We present a new generic framework which enables exact and efficient evaluation of all multiparticle azimuthal correlations. The framework can be readily used along with a correction framework for systematic biases in anisotropic flow analyses owing to various detector inefficiencies. A new recursive algorithm has been developed for higher-order correlators for the cases where their direct implementation is not feasible. We propose and discuss new azimuthal observables for anisotropic flow analyses which can be measured for the first time with our new framework. The effect of finite detector granularity on multiparticle correlations is quantified and discussed in detail. We point out the existence of a systematic bias in traditional differential flow analyses which stems solely from the applied selection criteria on particles used in the analyses and is also present in the ideal case when only flow correlations are present. Finally, we extend the applicability of our generic framework to the case of differential multiparticle correlations.

Background: In ${\pi }^{+}n$ and ${\pi }^{-}p$ electroproduction, conventional models cannot satisfactorily explain the data above the resonance region, in particular the transverse cross section. Although no high-energy l-t-separated cross-section data are available to date, a similar scenario can be inferred for $K^{+}\Lambda$ electroproduction.

Purpose: Develop a phenomenological model for the $p({\gamma }^{*},K^{+})\Lambda$ reaction at forward angles and high-energies. Propose a universal framework for interpreting charged-kaon and charged-pion electroproduction above the resonance region.

Method: Guided by the recent model for charged-pion electroproduction, developed by the authors, a framework for $K^{+}\Lambda$ electroproduction at high energies and forward angles is constructed. To this end, a Reggeized background model for $K^{+}\Lambda$ photoproduction is first developed. This model is used as a starting base to set up an electroproduction framework.

Results: The few available data of the unseparated $p({\gamma }^{*},K^{+})\Lambda$ cross section are well explained by the model. Predictions for the l-t-separation experiment planned with the 12 GeV upgrade at Jefferson Lab are given. The newly proposed framework predicts an increased magnitude for the transverse structure function, similar to the situation in charged-pion electroproduction.

Conclusions: Within a hadronic framework featuring Reggeized background amplitudes, $s$-channel resonance-parton effects can explain the observed magnitude of the unseparated $p({\gamma }^{*},K^{+})\Lambda$ cross section at high energies and forward angles. Thereby, no hardening of the kaon electromagnetic form factor is required.

Electric dipole ($E1$) response of ${}^6\mathrm{He}$ is studied with a fully microscopic six-body calculation. The wave functions for the ground and excited states are expressed as a superposition of explicitly correlated Gaussians. Final state interactions of three-body decay channels are explicitly taken into account. The ground state properties and the low-energy $E1$ strength are obtained consistently with observations. Two main peaks as well as several small peaks are found in the $E1$ strength function. The peak at the high-energy region indicates a typical macroscopic picture of the giant dipole resonance, the out-of-phase proton-neutron motion. The transition densities of the lower-lying peaks exhibit in-phase proton-neutron motion in the internal region, out-of-phase motion near the surface region, and spatially extended neutron oscillation, indicating a soft-dipole mode and its vibrationally excited mode. The compressional dipole strength is also examined in relation to the soft-dipole mode.

Nuclear double-$\beta$ decay with two neutrinos is a rare and important process for natural radioactivity of unstable nuclei. The experimental data of nuclear double-${\beta }^{-}$ decay with two neutrinos are analyzed and a systematic law to calculate the half-lives of this rare process is proposed. It is the first analytical and simple formula for double-$\beta$-decay half-lives where the leading effects from both the Coulomb potential and the nuclear structure are included. The systematic law shows that the logarithms of the half-lives are inversely proportional to the decay energies for the ground-state transitions between parent nuclei and daughter nuclei. The calculated half-lives are in agreement with the experimental data of ground-state transitions of all known 11 nuclei with an average factor of 3.06. The half-lives of other possible double-$\beta$-decay candidates with two neutrinos are predicted and these can be useful for future experiments. The law, without introducing any extra adjustment, is also generalized to the calculations of double-$\beta$-decay half-lives from the ground states of parent nuclei to the first $0^{+}$ excited states of daughter nuclei, and the calculated half-lives agree very well with the available data. The calculated half-lives from the ground states of parent nuclei ${}^{48}$Ca and ${}^{150}$Nd to the first $0^{+}$ excited states of daughter nuclei are the first theoretical results as far as we know. The similarity and difference between the law of $\alpha$ decay and that of double-${\beta }^{-}$ decay are also analyzed and discussed.

