Employing four different parametrizations of the pairing plus the multipolar type of effective two-body interaction and three different parametrizations of the Jastrow type of short-range correlations, the uncertainties in the nuclear transition matrix elements $M_N^{\left(0\nu \right)}$ due to the exchange of heavy Majorana neutrino for the $0^{+}\to 0^{+}$ transition of neutrinoless double beta decay of ${}^{94}$Zr, ${}^{96}$Zr, ${}^{98}$Mo, ${}^{100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te, and ${}^{150}$Nd isotopes in the PHFB model are estimated to be around 35$\%$. Excluding the nuclear transition matrix elements calculated with the Miller-Spencer parametrization of Jastrow short-range correlations, the uncertainties are found to be smaller than 20$\%$.

A photofission experiment was performed on targets of ${}^{235}$U, ${}^{238}$U, ${}^{239}$Pu, and ${}^{232}$Th using nearly 100$\%$ linearly polarized, high-intensity ($\sim$10${}^7$ $\gamma /$s), and nearly monoenergetic $\gamma$-ray beams having energies between 5.6 and 7.3 MeV at the High Intensity $\gamma$-ray Source (HI$\gamma$S). An array of 18 liquid scintillator detectors was used to measure prompt fission neutron polarization asymmetries. An asymmetry close to zero was found for ${}^{235}$U and ${}^{239}$Pu while a significant asymmetry ($\sim$0.5) was found for ${}^{238}$U and ${}^{232}$Th. A simplified model of near-threshold photofission has been developed in an attempt to explain the systematic difference between the even-even and even-odd targets. The results of a simulation, based on this model and using previous measurements of fission fragment angular distributions, are shown to accurately reproduce the essential features of the data.

In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/$c$ of the collision, when gluons thermalize into the quark-gluon plasma (QGP). After a roughly isentropic expansion that roughly conserves the number of quarks, a second wave ensues at hadronization, 5–10 fm/$c$ into the collision. Because entropy conservation requires the number of quasiparticles to stay roughly equal, and because each hadron contains at least two quarks, the majority of quark production occurs at this later time. For each quark produced in a heavy-ion collision, an antiquark of the same flavor is created at the same point in space-time. Charge balance functions identify, on a statistical basis, the location of balancing charges for a given hadron, and given the picture above one expects the distribution in relative rapidity of balancing charges to be characterized by two scales. After first demonstrating how charge balance functions can be defined using any pair of hadronic states, it is shown how one can identify and study both processes of quark production. Balance function observables are also shown to be sensitive to the charge-charge correlation function in the QGP. By considering balance functions of several hadronic species, and by performing illustrative calculations, this class of measurement appears to hold the prospect of providing the field's most quantitative insight into the chemical evolution of the QGP.

Correlation measurements imply that anisotropic flow in nuclear collisions includes an interesting triangular component along with the more familiar elliptic-flow contribution. Triangular flow has been attributed to eventwise fluctuations in the initial shape of the collision volume. The following two questions are asked. First, how do these shape fluctuations impact other event-by-event observables? Second, can fundamental information on the early time fluctuations be disentangled from the complex flow that results? Correlation and fluctuation observables are studied in a framework in which flux tubes in an early Glasma stage later produce hydrodynamic flow. The calculated collision-energy dependence of multiplicity and transverse momentum fluctuations is in good accord with data from 62.4 GeV Au $+$ Au up to 2.76 TeV Pb $+$ Pb.

