The collective bosonic Hamiltonian is derived from the microscopic nucleonic Hamiltonian by the generalized density matrix method. Independent parameters in the collective Hamiltonian are fixed completely, solutions are given in detail. The random phase approximation corresponds to the harmonic potential of the current approach. The full solution (very close to the exact diagonalization) is obtained over the whole region of parameters including and beyond the instability point of the random phase approximation. The method is tested in the simple Lipkin model.

The half-life of ${}^{38}$Ca, a $T_Z=-1$ superallowed $0^{+}$$\to$ $0^{+}$${\beta }^{+}$ emitter, has been measured to be 443.77(36) ms. In our experiment, pure sources of ${}^{38}$Ca were produced and the decay positrons were detected in a high-efficiency 4$\pi$ proportional gas counter. Since the ${\beta }^{+}$ decay of ${}^{38}$Ca feeds ${}^{38}$K${}^m$, which is itself a superallowed ${\beta }^{+}$ emitter, the data were analyzed as a linked parent-daughter decay. Our result, with a precision of 0.08$\%$, is a factor of 5 improvement on the best previous result.

Spin-polarized states in dense neutron matter with the recently developed Skyrme effective interaction (BSk20 parametrization) are considered in the magnetic fields $H$ up to ${10}^{20}$ G at finite temperature. In a strong magnetic field, the total pressure in neutron matter is anisotropic, and the difference between the pressures parallel and perpendicular to the field direction becomes significant at $H>H_{\mathrm{th}}\sim {10}^{18}$ G. The longitudinal pressure decreases with the magnetic field and vanishes in the critical field ${10}^{18}<H_c\lesssim {10}^{19}$ G, resulting in the longitudinal instability of neutron matter. With increasing temperature, the threshold $H_{\mathrm{th}}$ and critical $H_c$ magnetic fields also increase. The appearance of the longitudinal instability prevents the formation of a fully spin-polarized state in neutron matter and only the states with moderate spin polarization are accessible. The anisotropic equation of state is determined at densities and temperatures relevant to the interiors of magnetars. The entropy of strongly magnetized neutron matter turns out to be larger than the entropy of nonpolarized matter. This is caused by some specific details in the dependence of the entropy on the effective masses of neutrons with spin up and spin down in a polarized state.

In the framework of a constituent quark model, the effect of hidden color channels on the nucleon-nucleon ($NN$) interaction is studied. By adjusting the color confinement strength between the hidden color channels and color singlet channels and/or between the hidden color channels and hidden color channels, the experimental data of $S$- to $I$-partial-wave phase shifts of $NN$ scattering can be fitted well. The results show that the hidden color channel coupling might be important in producing the intermediate-range attraction of the $NN$ interaction. The deuteron properties and dibaryon candidates have also been studied with this model.

A modified variable phase method for the numerical solution of coupled radial Schrödinger equations, which maintains linear independence for different sets of solution vectors, is suggested. The modification involves rearrangement of coupled equations to avoid the usual numerical instabilities associated with components of the wave function in their classically forbidden regions. The modified method is applied to nuclear structure calculations of halo nuclei within the hyperspherical harmonics approach.

We analyze how the structure of the inner crust is influenced by the pairing correlations. The inner crust matter, formed by nuclear clusters immersed in a superfluid neutron gas and ultrarelativistic electrons, is treated in the Wigner-Seitz approximation. The properties of the Wigner-Seitz cells, i.e., their neutron-to-proton ratio and their radius at a given baryonic density, are obtained from the energy minimization at beta equilibrium. To obtain the binding energy of baryonic matter we perform Skyrme–Hartree-Fock-Bogoliubov (HFB) calculations with zero-range density-dependent pairing forces of various intensities. The most important effect of pairing is to smooth the dependence of Hartree-Fock (HF) energy on proton number. For some cells pairing can change significantly the proton number of the HF configurations. However, these changes are not so relevant because the energy difference between the absolute HFB minima and the energies corresponding to HF minima is very small. In the high-density cells, well-defined absolute minima are not found since the binding energies decrease continuously for small proton numbers. We show that the structure of these cells can be eventually determined by taking into account the underestimation of the binding energy due to the discretization of the energy spectrum of the nonlocalized neutrons induced by the boundary conditions at the border of the cells.