Ab initio calculations have shown that chiral two- and three-nucleon interactions correctly reproduce binding energy systematics and neutron drip lines of oxygen and nearby isotopes. Exploiting the novel Gorkov-Green's function approach applicable to genuinely open-shell nuclei, we present the first $ab$ initio investigation of Ar, K, Ca, Sc, and Ti isotopic chains. In doing so, stringent tests of internucleon interaction models are provided in the medium-mass region of the nuclear chart. Leading chiral three-nucleon interactions are shown to be mandatory to reproduce the trend of binding energies throughout these chains and to obtain a good description of two-neutron separation energies. At the same time, nuclei in this mass region are systematically overbound by about 40 MeV. While the fundamental $N=20$ and 28 magic numbers do emerge from basic internucleon interactions, the former is shown to be significantly overestimated, which points to deficiencies of state-of-the-art chiral potentials. The present results demonstrate that ab initio many-body calculations can now access entire medium-mass isotopic chains including degenerate open-shell nuclei and provide a critical testing ground for modern theories of nuclear interactions.

A study of interaction of neutron-rich oxygen isotopes ${}^{17,18}\mathrm{O}$ with light targets has been undertaken in order to determine the optical potentials needed for the transfer reaction ${}^{13}\mathrm{C}({}^{17}\mathrm{O},{}^{18}\mathrm{O}){}^{12}\mathrm{C}$. Optical potentials in both incoming and outgoing channels have been determined in a single experiment. This transfer reaction was used to infer the direct capture rate to the ${}^{17}\mathrm{F}(p,\gamma ){}^{18}\mathrm{Ne}$ which is essential to estimate the production of ${}^{18}\mathrm{F}$ at stellar energies in ONe novae. The success of the asymptotic normalization coefficient (ANC) as indirect method for astrophysics is guaranteed if the reaction mechanism is peripheral and the distorted wave Born approximation cross-section calculations are warranted and stable against the optical model potential (OMP) used. We demonstrate the stability of the ANC method and the OMP results by using good-quality elastic and inelastic-scattering data with stable beams before extending the procedures to rare-ion beams. The peripherality of our reaction is inferred from a semiclassical decomposition of the total-scattering amplitude into barrier and internal barrier components. Comparison between elastic scattering of ${}^{17}\mathrm{O}$, ${}^{18}\mathrm{O}$, and ${}^{16}\mathrm{O}$ projectiles is made.

We analyze the influence of the single-particle structure on the neutron density distribution and the neutron skin in Ca, Ni, Zr, Sn, and Pb isotopes. The nucleon density distributions are calculated in the Hartree-Fock+BCS approach with the SLy4 Skyrme force. A close correlation is found between the quantum numbers of the valence neutrons and the changes in the position and the diffuseness of the nuclear surface, which in turn affect the neutron skin thickness. Neutrons in the valence orbitals with low principal quantum number and high angular momentum mainly displace the position of the neutron surface outwards, while neutrons with high principal quantum number and low angular momentum basically increase the diffuseness of the neutron surface. The impact of the valence shell neutrons on the tail of the neutron density distribution is discussed.

We exhibit the existence of stable, saturated nuclear matter in the large $N_c$ and heavy quark mass limits of QCD. In this limit, baryons (with the same spin flavor structure) interact at leading order in $N_c$ via a repulsive interaction due to the Pauli exclusion principle and at subleading order in $1/N_c$ via the exchange of glueballs. Assuming that the lightest glueball is a scalar, which implies that the subleading baryon interaction is attractive, we find that nuclear matter saturates since the subleading attractive interaction is longer ranged than the leading order repulsive one. We find that the saturated matter is in the form of a crystal with either a face-centered-cubic or a hexagonal-close-packed symmetry with baryon densities of $\mathcal{O}\left({\left\{{\tilde{\alpha }}_s{m}_q{[ln\left(N_c{m}_q{\Lambda }_{\mathrm{QCD}}^{-1}\right)]}^{-1}\right\}}^3\right)$. Remarkably, the leading order expression for the density of saturated nuclear matter is independent of the lightest glueball mass and scalar-glueball-baryon coupling in the extreme large $N_c$ limit or heavy quark limit (or both), which we define precisely in this work.