A large set of cross sections for semi-inclusive electroproduction of charged pions (${\pi }^{\pm }$) from both proton and deuteron targets was measured. The data are in the deep-inelastic scattering region with invariant mass squared $W^2>4$ GeV${}^2$ (up to $\approx$7 GeV${}^2$) and range in four-momentum transfer squared $2<Q^2<4$ (GeV/$c$)${}^2$, and cover a range in the Bjorken scaling variable $0.2<x<0.6$. The fractional energy of the pions spans a range $0.3<z<1$, with small transverse momenta with respect to the virtual-photon direction, $P_t^2<0.2$ (GeV/$c$)${}^2$. The invariant mass that goes undetected, $M_x$ or $W^{\prime }$, is in the nucleon resonance region, $W^{\prime }<2$ GeV. The new data conclusively show the onset of quark-hadron duality in this process, and the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent $\mathrm{quark}\to \mathrm{pion}$ production mechanisms. The $x$, $z$, and $P_t^2$ dependences of several ratios (the ratios of favored-unfavored fragmentation functions, charged pion ratios, deuteron-hydrogen and aluminum-deuteron ratios for ${\pi }^{+}$ and ${\pi }^{-}$) have been studied. The ratios are found to be in good agreement with expectations based upon a high-energy quark-parton model description. We find the azimuthal dependences to be small, as compared to exclusive pion electroproduction, and consistent with theoretical expectations based on tree-level factorization in terms of transverse-momentum-dependent parton distribution and fragmentation functions. In the context of a simple model, the initial transverse momenta of $d$ quarks are found to be slightly smaller than for $u$ quarks, while the transverse momentum width of the favored fragmentation function is about the same as for the unfavored one, and both fragmentation widths are larger than the quark widths.

$\beta$ decays of the isotones with $N=126$ are studied by shell-model calculations taking into account both the Gamow-Teller (GT) and first-forbidden (FF) transitions. The FF transitions are found to be important to reduce the half-lives, by nearly twice to several times, from those by the GT contributions only. Possible implications of the short half-lives of the waiting point nuclei on the $r$-process nucleosynthesis during the supernova explosions are discussed. A slight shift of the third peak of the element abundances in the $r$ process toward a higher mass region is found.

Set of vector analyzing power data of the $\vec{d}p$ elastic scattering and ${}^{1}H(\vec{d},pp)n$ breakup reactions at 130-MeV deuteron beam energy has been measured in the domain of very forward polar angles. The results are compared with theoretical predictions originating from various approaches: realistic nucleon-nucleon (NN) potentials and the NN potentials combined with a three-nucleon force (3NF) model and with predictions based on the ChPT framework. In case of the breakup process, none of the theoretical calculations reveal sensitivity to any of the dynamical effects such as 3NF or Coulomb interaction and they describe the experimental data equally well. For the elastic scattering, the Coulomb correction appears not negligible at very small ${\theta }_d^{\text{c.m.}}$. The effect seems to be confirmed by the data.

The evolution of the $N=50$ gap is analyzed as a function of the occupation of the proton $\pi f_{5/2}$ and $\pi p_{3/2}$ orbits. It is based on experimental atomic masses, using three different methods of one- or two-neutron separation energies of ground or isomeric states. We show that the effect of correlations, which is maximized at $Z=32$ could be misleading with respect to the determination of the size of the shell gap, especially when using the method with two-neutron separation energies. From the methods that are the least perturbed by correlations, we estimate the $N=50$ spherical shell gap in ${}_{28}^{78}$Ni${}_{50}^{}$. Whether ${}^{78}$Ni would be a rigid spherical or deformed nucleus is discussed in comparison with other nuclei in which similar nucleon-nucleon forces are at play.

We extend the relativistic point-coupling model to single-$\Lambda$ hypernuclei. For this purpose, we add $N$-$\Lambda$ effective contact couplings to the model Lagrangian and determine the parameters by fitting to the experimental data for $\Lambda$ binding energies. Our model well reproduces the data over a wide range of mass region although some of our interactions yield the reverse ordering of the spin-orbit partners from that of nucleons for heavy hypernuclei. The consistency of the interaction with the quark model predictions is also discussed.

A recent updated version of Lanzhou quantum molecular dynamics, in which the momentum dependence of the symmetry potential and the effective mass splitting of protons and neutrons in the nuclear medium are included in the model, is reviewed,. The in-medium nucleon-nucleon (NN) elastic cross sections are evaluated with the scaling approach according to the effective mass and their influence on collective flows in heavy-ion collisions are discussed. The inelastic cross sections, in particular for the process of the channel N$\Delta \to$ NN, are parametrized in accordance with the available experimental data. It is found that the in-medium cross sections play a significant role in isospin emission and result in a flatter distribution for transverse flows and elliptic flows of free nucleons compared with the in-vacuum ones. The rapidity distribution of the difference between neutron and proton transverse flows is sensitive to the stiffness of the nuclear symmetry energy as a promising observable, which cannot be influenced by the in-medium effect and collision centrality. Furthermore, the elliptic flow of free energetic nucleons in the case of the mass splitting of $m_n^{*}>m_p^{*}$ is also related to the symmetry energy. However, the pion flows weakly depend on the symmetry energy and the mass splitting.