Recently discovered $\alpha$ decays with new or improved data, covering naturally occurring $\alpha$ emitters with long lifetimes, short-lived ones approaching the proton drip line, and decays of heavy and superheavy elements, have been studied in a systematic investigation within the modified two-potential approach for deformed nuclei by constructing the microscopic double-folding potential. It is found that the experimental half-lives are well reproduced in the density-dependent cluster model. Some predictions on natural $\alpha$ emitters and $\alpha$ decays of several proton emitters are made in this study. Moreover, the $\alpha$-decay half-lives of even-even superheavy nuclei with $Z=110$–114 and $N=184$–194 are estimated to pursue the quite stable nuclei around the proton $Z\sim 114$ and neutron $N\sim 184$ shell closures. These predictions can be useful for future experiments aimed at searching for long-lived natural elements.

Time evolution of a “little bang” created in heavy-ion collisions can be divided into two phases, the pre-equilibrium and hydrodynamic. At what moment does the evolution become hydrodynamic and is there any universality in the hydrodynamic flow? To answer these questions we briefly discuss various versions of hydrodynamics and their applicability conditions. In particular, we elaborate on the idea of “universal” (all-order resumed) hydrodynamics and propose a simple new model for it. The model is motivated by results obtained recently via the Anti–de Sitter and conformal field correspondence. Finally, charged hadron multiplicities in heavy-ion collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider are discussed. At the freeze-out, the multiplicities can be related to total entropy produced in the collision. Assuming the universal hydrodynamics to hold, we calculate the entropy production in the hydro stage of the collision. We end up speculating about a connection between the multiplicity growth and the temperature dependence of the quark-gluon plasma viscosity.

Using the Hellmann-Feynman theorem we analyze the contribution of the different terms of the nucleon-nucleon interaction to the nuclear symmetry energy $E_{\mathrm{sym}}$ and the slope parameter $L$. The analysis is performed within the microscopic Brueckner-Hartree-Fock approach using the Argonne V18 potential plus the Urbana IX three-body force. We find that the main contribution to $E_{\mathrm{sym}}$ and $L$ comes from the tensor component of the nuclear force.

We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity ($P$) and time-reversal ($T$) violation which, at the quark-gluon level, originates from the QCD vacuum angle and dimension-six operators capturing physics beyond the standard model. We argue that EDMs of light nuclei can be expressed in terms of six low-energy constants that appear in the $P$- and $T$-violating nuclear potential and electric current. As examples, we calculate the EDMs of the deuteron, the triton, and ${}^3$He in leading order in the EFT expansion.

We present a new exactly solvable Hamiltonian with a separable pairing interaction and nondegenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the Hartree-Fock basis.

Two investigations of parity-violating electron scattering are performed theoretically. One is to investigate the sensitivity of the theoretical parity-violating asymmetries to different nonlinear $\omega$-$\rho$ coupling parameter ${\Lambda }_{\mathrm{v}}$, while keeping the other parameters unchanged in the relativistic mean field (RMF) model. The other is to study the neutron properties and parity-violating asymmetries with three different RMF parameter sets: NL3, FSUGold, and IU-FSU. For the first topic, the neutron skin thickness reduces and corresponding oscillation amplitudes of the parity-violating asymmetries become small with the value of ${\Lambda }_{\mathrm{v}}$ increasing. For the second topic, results show there are significant differences between the parity-violating asymmetries in some scattering angles when calculated with different parameter sets. These angles are the best measuring angles in the experiments and the results are helpful to constrain the parameters in the RMF model.

We study the resonance spectroscopy of the proton-rich nucleus ${}^7$B in the ${}^4\mathrm{He}+p+p+p$ cluster model. Many-body resonances are treated under the correct boundary condition as Gamow states using the complex scaling method. We predict five resonances of ${}^7$B and evaluate the spectroscopic factors of the ${}^6$Be-$p$ components. The importance of the ${}^6$Be($2^{+}$)-$p$ component is shown in several states of ${}^7$B; this is a common feature of ${}^7$He, a mirror nucleus of ${}^7$B. For only the ground state of ${}^7$B, the mixing of the ${}^6$Be($2^{+}$) state is larger than that of ${}^6$He($2^{+}$) in ${}^7$He, which indicates a breaking of mirror symmetry. This is caused by the small energy difference between ${}^7$B and the excited ${}^6$Be($2^{+}$) state, the origin of which is Coulomb repulsion.

