on light-front quantization via BLFQ collaboration. The results are consistent with the valence quark distributions of the E615 experiment, and the pion structure function of the H1 experiment. The structure function data highlight the necessity for a higher-twist modification in the small $x$ region. Comparisons with some other models are also given.

The acceleration of decay induced by frequency measurements, namely the quantum anti-Zeno effect (AZE), was first predicted by Kofman and Kurizki [Nature 405 (2000) 546 ]. The effect of the frequency measurements on nuclear $\beta$ decay rate is analyzed based on the time-dependent perturbation theory. We present a detailed calculation of the decay rates of $^{3}$H, $^{60}$Co ($\beta^{-}$ type), $^{22}$Na, $^{106}$Ag ($\beta^{+}$ type) and $^{18}$F, $^{57}$Co and $^{111}$Sn (EC type) under frequency measurements. It is found that the effects of frequency measurements on the decay rates of $\beta^{+}$ and $\beta^{-}$ cases are different from the case of EC, and the smaller the $\beta$ decay energy is, the more favorable it is to observe the AZE in experiment. Based on our analysis, it is suggested that possible experimental candidates should have a small decay energy and a reasonable half life (such as $^{3}$H) for observing the AZE in $\beta$ decay.

The deformations and the corresponding configurations of the odd-odd As isotopes are investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) theory. Energy minima with triaxial deformations and high-$j$ particle-hole configurations are obtained in $^{72,74,76,78,80}$As, where the chiral doublet bands are possible to appear. The existence of multiple chiral doublet (M$\chi$D) is demonstrated in $^{74,76,78}$As. Based on the calculated single-particle levels, we also find possible coexistence of chiral and pseudospin symmetries in the odd-odd As isotopes.

The geometry of fireballs in relativistic heavy ion collisions is approximated by a static box, which is infinite in two directions while finite in the other direction. The critical temperature of deconfinement phase transition is calculated explicitly in the MIT bag model at vanishing baryon density. It is found that the critical temperature shifts to a value higher than that in an unconstrained space.

Nuclear reaction rate $\lambda$ is a significant factor in processes of nucleosyntheses. A multi-layer directed-weighted nuclear reaction network, in which the reaction rate is taken as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criteria for different reaction layers, is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase in the stellar temperature $T_{9}$, the distribution of nuclear reaction rates on the R-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the R-layer in the region of $\lambda = [1,2.5\times10^{1}]$ have a more complicated out-going degree distribution than that in the region of $\lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $\lambda = [1, 2.5\times10^{1}]$ at $T_{9} = 3$ prefer $(\gamma,{\rm p})$ and $({\gamma,\alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $\beta$ stable line. This work offers a novel way to the big-data analysis on the nuclear reaction network at stellar temperatures.

We numerically investigate the effects of ion-to-electron temperature ratio $T_{\rm i}/T_{\rm e}$ and temperature gradient ratio $\eta_{\rm i}/\eta_{\rm e}$ on resistive ballooning modes (RBMs) under tokamak edge plasma conditions. The results show that the growth rates of the RBMs exhibit the characteristic of a quite broad poloidal wavenumber spectrum in the cold ion limit. The growth rate spectrum becomes narrower and the peak of the spectrum shifts from the short to long wavelength side with increasing $T_{\rm i}/T_{\rm e}$ and $\eta_{\rm i}/\eta_{\rm e}$. The electron temperature gradient has a very weak effect on the stability of RBMs. However, the ion-to-electron temperature ratio and the temperature gradient ratio have strong stabilizing effects on short-wavelength RBMs, while they have relatively weak effects on long-wavelength RBMs.

It is very important to increase the quantum efficiency (QE) and prolong the lifetime of the photocathode in a variety of applications. We have succeeded in preparing a high QE cesium potassium antimonide (K–Cs–Sb) photocathode by K and Cs co-evaporation in the photocathode preparation facility. In order to better understand the effect of the substrate (photocathode) temperature on the photocathode performance, the photocathode preparation, photocathode performance degradation, photocathode performance recovery and photocathode removal are studied in detail.

New experimental cross-section data for the $^{180}$W(n,2n)$^{179{\rm m}}$W, $^{186}$W(n,2n)$^{185{\rm m}}$W and $^{186}$W(n,p)$^{186}$Ta reactions at the neutron energies of 13.5 and 14.4 MeV are obtained by the activation technique. The neutron beams are produced by means of the $^{3}$H(d,n)$^{4}$He reaction. The gamma activities of the product nuclei are measured by a high-resolution gamma-ray spectrometer with a coaxial high-purity germanium detector. The neutron fluence is determined using the monitor reaction $^{93}$Nb(n,2n)$^{92{\rm m}}$Nb. The results in the current work are discussed and compared with the measurement results found in the literature. It is shown that these higher accuracy experimental cross-section data around the neutron energy of 14 MeV agree with some previous experimental values from the literature within experimental uncertainties.

Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around $N=20$. With both proton and neutron numbers around the magic number of 20, the neutron-rich $^{39}$Cl isotope provides a good test case for the study of the quantum-state evolution across the major shell. In the present work, the negative parity states in $^{39}$Cl are investigated through the $\beta$ decay spectroscopy of $^{39}$S. Newly observed $\gamma$ transitions together with a new state are assigned into the level scheme of $^{39}$Cl. The spin parity of ${5/2}^{-}$ for the lowest negative parity state in $^{39}$Cl is reconfirmed using the combined $\gamma$ transition information. These systematic observations of the negative parity states in $^{39}$Cl allow a comprehensive comparison with the theoretical descriptions. The lowest ${5/2}^{-}$ state in $^{39}$Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.

A new observable, the angle between ${\it \Lambda}$ and $\bar{\it \Lambda}$ decay planes, is proposed to test the theoretical predictions on the spin correlation. With 10 billion $J/\psi$ events collected with the BESIII detector at the BEPCII $e^+e^-$ collider, the distribution of the angle could be measured to verify whether or not a correlation exists.

In the framework of the Skyrme–Hartree–Fock–Bogoliubov approach with the SkT interaction, the pairing effects on the proton bubble structures of $^{46}$Ar and $^{206}$Hg are discussed. In calculations, three kinds of pairing forces (volume, surface and mixed pairing interactions) are used. For $^{46}$Ar, it is shown that the bubble structure with the volume pairing is almost the same as that with the mixed pairing. The bubble with the surface pairing is less pronounced than those with the volume and mixed pairings. Analyzing the density distributions and occupation probabilities of the proton $s$ states and the quasi-degeneracy between the proton 2$s_{1/2}$ and 1$d_{3/2}$ orbitals, we explain the difference between the bubble structure with the surface pairing and those with the volume and mixed pairings. For $^{206}$Hg, it is seen that the proton density distribution with the surface pairing is different from those with the volume and mixed pairings in the whole region of the radial distance. In addition, it is found that the bubbles with the three pairing forces are different from each other and the least pronounced bubble is obtained with the surface pairing. Thus the selection of the pairing force is important for the study of the nuclear bubble structure.

The next generation of advanced light sources requires photons with large average flux and high brightness, which needs advanced electron gun matched with excellent photocathode materials. K$_{2}$CsSb photocathode has the advantages of high quantum efficiency, long lifetime and instantaneous response. This study introduces the design of a set of K$_{2}$CsSb photocathode preparation systems and detailed preparation process of K$_{2}$CsSb photocathodes, including sequential deposition process and co-deposition process, and finally develops a K$_{2}$CsSb photocathode. The influence of laser power on the quantum efficiency is also investigated.

Energies of the yrast positive- and negative-parity excited states in $^{140}$Xe are reproduced by two different models considering quadrupole-octupole deformations, namely the axial vibrational-rotational model and the triaxial rigid rotor model, and compared with the stable octupole-deformed $^{222}$Th. The origin of the energy difference between the opposite parity sequences is considered from two different mechanisms, the vibration in axial deformed energy minima and the rotation considering the effective triaxial deformation. The success of reproducing the data in both the models implies that these two mechanisms are equivalent on some level for the octupole-soft nuclei. By investigating the probability distributions for projection of total angular momentum in the triaxial rigid rotor model, it is found that such an energy difference is associated with the difference of orientation of the rotational axis.

A prototype of a laser driven proton accelerator is built at Peking University. Protons exceeding 10 MeV are accelerated from micrometer-thick aluminum targets irradiated by tightly focused laser pulse with 1.8 J energy and 30 fs duration. The beam energy spectrum and charge distribution are measured by a Thomson parabola spectrometer and radiochromic film stacks. The sensitivity of proton cut-off energy to the focusing of the laser beam, the pulse duration, and the foil thickness are systematically investigated in the experiments. Stable proton beams have been produced with an optimized parameter set, providing a cornerstone for the future applications of laser accelerated protons.

A new $^{11}$Be($p$,$d$) transfer reaction experiment is performed in inverse kinematics with a radioactive $^{11}$Be beam at 26.9$A$ MeV. Three low-lying states, namely the 0$^{+}$ ground state, the 2$^{+}$ state at $E_x=3.37$ MeV, and the multiplet at around 6 MeV in $^{10}$Be, are populated by this one-neutron transfer reaction. These three states in $^{10}$Be are clearly discriminated from the $Q$-value spectrum, which is rebuilt from energies and angles of the recoil deuterons in coincidence with $^{10}$Be. A spectroscopic factor for each state is extracted by comparing the experimental differential cross sections to the theoretical calculation results using the finite range adiabatic distorted wave approximation method with different global nucleon-nucleus potentials. It is found that the newly extracted spectroscopic factors for the 0$^+$ and 2$^+$ states are consistent with the previous ones, but the factor for the multiplet is smaller than the value in the reference, and the possible reason is discussed.

A diamond p-n junction is used to convert the decay energy of $^{63}$Ni source into electrical energy. The self-absorption effect of the $^{63}$Ni source, the backscatter process and the transport process of beta particles in diamond materials are studied. Then the theoretical maximum of electrical properties and the energy conversion efficiencies of diamond-$^{63}$Ni p-n junction batteries are achieved. Finally, a feasible design of $p^{+}p^{-}n^{+}$ junction battery, which has the maximum output power density of 0.42 $\mu$W/cm$^{2}$ and the optimal device conversion efficiency of 26.8%, is proposed.