The heavy-ion fusion reactions induced by neutron-rich nuclei are investigated with the improved quantum molecular dynamics (ImQMD) model. With a subtle consideration of the neutron skin thickness of nuclei and the symmetry potential, the stability of nuclei and the fusion excitation functions of heavy-ion fusion reactions ${}^{16}\mathrm{O}$ + ${}^{76}\mathrm{Ge}$, ${}^{16}\mathrm{O}$ + ${}^{154}\mathrm{Sm}$, ${}^{40}\mathrm{Ca}$ + ${}^{96}\mathrm{Zr}$, and ${}^{132}\mathrm{Sn}$ + ${}^{40}\mathrm{Ca}$ are systematically studied. The fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD model. The corresponding slope parameter of the symmetry energy adopted in the calculations is $L\approx 78$ MeV and the surface energy coefficient is $g_{\mathrm{sur}}=18\pm 1.5$ MeV fm${}^2$. In addition, it is found that the surface-symmetry term significantly influences the fusion cross sections of neutron-rich fusion systems. For sub-barrier fusion, the dynamical fluctuations in the densities of the reaction partners and the enhanced surface diffuseness at neck side result in the lowering of the fusion barrier.

We explore the equation of state for nuclear matter in the quark-meson coupling model, including full Fock terms. The comparison with phenomenological constraints can be used to restrict the few additional parameters appearing in the Fock terms which are not present at the Hartree level. Because the model is based upon the in-medium modification of the quark structure of the bound hadrons, it can be readily extended to include hyperons and to calculate the equation of state of dense matter in $\beta$ equilibrium. This leads naturally to a study of the properties of neutron stars, including their maximum mass, radii, and density profiles.

A comprehensive study of various ground-state properties of neutron-rich and neutron-deficient Mg isotopes with $A=20$–36 is performed in the framework of the self-consistent deformed Skyrme–Hartree–Fock plus BCS method. The correlation between the skin thickness and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for this isotopic chain following the theoretical approach based on the coherent density fluctuation model and using the Brueckner energy-density functional. The results of the calculations show that the behavior of the nuclear charge radii and the nuclear symmetry energy in the Mg isotopic chain is closely related to the nuclear deformation. We also study, within our theoretical scheme, the emergence of an “island of inversion” at the neutron-rich ${}^{32}\mathrm{Mg}$ nucleus, which was recently proposed from the analyses of spectroscopic measurements of the ${}^{32}\mathrm{Mg}$ low-lying energy spectrum and the charge rms radii of all magnesium isotopes in the $sd$ shell.

A recent proposed universal decay law (UDL) for $\alpha$-decay and cluster radioactivity (CR) half-lives [C. Qi, F. R. Xu, R. J. Liotta, and R. Wyss, Phys. Rev. Lett 103, 072501 (2009)] that can accurately reproduce the experimental data was introduced starting from $\alpha$-like $R$-matrix theory. The UDL formula depends only on the mass and charge numbers of the charged particle and the $Q$ value. The new mass table AME2012 and the theoretical FRDM95, KTUY05, and WS2011 masses are used to determine the $Q$ values. We systematically investigate the branching ratios of cluster radioactivity with respect to $\alpha$ decay for even-even superheavy nuclei (SHN) with $Z=104$–120 using the UDL formula. It is found that cluster radioactivity can be compared to $\alpha$ decay in neutron-rich SHN.

Coulomb displacement energies of $T=1/2$ mirror nuclei have been studied via a series of high-precision $Q_{\mathrm{EC}}$-value measurements with the double Penning trap mass spectrometer JYFLTRAP. Most recently, the $Q_{\mathrm{EC}}$ values of the $f_{7/2}$-shell mirror nuclei ${}^{45}\mathrm{V}$ ($Q_{\mathrm{EC}}=7123.82\left(22\right)$ keV) and ${}^{49}\mathrm{Mn}$ ($Q_{\mathrm{EC}}=7712.42\left(24\right)$ keV) have been measured with unprecedented precision. The data reveal a 16-keV ($1.6\sigma$) offset in the adopted Atomic Mass Evaluation 2012 value of ${}^{49}\mathrm{Mn}$, suggesting the need for further measurements to verify whether there is a breakdown of the quadratic form of the isobaric multiplet mass equation in the $fp$ shell. Precisely measured $Q_{\mathrm{EC}}$ values confirm that the pairing effect in the Coulomb energies is quenched when entering the $f_{7/2}$ shell and reaches a minimum in the midshell.

The structure of the nucleus ${}_9^{25}$F was investigated through in-beam $\gamma$-ray spectroscopy of the fragmentation of ${}^{26}\mathrm{Ne}$ and ${}^{27,28}\mathrm{Na}$ ion beams. Based on the particle-$\gamma$ and particle-$\gamma \gamma$ coincidence data, a level scheme was constructed and compared with shell model and coupled-cluster calculations. Some of the observed states were interpreted as quasi-single-particle states built on top of the closed-shell nucleus ${}^{24}\mathrm{O}$, while the others were described as states arising from coupling of a single proton to the $2^{+}$ core excitation of ${}^{24}\mathrm{O}$.