Within the framework of a multiphase transport model, harmonic flows $v_n$ ($n=2,3,$ and 4) are investigated for Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. The event-by-event geometry fluctuations significantly contribute to harmonic flows. Triangular flow ($v_3$) originates from initial triangularity (${\varepsilon }_3$) and is developed by partonic interactions. The conversion efficiency ($v_n/{\varepsilon }_n$) decreases with the harmonic order and increases with the partonic interaction cross section. A mass ordering in the low-$p_T$ region and a constituent quark number scaling in the middle-$p_T$ region seem to work roughly for $n$th harmonic flows at both energies. All features of harmonic flows show similar qualitative behaviors at BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider energies, which implies that the formed partonic matters are similar at the two energies.

The higher order moments of the net-baryon distributions in relativistic heavy ion collisions are useful probes for the QCD critical point and fluctuations. We study the net-proton distributions and their moments in a simple model which considers the baryon stopping and pair production effects in the processes. It is shown that a single emission source model can explain the experimental data well. The centrality dependence and the energy dependence of the distributions and higher moments are discussed.

The specific viscosity of neutron-rich nuclear matter is studied from the relaxation time approach using an isospin- and momentum-dependent interaction and the nucleon-nucleon cross sections taken as those from the experimental data modified by the in-medium effective masses as used in the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model calculations. The relaxation time of neutrons is larger while that of protons is smaller in neutron-rich nuclear matter compared with that in symmetric nuclear matter, and this leads to a larger specific viscosity in neutron-rich nuclear matter. In addition, the specific viscosity decreases with increasing temperature because of more frequent collisions and weaker Pauli blocking effect at higher temperatures. At lower temperatures the specific viscosity increases with increasing density due to the Pauli blocking effect, while at higher temperatures it slightly decreases with increasing density as a result of smaller in-medium effective masses at higher densities.

Possible formation of large hyperfragments in relativistic heavy-ion collisions is studied within two transport models, the Dubna cascade model and UrQMD model. Our goal is to explore a new mechanism for the formation of strange nuclear systems via capture of hyperons by relatively cold spectator matter produced in semiperipheral collisions. We investigate basic characteristics of the produced hyperspectators and estimate the production probabilities of multistrange systems. Advantages of the proposed mechanisms over an alternative coalescence process are analyzed. We also discuss how such hyperfragments can be detected by taking into account the background of free hyperons. This investigation is important for the development of new experimental methods for producing hypernuclei in peripheral relativistic nucleus-nucleus collisions, which are now underway at GSI and are planned for the future FAIR and NICA facilities.

An expanding fireball model with two freeze-outs, which assumes that the chemical freeze-out occurs earlier at a higher temperature and the thermal freeze-out occurs later at a lower temperature, is developed and successfully applied to fit simultaneously the hadron ratios, the transverse momentum spectra of measured hadrons, and the rapidity distribution of charged hadrons measured in $\mathrm{Au}+\mathrm{Au}$ collisions at $200A$ GeV by the STAR, PHENIX, and PHOBOS Collaborations. The quality of all the fittings is very good, and the resulting parameters are in agreement with published values.

Theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. By diagonalizing the matrix of second derivatives, one gains access to a wealth of information—in the form of powerful correlations—that would normally remain hidden. We illustrate the power of the covariance analysis by using two relativistic mean-field models: (a) the original linear Walecka model and (b) the accurately calibrated FSUGold parametrization. In addition to providing meaningful theoretical uncertainties for both model parameters and predicted observables, the covariance analysis establishes robust correlations between physical observables. In particular, we show that, whereas the correlation coefficient between the slope of the symmetry energy and the neutron-skin thickness of lead is indeed very large, a 1$\%$ measurement of the neutron radius of lead may only be able to constrain the slope of the symmetry energy to about 30$\%$.

Background: The next-to-next-to-next-to-leading order (N${}^3$LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required as a step preliminary to the adjustment of the coupling constants.

Purpose: We determine to what extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, we study the relations between the validity of the continuity equation and the invariance of the functional under gauge transformations.

Methods: We derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix.

Results: We obtained four sets of constraints on the coupling constants of the N${}^3$LO energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions.

Conclusions: The validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces.