Background: The $R$ matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled-channel systems. The theory provides solutions for bound states, scattering states, and resonances for microscopic models in one formalism.

Purpose: The first purpose is to extend this formalism to the relativistic case so that the many-coupled-channel problems may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The second purpose is to employ this formalism in a relativistic continuum shell model.

Methods: Expressions for the collision matrix and the scattering amplitude, from which observables may be calculated, are derived. The formalism is applied to the 1$p$-1$h$ relativistic continuum shell model with an interaction extracted from relativistic mean-field theory.

Results: The simplest of the $\sigma +\omega +\rho$ exchange interactions produces a good description of the single-particle energies in ${}^{16}$O and ${}^{90}$Zr and a reasonable description of proton scattering from ${}^{15}$N.

Conclusion: The development of a calculable, relativistic $R$ matrix and its implementation in a $1p-1h$ relativistic continuum shell model provide a simple relatively self-consist physically justifiable model for use in knockout reactions.

The nucleon properties due to the restoration of the chiral symmetry at nonzero temperature $T$ are investigated within the framework of the linear $\sigma$ model. The field equations are solved using the coherent-pair approximation. In this approach, the quantum fields are treated in a nonperturbative fashion. We minimize the expectation value of the chiral Hamiltonian using the ansatz of the coherent-pair ground-state configuration. The obtained results show that the nucleon mass and mean-square radius of the proton and the neutron increase monotonically with the temperature $T$ and that the pion-nucleon coupling constant $g_{\pi NN}$ decreases with temperature values that are near the value of the critical temperature $T_c$. The nucleon mass and mean-square radius of the proton are examined in the $(x,T)$ plane, showing a sensitive dependence on the coherence parameter $x$. This means that an increase of both the coherence parameter $x$ and the temperature $T$ leads to an increase in the values of the nucleon mass and the mean-square radius of the proton. This is evidence for the quark-gluon deconfinement phase transition.

We construct all ${\mathrm{SU}}_L\left(3\right)\times {\mathrm{SU}}_R\left(3\right)$ chirally invariant anomalous magnetic, i.e., involving a Pauli tensor and one-derivative, interactions of one chiral $\left[\right(\mathbf{8},\mathbf{1})\oplus (\mathbf{1},\mathbf{8}\left)\right]$ meson field with chiral $\left[\right(\mathbf{6},\mathbf{3})\oplus (\mathbf{3},\mathbf{6}\left)\right]$, $[(\mathbf{3},\overline{\mathbf{3}})\oplus (\overline{\mathbf{3}},\mathbf{3})]$, and $\left[\right(\mathbf{8},\mathbf{1})\oplus (\mathbf{1},\mathbf{8}\left)\right]$ baryon fields and their “mirror” images. We find strong chiral selection rules; e.g., there is only one off-diagonal chirally symmetric anomalous magnetic interaction between $J=\frac{1}{2}$ fields belonging to the $\left[\right(\mathbf{6},\mathbf{3})\oplus (\mathbf{3},\mathbf{6}\left)\right]$ and the $[(\mathbf{3},\overline{\mathbf{3}})\oplus (\overline{\mathbf{3}},\mathbf{3})]$ chiral multiplets. We also study the chiral selection rules for the anomalous magnetic interactions of the $[(\mathbf{3},\overline{\mathbf{3}})\oplus (\overline{\mathbf{3}},\mathbf{3})]$ and the $\left[\right(\mathbf{8},\mathbf{1})\oplus (\mathbf{1},\mathbf{8}\left)\right]$ baryon fields. Again, no diagonal and only one off-diagonal chiral ${\mathrm{SU}}_L\left(3\right)\times {\mathrm{SU}}_R\left(3\right)$ interaction of this type is allowed, that turns out also to conserve the ${\mathrm{U}}_A\left(1\right)$ symmetry. We calculate the $F/D$ ratios for the baryons' anomalous magnetic moments predicted by these interactions in the SU(3) symmetry limit and find that only the $\left[\right(\mathbf{6},\mathbf{3})\oplus (\mathbf{3},\mathbf{6}\left)\right]$-$[(\mathbf{3},\overline{\mathbf{3}})\oplus (\overline{\mathbf{3}},\mathbf{3})]$ one reproduces $F/D=1/3$, in close proximity to the value extracted from experiment.