Measurements of the ${}^4$He(${}^7\text{Be},\alpha$)${}^7$Be and ${}^4$He(${}^7\text{Be},p$)${}^{10}$B reactions were performed using ${}^7$Be beam energies of 7.1 and 23 MeV and a helium-4 target, employing the thick target technique. Resonances were observed between $E_x{(}^{11}\text{C})=8.6$ to 13.8 MeV. An $R$-matrix analysis was performed to characterize the spins and partial widths. This analysis showed that the observed sequence of states was consistent with that found for ${}^7$Li $+$ $\alpha$ resonant scattering populating resonances in ${}^{11}$B. A comparison of the proposed partial widths for decay with the Wigner limit indicates that several of the states are associated with cluster-like structures.

In the past decades, the $\gamma$ decay of giant resonances has been studied using phenomenological models. In keeping with possible future studies performed with exotic beams, microscopically based frameworks should be envisaged. In the present paper, we introduce a model which is entirely based on Skyrme effective interactions, and treats the ground-state decay within the fully self-consistent random phase approximation (RPA) and the decay to low-lying states at the lowest order beyond RPA. The model is applied to ${}^{208}$Pb and ${}^{90}$Zr, and the results are compared with the experimental data.

Two-particle azimuthal ($\Delta \phi$) and pseudorapidity ($\Delta \eta$) correlations using a trigger particle with large transverse momentum ($p_T$) in $d$+Au, Cu+Cu, and Au+Au collisions at $\sqrt{s_{NN}}$ $=$ 62.4 GeV and 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider are presented. The near-side correlation is separated into a jet-like component, narrow in both $\Delta \phi$ and $\Delta \eta$, and the ridge, narrow in $\Delta \phi$ but broad in $\Delta \eta$. Both components are studied as a function of collision centrality, and the jet-like correlation is studied as a function of the trigger and associated $p_T$. The behavior of the jet-like component is remarkably consistent for different collision systems, suggesting it is produced by fragmentation. The width of the jet-like correlation is found to increase with the system size. The ridge, previously observed in Au+Au collisions at $\sqrt{s_{NN}}$ $=$ 200 GeV, is also found in Cu+Cu collisions and in collisions at $\sqrt{s_{NN}}$ $=$ 62.4 GeV, but is found to be substantially smaller at $\sqrt{s_{NN}}$ $=$ 62.4 GeV than at $\sqrt{s_{NN}}$ $=$ 200 GeV for the same average number of participants ($\langle N_{\mathrm{part}}\rangle$). Measurements of the ridge are compared to models.

Dilepton production in the low-invariant-mass region in $p+p$ and Au + Au collisions at $\sqrt{s_{NN}}=200$ GeV and in Pb + Au collisions at 158 $A$GeV is studied in the relativistic hadron resonance gas model with Hagedorn mass spectrum that grows exponentially. The model provides good agreement with the observed yield and spectra of stable hadrons and resonances produced in both $p+p$ and nucleus-nucleus collisions. While the measured dilepton yields in $p+p$ collisions are well understood in the model with Dalitz and direct decays of conventional neutral meson sources, a sizable amount of the mesons produced from the Hagedorn states still cannot explain the large enhancement observed in the invariant mass region 200–700 MeV/c${}^2$ in Pb + Au and especially in Au + Au collisions. In a multiphase transport (AMPT) model, the dilepton produced from the standard hadronic sources in absence of Hagedorn states underpredicts the data to a larger extent. The study suggests that Hagedorn states in conjugation with in-medium modification of the properties of $\rho$ mesons may be essential for the enhanced dilepton production.

We investigate the odd-even staggering (OES) in reaction cross sections of weakly bound nuclei with Glauber theory, taking into account the pairing correlation with the Hartree-Fock-Bogoliubov (HFB) method. We first discuss the pairing gap in extremely weakly bound nuclei and show that the pairing gap persists in the zero separation energy limit even for single-particle orbits with the orbital angular momenta $l=0$ and $l=1$. We then introduce the OES parameter, defined as the second derivative of reaction cross sections with respect to the mass number, and clarify the relation between the magnitude of OES and the neutron separation energy. We find that the OES parameter increases considerably in the zero separation energy limit for $l=0$ and $l=1$ single-particle states, while no increase is found for higher angular momentum orbits with, for example, $l=3$. We point out that the increase of OES parameter is also seen in the experimental reaction cross sections for Ne isotopes, which is well accounted for by our calculations.

Recent experimental results for the fusion of the proton-halo system ${}^8\text{B}+{}^{58}\text{Ni}$ are discussed. A strong enhancement is observed both below and above the barrier. This is qualitatively different from the usual sub-barrier enhancement observed for many heavy-ion systems. Arguments are given that relate the enhancement to a static halo effect directly associated to the extended size of the proton-halo state. A simple single-barrier model is proposed which describes the fusion cross sections in terms of a maximum angular momentum for fusion, $L_f$. It is shown that a linear energy dependence for $L_f$ gives a surprisingly good description of the experimental fusion excitation function not only for ${}^8\text{B}+{}^{58}\text{Ni}$ but also for the neutron-halo systems ${}^6\text{He}+{(}^{209}\text{Bi},{}^{64}\text{Zn})$. The model is also applied to several weakly bound systems.

Using the two-component model that includes both initial production from nucleon-nucleon hard scattering and regeneration from produced quark-gluon plasma, we study the effect of medium modifications of the binding energies and radii of bottomonia on their production in heavy-ion collisions. We find that the contribution to bottomonia production from regeneration is small and the inclusion of medium effects is helpful for understanding the observed suppression of bottomonia production in experiments carried out at both the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.

The quasi-particle structures of nuclei in the $\alpha$-decay chains of ${}^{291,293}117$ are studied with a modified two-center shell model. The calculated values of $Q_{\alpha }$ are compared with available experimental data. The termination of the $\alpha$-decay chain of ${}^{293}117$ is explained.

The formation of intruder states in the low-lying states of ${}^{12}\mathrm{Be}=\alpha +\alpha +4N$ is studied by applying the generalized two-center cluster model, which can optimize the excess neutrons' orbits depending on the $\alpha -\alpha$ distance. The correlation energy for the intruder states is analyzed from the viewpoint of two different pictures based on the cluster structure: the covalent picture around two $\alpha$ clusters and the binary He-cluster picture. In the covalent picture, the binding energy of ${\left({\pi }_{32}^{-}\right)}^2{\left({\sigma }_{12}^{+}\right)}^2$, corresponding to $\nu {\left(0p\right)}^4{\left(1s0d\right)}^2$ in a naive shell model, gains largely owing to the spin-triplet pairing of the $0d$-wave neutrons, which is induced by the two-body spin-orbit interaction. The spin-triplet pairing gives rise to the reduction of the kinetic energy and the increase of the attractive spin-orbit interaction for the excess neutrons. As a result of these correlation energies, the $\nu {\left(0p\right)}^4{\left(1s0d\right)}^2$ configuration becomes dominant in the ground state. In the binary cluster picture, the correlation energy is investigated from the coupled channels among $\alpha +{}^8\mathrm{He}$, ${}^6\mathrm{He}+{}^6\mathrm{He}$, and ${}^5\mathrm{He}+{}^7\mathrm{He}$. The coupling to ${}^5\mathrm{He}+{}^7\mathrm{He}$, which is neglected in usual binary-cluster models, plays an important role for a large reduction of kinetic energy and the formation of a pair of the low-lying 0${}^{+}$ states with a close energy spacing recently observed in experiment. The rotational bands are also discussed from the viewpoint of these two cluster pictures.