We reply to the Comment by Potekhin and Yakovlev concerning the maximum inner magnetic field estimate in compact stars and the anisotropic nature of the equation of state of a magnetized medium reported in our paper Phys. Rev. C 82, 065802 (2010). We call attention to the relation between the state of matter in the star core and the maximum value of the inner field for hybrid neutron stars. We point out that the maximum field can reach much larger values if the core is made of quark matter rather than of nuclear matter. We also discuss why the anisotropy in the equation of state of a magnetized medium is unavoidable for static media in a uniform magnetic field.

The cross sections of ${}^{\mathrm{nat}}$Cr($n$,$x$)${}^{52}$V, ${}^{52}$Cr($n$,$p$)${}^{52}$V, ${}^{\mathrm{nat}}$Cr($n$,$x$)${}^{53}$V, ${}^{53}$Cr($n$,$p$)${}^{53}$V, ${}^{\mathrm{nat}}$Zn($n$,$x$)${}^{66}$Cu, ${}^{66}$Zn($n$,$p$)${}^{66}$Cu, ${}^{\mathrm{nat}}$Zn($n$,$x$)${}^{68}$Cu${}^m$, ${}^{68}$Zn($n$,$p$)${}^{68}$Cu${}^m$, ${}^{\mathrm{nat}}$Mo($n$,$x$)${}^{97}$Nb${}^g$, ${}^{97}$Mo($n$,$p$)${}^{97}$Nb${}^g$, ${}^{\mathrm{nat}}$Mo($n$,$x$)${}^{97}$Nb${}^m$, ${}^{97}$Mo($n$,$p$)${}^{97}$Nb${}^m$, ${}^{\mathrm{nat}}$Sn($n$,$x$)${}^{116}$In${}^m$${}^{1+m2}$, ${}^{116}$Sn($n$,$p$)${}^{116}$In${}^m$${}^{1+m2}$, ${}^{\mathrm{nat}}$Sn($n$,$x$)${}^{117}$In${}^g$, ${}^{117}$Sn($n$,$p$)${}^{117}$In${}^g$, ${}^{\mathrm{nat}}$Sn($n$,$x$)${}^{118}$In${}^m$${}^{1+m2}$, ${}^{118}$Sn($n$,$p$)${}^{118}$In${}^m$${}^{1+m2}$, ${}^{\mathrm{nat}}$Sn($n$,$x$)${}^{120}$In${}^x$, ${}^{120}$Sn($n$,$p$)${}^{120}$In${}^x$, ${}^{\mathrm{nat}}$Ba($n$,$x$)${}^{138}$Cs, and ${}^{138}$Ba($n$,$p$)${}^{138}$Cs reactions have been measured at 14.8 MeV neutron energy. In the present work, the contributions of ($n$,$np$), ($n$,$pn$), and ($n$,$d$) reactions from heavier isotopes are subtracted. The cross sections were also estimated with the talys-1.2 nuclear model code using different level density models, at neutron energies varying from the reaction threshold to 20 MeV. The variations in the ($n$,$p$) cross sections with the neutron number in the isotopes of an element are also discussed in brief.

We address dilepton production in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s{}_{NN}}=200$ GeV by employing the parton-hadron-string dynamics (PHSD) off-shell transport approach. Within the PHSD, one goes beyond the quasiparticle approximation by solving generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for the Green's functions in the phase-space representation. The approach consistently describes the full evolution of a relativistic heavy-ion collision, from the initial hard scatterings and string formation, through the dynamical deconfinement phase transition to the quark-gluon plasma (QGP) as well as hadronization, to the subsequent interactions in the hadronic phase. With partons described in the PHSD by the dynamical quasiparticle model (DQPM)—matched to reproduce lattice QCD results in thermodynamic equilibrium—we calculate, in particular, the dilepton radiation from partonic interactions through the reactions $q\overline{q}\to {\gamma }^{*}$, $q\overline{q}\to {\gamma }^{*}+g$, and $qg\to {\gamma }^{*}q$ ($\overline{q}g\to {\gamma }^{*}\overline{q}$) in the early stage of relativistic heavy-ion collisions. By comparing our results to the data from the PHENIX Collaboration, we study the relative importance of different dilepton production mechanisms and point out the regions in phase space where partonic channels are dominant. Furthermore, explicit predictions are presented for dileptons within the acceptance of the STAR detector system and compared to the preliminary data.

Based on a relativistic Boltzmann-Uehling-Uhlenbeck transport model, proton- and ${}^3$He-induced reactions on a ${}^{197}$Au target at beam energies of 2.8, 5, 10, and 16.587 GeV/nucleon are studied. It is found that compared with proton-induced reactions, ${}^3$He-induced reactions give larger cross sections of pion production, about 5 times those of the proton-induced reactions. And more importantly, pion production from ${}^3$He-induced reaction is more inclined to low-angle emission. Neutrino production via positively charged pion is also discussed accordingly.

The one-quasiparticle structures of nuclei in the $\alpha$-decay chains of ${}^{287}$114 and ${}^{293}$116 are studied with a modified two-center shell model. The two-quasiparticle states are revealed in the $\alpha$-decay chain of even-even nuclei ${}^{286,288}$114. The calculated values of $Q_{\alpha }$ are compared with available experimental data. The termination of the $\alpha$-decay chains by spontaneous fission is analyzed.

A framework to evolve three-nucleon ($3\mathrm{N}$) forces in a plane-wave basis with the similarity renormalization group (SRG) is presented and applied to consistent interactions derived from chiral effective field theory at next-to-next-to-leading order. We demonstrate the unitarity of the SRG transformation, show the decoupling of low and high momenta, and present the first investigation of universality in chiral $3\mathrm{N}$ forces at low resolution scales. The momentum-space-evolved $3\mathrm{N}$ forces are consistent and can be directly combined with the standard SRG-evolved two-nucleon (NN) interactions for ab initio calculations of nuclear structure and reactions.

Most current implementations of the quadrupole collective Hamiltonian model do not include the contributions of time-odd mean fields to the moments of inertia and mass parameters (Thouless-Valatin dynamical rearrangement contributions). A hybrid model is introduced that allows a quantitative estimate of these contributions to the inertial functions of a five-dimensional collective Hamiltonian based on microscopic energy density functionals. Fully self-consistent constrained relativistic Hartree-Bogoliubov calculations of triaxial energy surfaces in the $\beta -\gamma$ plane are used to determine the parameters of an equivalent pairing-plus-quadrupole ($P+Q$) Hamiltonian. This Hamiltonian is employed in constrained Hartree-Fock-Bogoliubov (CHFB) plus local quasiparticle random-phase approximation (LQRPA) calculation of the deformation-dependent corrections to the Inglis-Belyaev moments of inertia and cranking mass parameters. This hybrid model is used to evaluate the influence of time-odd mean fields on vibrational and rotational collective masses and investigate their effect on the low-energy collective excitation spectra and transition rates of $\gamma$-soft Xe and Ba nuclei.

The anomalously fast decay of a $19/2^{+}$ three-quasiparticle isomer in ${}^{171}$Tm was interpreted recently as an example of $K$ mixing induced by a very small mixing matrix element but a (random) close proximity to a collective state. To understand the source of the residual interaction we have generalized the projected shell model by introducing two-body octupole and hexadecupole forces into the Hamiltonian and expanding the model space with inclusion of specific three-quasiparticle configurations. It is found that the $K$ mixing is built up from small interactions transferred through numerous highly excited configurations that contain high-$j$ orbitals. While the chance near-degeneracy enhances the transition strength, the octupole correlation and Coriolis coupling produce the mixing matrix element.