The charged and neutral pion photoproduction reactions are investigated in a dynamical coupled-channels approach based on the formulation of Haberzettl, Huang, and Nakayama [Phys. Rev. C 83, 065502 (2011)]. The hadronic final-state interaction is provided by the Jülich $\pi N$ model, which includes the channels $\pi N$ and $\eta N$ comprising stable hadrons as well as the effective $\pi \pi N$ channels $\pi \Delta$, $\sigma N$, and $\rho N$. This hadronic model has been quite successful in describing $\pi N\to \pi N$ scattering for center-of-mass energies up to $1.9$ GeV. By construction, the full pion photoproduction current satisfies the generalized Ward-Takahashi identity and thus is gauge invariant as a matter of course. The calculated differential cross sections and photon spin asymmetries up to 1.65 GeV center-of-mass energy for the reactions $\gamma p\to {\pi }^{+}n$, $\gamma p\to {\pi }^{0}p$, $\gamma n\to {\pi }^{-}p$, and $\gamma n\to {\pi }^{0}n$ are in good agreement with the experimental data.

Cross-section measurements have been made at 16 and 19 MeV in two exit-channel configurations of neutron-deuteron breakup: the space star and coplanar star. In this kinematically complete measurement, the outgoing proton and one of the neutrons were detected in coincidence and their energies were determined via time-of-flight techniques. Monte Carlo simulations based on rigorous three-nucleon Faddeev calculations using the charge-dependent-Bonn (CD-Bonn) nucleon-nucleon potential were used to compare the experimental results with theory. Large discrepancies between data and theory were found in both breakup configurations measured at both energies, suggesting deficiencies in current theoretical treatment of three-nucleon forces or in present knowledge of the neutron-neutron ${}^1{S}_0$ force.

We present a systematic study of the effects from initial condition fluctuations in systems formed by heavy-ion collisions using the hydrodynamical simulation code NeXSPheRIO. The study was based on a sample of events generated simulating Au+Au collisions at center-of-mass energy of 200 GeV per nucleon pair with an impact parameter ranging from most central to peripheral collisions. The capability of the NeXSPheRIO code to control and save the initial condition (IC) as well as the final state particles after the three-dimensional hydrodynamical evolution allows for the investigation of the sensitivity of the experimental observables to the characteristics of the early IC. Comparisons of results from simulated events generated using fluctuating initial conditions and a smooth initial condition are presented for the experimental observable elliptic flow parameter ($v_2$) as a function of the transverse momentum $p_t$ and centrality. We compare $v_2$ values estimated using different methods, and how each method responds to the effects of fluctuations in the initial condition. Finally, we quantify the flow fluctuations and compare them to the fluctuations of the initial eccentricity of the energy density distribution in the transverse plane.

A quasistatistical equilibrium model is constructed to simulate the multicomponent composition of the crust of an accreting neutron star. The ashes of rp-process nucleosynthesis are driven by accretion through a series of electron captures, neutron emissions, and pycnonuclear fusions up to densities near the transition between the neutron star crust and core. A liquid droplet model which includes nuclear shell effects is used to provide nuclear masses far from stability. Reaction pathways are determined consistently with the nuclear mass model. The nuclear symmetry energy is an important uncertainty in the masses of the exotic nuclei in the inner crust and varying the symmetry energy changes the amount of deep crustal heating by as much as a factor of two.

High spin states of ${}^{109}$In were investigated using the reaction ${}^{96}$Zr(${}^{19}$F, 6n)${}^{109}$In at a beam energy of 105 MeV. New level sequences have been found in this nucleus. In an earlier known band, the ordering of some of the transitions have been changed and assigned a three-quasiparticle $\pi$(g${}_{9/2}$)${}^{-1}$ $\otimes$ $\nu$[h${}_{11/2}$(d${}_{5/2}$/g${}_{7/2}$)] configuration. Similar three-quasiparticle bands have also been found earlier in lighter mass ${}^{105}$In and ${}^{107}$In nuclei. Systematics of these bands in ${}^{105}$In, ${}^{107}$In, and ${}^{109}$In nuclei are discussed in the present work within the framework of the tilted axis cranking model.

We analyze recent experimental data of heavy-ion fusion cross sections available up to deep-subbarrier energies in order to discuss the threshold incident energy for a deep-subbarrier fusion hindrance phenomenon. To this end, we employ a one-dimensional potential model with a Woods-Saxon internuclear potential. Fitting the experimental data in two different energy regions with different Woods-Saxon potentials, we define the threshold energy as an intersection of the two fusion excitation functions. We show that the threshold energies so extracted are in good agreement with the empirical systematics as well as with the values of the Krappe-Nix-Sierk (KNS) potential at the touching point. We also discuss the asymptotic energy shift of fusion cross sections with respect to the potential model calculations, and show that it decreases with decreasing energies in the deep-subbarrier region, although it takes a constant value at subbarrier energies.

Following a previous Letter [P. W. Zhao et al., Phys. Rev. Lett. 107, 122501 (2011)] on the first microscopic description of the antimagnetic rotation (AMR) in ${}^{105}\mathrm{Cd}$, a systematic investigation and detailed analysis for the AMR band in the framework of the tilted-axis cranking (TAC) model based on covariant density functional theory are carried out. After the microscopic and self-consistent TAC calculations are performed with a given density functional, the configuration for the observed AMR band in ${}^{105}\mathrm{Cd}$ is obtained from the single-particle Routhians. With the configuration thus obtained, the tilt angle ${\theta }_{\Omega }$ for a given rotational frequency is determined self-consistently by minimizing the total Routhian with respect to the angle ${\theta }_{\Omega }$. In such a way, the energy spectrum, total angular momenta, kinetic and dynamic moments of inertia, and the $B\left(E2\right)$ values for the AMR band in ${}^{105}\mathrm{Cd}$ are calculated. Good agreement with the data is found. By investigating microscopically the contributions from neutrons and protons to the total angular momentum, the “two-shears-like” mechanism in the AMR band is clearly illustrated. Finally, the currents leading to time-odd mean fields in the Dirac equation are presented and discussed in detail. It is found that they are essentially determined by the valence particles and/or holes. Their spatial distribution and size depend on the specific single-particle orbitals and the rotational frequency.

High-spin states in ${}^{122}$I have been investigated using the ${}^{116}$Cd(${}^{11}$B,5n)${}^{122}$I reaction at a beam energy of 65 MeV and $\gamma$-ray coincidence events were recorded with the INGA spectrometer. The level scheme of ${}^{122}$I has been extended up to spin $I=30$. Experimental features, such as band-crossing frequencies, aligned angular momenta, signature splitting, and $B\left(M1\right)/B\left(E2\right)$ ratios have been used for configuration assignments to low-energy band structures. Maximally aligned states involving all eight particles outside the ${}^{114}$Sn core and states with one particle antialigned have been identified. Cranked Nilsson-Strutinsky calculations have been used to interpret high-spin structures.

Dirac Hamiltonian is scaled in the atomic units $\hslash =m=1$, which allows us to take the nonrelativistic limit by setting the Compton wavelength $\lambda \to 0$. The evolutions of the spin and pseudospin symmetries toward the nonrelativistic limit are investigated by solving the Dirac equation with the parameter $\lambda$. Setting the $\lambda$ transformation from the original Compton wavelength to 0, the spin splittings decrease monotonously in all spin doublets, and the pseudospin splittings increase in several pseudospin doublets, show no change, or even reduce in several other pseudospin doublets. The various energy splitting behaviors of both the spin and pseudospin doublets with $\lambda$ are well explained by the perturbation calculations of the Dirac Hamiltonian in the present units. It indicates that the origin of spin symmetry is entirely due to the relativistic effect, while the origin of pseudospin symmetry cannot be uniquely attributed to the relativistic effect.

Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by a dense plasma environment. Simulations of superbursts, deep crustal heating, and other nuclear burning phenomena in neutron stars require astrophysical $S$ factors for these reactions (as a function of center-of-mass energy $E$ of colliding nuclei). A large database of $S$ factors is created for about 5000 nonresonant fusion reactions involving stable and unstable isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si. It extends the previous database of about 1000 reactions involving isotopes of C, O, Ne, and Mg. The calculations are performed using the São Paulo potential and the barrier penetration formalism. All calculated $S$ data are parameterized by an analytic model for $S\left(E\right)$ proposed before [Phys. Rev. C 82, 044609 (2010)] and further elaborated here. For a given reaction, the present $S\left(E\right)$ model contains three parameters. These parameters are easily interpolated along reactions involving isotopes of the same elements with only seven input parameters, giving an ultracompact, accurate, simple, and uniform database. The $S\left(E\right)$ approximation can also be used to estimate theoretical uncertainties of $S\left(E\right)$ and nuclear reaction rates in dense matter, as illustrated for the case of the ${}^{34}$Ne${+}^{34}$Ne reaction in the inner crust of an accreting neutron star.

Sea-quark content of the octet baryons are investigated by employing an extended chiral constituent quark approach, which embodies higher Fock five-quark components in the baryons wave functions. The well-known flavor asymmetry of the nucleon sea $\overline{d}-\overline{u}$, is used as input to predict the probabilities of $\overline{u}$, $\overline{d}$, and $\overline{s}$ in the nucleon, $\Lambda$, $\Sigma$, and $\Xi$ baryons, due to the intrinsic five-quark components in the baryons wave functions.

The universal experimental data for the energy-integrated angular distribution and the angle-integrated energy spectra for protons emitted from the ($n$,$p$) reactions at 14.8 MeV incident energy were analyzed earlier using the computer code preco-d2, developed on the basis of Kalbach's semiempirical model for the preequilibrium reactions. The results of the analysis provided the semiempirical systematics of the single-particle level densities $g_R\left(\exp \right)$ (effective in the residual nuclei) and $g_c\left(\exp \right)$ (effective in the composite system). In order to interpret these results, we have carried out the theoretical calculations with Shlomo's theory developed on the basis of the Green's function approach. The theoretical values based on Shlomo's theory for $g_{Rn}^{Th}\left({\varepsilon }_{Rn}\right)$ and $g_{Rp}^{Th}\left({\varepsilon }_{Rp}\right)$ for the residual nucleus and $g_{cn}^{Th}\left({\varepsilon }_{cn}\right)$ and $g_{cp}^{Th}\left({\varepsilon }_{cp}\right)$ for the composite systems, respectively, were calculated at various excitation energies by using a reasonable single-particle nuclear potential strength $V_0$, available from systematics in literature. Here, ${\varepsilon }_{Rn}$ and ${\varepsilon }_{Rp}$ are the single-particle excitation energies for single-particle level densities for the residual nucleus, and ${\varepsilon }_{cn}$ and ${\varepsilon }_{cp}$ are the single-particle excitation energies of effective single-particle level densities for the composite system for neutrons and protons, respectively. The Coulomb interaction potential $V_c$ was included for protons over and above the nuclear potential $V_0$. The total theoretical values were taken as $g_R^{TTh}\left({\varepsilon }_R\right)=g_{Rn}^{Th}\left({\varepsilon }_{Rn}\right)+g_{Rp}^{Th}\left({\varepsilon }_{Rp}\right)$ for residual nuclei and $g_c^{TTh}\left({\varepsilon }_c\right)=g_{cn}^{Th}\left({\varepsilon }_{cn}\right)+g_{cp}^{TTh}\left({\varepsilon }_{cp}\right)$ for the composite system. ${\varepsilon }_R$ is the Fermi energy of the total effective single-particle level density for residual nuclei, and ${\varepsilon }_c$ is the excitation energy of the effective single-particle level density of the composite system. Careful comparison of theoretical and experimental results shows that $g_R\left(\exp \right)$ matches with $g_R^{TTh}\left({\varepsilon }_f\right)$ for $V_0^i=45\mathrm{MeV}\mathrm{where}\left({\varepsilon }_f\right)\text{is}\text{the}\text{Fermi}\text{energy}.$ The theoretical values $g_R^{TTh}\left({\varepsilon }_f\right)$ also nearly agree with the previously reported values by various groups, obtained through different approaches for a large number of cases. The values of $g_c\left(\exp \right)$ always are found to be greater than $g_R\left(\exp \right)$ and match with $g_c^{TTh}\left({\varepsilon }_c\right)$ at effective excitation energies ${\varepsilon }_c$, which are found to be invariably much higher than the respective ${\varepsilon }_f$ and are positive and follow the nuclear shell model structure when plotted against $A$. This supports the concept that the values of effective $g_c\left(\exp \right)$ are decided mainly by dominant transition, which occurs during initial stages of the multistep statistical direct preequilibrium process that involves unbound states. The values of $g_R\left(\exp \right)$, on the other hand, are found to correspond to the effective ${\varepsilon }_R$ around the Fermi energies of the bound states of residual nuclei involved in the decay processes. The ratios of $g_c\left(\exp \right)/g_R\left(\exp \right)$ are found to follow the ${\left(\frac{\langle {\varepsilon }_c\rangle }{\langle {\varepsilon }_f\rangle }\right)}^{1/2}f$ description and to match Shlomo's theory.

The interpretation of the measured elliptic and higher order collective flows in heavy-ion collisions in terms of viscous hydrodynamics depends sensitively on the ratio of shear viscosity to entropy density. Here we perform a quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods for selected test cases with specified elastic differential cross sections: (i) the nonrelativistic, relativistic and ultrarelativistic hard sphere gas with angle and energy independent differential cross section, (ii) the Maxwell gas, (iii) chiral pions, and (iv) massive pions for which the differential elastic cross section is taken from experiments. Our quantitative results (i) reveal that the extent of agreement (or disagreement) depends sensitively on the energy dependence of the differential cross sections employed, and (ii) stress the need to perform quantum molecular dynamical (URQMD) simulations that employ Green-Kubo techniques with similar cross sections to validate the codes employed and to test the accuracy of other methods.

We investigate compact star properties within the quark-meson-coupling model with a soft symmetry energy density dependence at large densities. In particular, the hyperon content and the mass/radius curves for the families of stars obtained within the model are discussed. The hyperon-meson couplings are chosen according to experimental values of the hyperon nuclear matter potentials, and possible uncertainties are considered. It is shown that a softer symmetry energy gives rise to stars with less hyperons, smaller radii, and larger masses. Hyperon-meson couplings may also have a strong effect on the mass of a star.

We propose a new computational method for astrophysical reaction rate of the radiative capture process. In the method, an evolution of a wave function is calculated along the imaginary-time axis, which is identified as the inverse temperature. It enables direct evaluation of reaction rate as a function of temperature without solving any scattering problem. The method is tested for two-body radiative capture reaction, ${}^{16}\mathrm{O}(\alpha ,\gamma ){}^{20}\mathrm{Ne}$, showing that it gives identical results to those calculated by the ordinary procedure. This method will be suited for calculation of triple-$\alpha$ radiative capture rate, for which an explicit construction of the scattering solution is difficult.