The iterative quasiparticle random-phase approximation (QRPA) method we previously developed [Phys. Rev. C 81, 034312 (2010); Phys. Rev. C 86, 024303 (2012); Phys. Rev. C 86, 014307 (2012)] to accurately calculate properties of individual nuclear states is extended so that it can be applied for nuclei with odd numbers of neutrons and protons. The approach is based on the proton-neutron QRPA ($pn$QRPA) and uses an iterative non-Hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method is used to calculate excitation energies of proton-neutron multiplets for several nuclei. The influence of a pairing interaction in the $T=0$ channel is studied.

The only way to obtain the space-time structure of heavy-ion collision is through the study of two-particle momentum correlations. Thus we have studied the intensity correlation for the photons at most central collision at Relativistic Heavy Ion Collider (RHIC) energy having fixed transverse momentum of one of the photons ($k_{1T}=2$ GeV) to have an idea about the emission zone in the presence of initial momentum space anisotropy. For the evolution in anistropic quark-gluon plasma (aQGP), the free streaming interpolating model with fixed initial condition has been used, whereas for the space-time evolution for both the isotropic quark-gluon plasma (iQGP) and the hadronic phases, relativistic (1 + 2)$d$ hydrodynamics model with cylindrical symmetry and boost invariance along longitudinal direction has been used. The variation of Bose-Einstein correlation function (BECF), $C_2$, for two identical photons as a function of $q_{\mathrm{out}}$, $q_{\mathrm{side}}$, and $q_{\mathrm{long}}$ is evaluated. Our analysis is based on the sensitivity of the momentum space anisotropy on the correlation function and also on the extracted Hanbury-Brown and Twiss radii from it. It is observed that the value of $C_2$ as function of $q$'s is reduced for the anisotropic scenario compared to that of isotropic case for all the directions. As a result, the spatial dimension of the reaction zone increases due to the presence of momentum space anisotropy in the medium in all directions.

The STAR experiment has measured $p\Lambda$, $\overline{p}\overline{\Lambda }$, $\overline{p}\Lambda$, and $p\overline{\Lambda }$ femtoscopic correlation functions in central Au + Au collisions at $\sqrt{s_{NN}}=200$ GeV. The system size extracted for $p$$\Lambda$ and $\overline{p}$$\overline{\Lambda }$ is consistent with model expectations and results for other pair types, while for $p$$\overline{\Lambda }$ and $\overline{p}$$\Lambda$ it is not consistent with the other two and significantly lower. In addition an attempt was made to extract the unknown parameters of the strong interaction potential for this baryon-antibaryon ($B\overline{B}$) pair. In this work we reanalyze the STAR data, taking into account residual femtoscopic correlations from heavier $B\overline{B}$ pairs. We obtain different estimates for the system size, consistent with the results for $p$$\Lambda$ and $\overline{p}$$\overline{\Lambda }$ pairs and with model expectations. We give these estimates for the strong interaction potential parameters for $p$$\overline{\Lambda }$ and show that similar constraints can be given for parameters for other, heavier $B\overline{B}$ pairs.

Here we investigate mixing of the low-lying three- and five-quark $\Omega$ states with spin-parity quantum numbers 1/2${}^{-}$ and 3/2${}^{-}$, employing the quark-antiquark creation triggered by Nambu–Jona-Lasinio (NJL) interaction. Wave functions of the three- and five-quark configurations are constructed by using the extended constituent quark model, within which the hyperfine interaction between quarks is also taken to be the NJL-induced one. Numerical results show that the NJL-interaction-induced pair creation results in vanishing mixing between three- and five-quark $\Omega$ configurations with spin-parity $1/2^{-}$, but mixing between three- and five-quark $3/2^{-}$ $\Omega$ states should be very strong. The mixing decreases energy of the lowest $3/2^{-}$$\Omega$ state to be $1785\pm 25$ MeV, which is lower than energy of the lowest $1/2^{-}$ state in this model. This is consistent with our previous predictions within the instanton-induced quark-antiquark creation model.

In order to characterize the higher-order moments of particle multiplicity, we implement the linear-sigma model with Polyakov-loop correction. We first studied the critical phenomena and estimated some thermodynamic quantities. Then, we compared all these results with first-principle lattice QCD calculations. Then, the extensive study of non-normalized four-moments is followed by investigating their thermal and density dependences. We repeat this for moments normalized to temperature and chemical potential. The fluctuations of the second-order moment are used to estimate the chiral phase transition. Then, we implement all these in mapping out the chiral phase transition, which is compared with the freeze-out parameters estimated from the lattice QCD simulations, and the thermal models are compared with the chiral phase diagram.