We have studied the effect of nonzero bulk viscosity with a peak near the lattice-QCD predicted crossover temperature $T_{co}\sim 175$ MeV on charged-particle transverse-momentum spectra and elliptic flow. The Israel-Stewart theory of second-order causal dissipative relativistic fluid dynamics is used to simulate the space-time evolution of the matter formed in Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV, assuming longitudinal boost invariance. A systematic comparison of temperature, transverse velocity, and spatial and momentum anisotropy evolution of the ideal, bulk, and shear viscous fluids has been carried out. Two different temperature-dependent forms of $\zeta /s$ and a constant $\eta /s$ were used. Both the bulk and shear viscous corrections to the ideal freeze-out distribution function are included. The dissipative correction to the freeze-out distribution for bulk viscosity was calculated using Grad's 14-moment method. From our simulation we show that the method is applicable only for ${\zeta /s<0.005\eta /s|}_{\mathrm{KSS}}$ for freeze-out temperatures 130 and 160 MeV.

Motivated by recent observational data, the equations of state with the inclusion of strangeness-bearing $\Lambda$ hyperons and the corresponding properties of neutron stars are studied based on the covariant density functional (CDF) theory. To this end, we specifically employ the density-dependent relativistic Hartree-Fock (DDRHF) theory and the relativistic mean field (RMF) theory. The inclusion of $\Lambda$ hyperons in neutron stars shows substantial effects in softening the equation of state. Because of the extra suppression effect originating from the Fock channel, large reductions on both the star mass and radius are predicted by the DDRHF calculations. It is also found that the mass-radius relations of neutron stars with $\Lambda$ hyperons determined by DDRHF with the PKA1 parameter set are in fairly good agreement with the observational data, where a relatively small neutron-star radius is required. Therefore, it is expected that the exotic degrees of freedom such as the strangeness-bearing structure may appear and play significant roles inside the neutron stars, which is supported further by the systematical investigations on the consistency between the maximum neutron-star mass and $\Lambda$-coupling strength.

We present a lattice QCD calculation of the leading-order momentum-independent parity-violating coupling between pions and nucleons, $h_{\pi NN}^1$. The calculation performs measurements on dynamical anisotropic clover gauge configurations, with a spatial extent of $L\sim 2.5$ fm, a spatial lattice spacing of $a_s\sim 0.123$ fm, and a pion mass of $m_{\pi }\sim 389$ MeV. While this calculation does not include nonperturbative renormalization of the bare parity-violating operators, a chiral extrapolation to the physical pion mass, or contributions from disconnected (quark-loop) diagrams, these are expected to result in systematic errors within the quoted statistical error. We find a contribution from the “connected” diagrams of $h_{\pi NN}^{1,\mathrm{con}}=(1.099\pm {0.505}_{-0.064}^{+0.058})\times {10}^{-7}$, consistent with current experimental bounds and previous model-dependent theoretical predictions.

We demonstrate that the high-quality cooling data observed for the young neutron star in the supernova remnant Cassiopeia A over the past 10 years—as well as all other reliably known temperature data of neutron stars—can be comfortably explained within the “nuclear medium cooling” scenario. The cooling rates of this scenario account for medium-modified one-pion exchange in dense matter and polarization effects in the pair-breaking formations of superfluid neutrons and protons. Crucial for the successful description of the observed data is a substantial reduction of the thermal conductivity, resulting from a suppression of both the electron and nucleon contributions to it by medium effects. In a few more decades of continued monitoring of Cassiopeia A, the observed data may allow one to put additional constraints on the efficiency of different cooling processes in neutron stars.

We have developed a method of implanted ion counting in order to determine the absolute decay probability of the 776.5 keV $\gamma$-ray transition in the decay sequence of ${}^{82}$Sr${\to }^{82}$Rb${\to }^{82}$Kr. A 215 MeV beam of ${}^{82}$Sr was produced at the Holifield Radioactive Ion Beam Facility and passed through an ionization chamber that counted and identified the ions before they were implanted into thin aluminum foils. Subsequent offline measurements using a Ge detector deduced the probability per decay of ${}^{82}$Rb for the 776.5 keV $\gamma$ ray in ${}^{82}$Kr to be 0.1493(37), in agreement with the accepted average value of 0.1508(16). This new technique measures directly the number of decaying nuclei in a given sample and significantly reduces the dependence on knowledge of the complete decay level scheme.

The $Q$ values of $\alpha$ decay and the half-lives [${\log }_{10}{T}_{1/2}^{\alpha }$(s)] are calculated for the $\alpha$-decay chains of ${}^{293,294}117$ nuclei, within the framework of the isospin cluster model (ICM). In the ICM model the proximity energy is improved by using the isospin dependent radius of parent, daughter, and $\alpha$ particle. For the $Q$ values the binding energy $B(A_i,Z_i)$ ($i=1$,2) of any nucleus of mass number $A$ and atomic number $Z$ was obtained from a phenomenological and more generalized BW mass formula given by Samanta and Adhikari [Phys. Rev. C 65, 037301(2002)]. The calculated results in ICM using different $Q$ values, are compared with the experimental data and the other theoretical macro-microscopic (MM) Relativistic Mean Field (RMF) (with NL3 and FSU gold force parameters) model calculations. The estimated values of $\alpha$-decay half-lives are in good agreement with the recent experimental data. The ICM calculation is in favor of the presence of neutron magic number at $N=172$.

The nonmesonic weak decay of polarized $\Lambda$ hypernuclei is studied with a microscopic diagrammatic formalism in which one- and two-nucleon-induced decay mechanisms, $\vec{\Lambda }N\to NN$ and $\vec{\Lambda }NN\to NNN$, are considered together with (and on the same ground of) nucleon final state interactions. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation. Our approach adopts different one-meson-exchange weak transition potentials, while the strong interaction effects are accounted for by a Bonn nucleon-nucleon interaction. We also consider the two-pion-exchange effect in the weak transition potential. Both the two-nucleon-induced decay mechanism and the final state interactions reduce the magnitude of the asymmetry. The quantum interference terms considered in the present microscopic approach give rise to an opposite behavior of the asymmetry with increasing energy cuts to that observed in models describing the nucleon final state interactions semiclassically via the intranuclear cascade code. Our results for the asymmetry parameter in ${}_{\Lambda }^{12}$C obtained with different potential models are consistent with the asymmetry measured at KEK.

We study the predictions of three mean-field theoretical approaches in the description of the ground state properties of some spherical nuclei far from the stability line. We compare binding energies, single particle spectra, density distributions, charge and neutron radii obtained with nonrelativistic Hartree-Fock calculations carried out with both zero and finite-range interactions, and with a relativistic Hartree approach which uses a finite-range interaction. The agreement between the results obtained with the three different approaches indicates that these results are more related to the basic hypotheses of the mean-field approach rather than to its implementation in actual calculations.

Background: Analysis of data involving nuclei far from stability often requires the optical potential (OP) for neutron scattering. Because neutron data are seldom available, whereas proton scattering data are more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-${}^{208}$Pb system.

Purpose: The goal of this paper is to obtain accurate $n+{}^{208}\text{Pb}$ scattering data and use it, together with existing $p+{}^{208}\text{Pb}$ and ${}^{208}$Pb${(p,n)}^{208}$Bi${}_{\mathrm{IAS}}^{*}$ data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30–60-MeV range.

Method: Cross sections for $n+{}^{208}\text{Pb}$ scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2–4$\%$ (3$\%$). An angular range of 15${}^{\circ }$ to 130${}^{\circ }$ was covered using the beam-swinger time-of-flight system at Michigan State University. These data were analyzed by a consistent optical-model study of the neutron data and of elastic $p+{}^{208}\text{Pb}$ scattering at 45 and 54 MeV. These results were combined with a coupled-channel analysis of the ${}^{208}$Pb$(p,n)$ reaction at 45 MeV, exciting the 0${}^{+}$ isobaric analog state (IAS) in ${}^{208}$Bi.

Results: The new data and analysis give an accurate estimate of the isospin impurity of the nucleon-${}^{208}$Pb OP at 30.4 MeV caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics were found to be only a few percent, whereas for the imaginary potential it was greater than 20$\%$ at the nuclear surface. On the basis of the analysis of the measured elastic $n+{}^{208}\text{Pb}$ data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the $p+{}^{208}\text{Pb}$ OP at energies around 54 MeV.

Conclusions: Accurate neutron scattering data can be used in combination with proton scattering data and $(p,n)$ charge exchange data leading to the IAS to obtain reliable estimates of the isospin impurity of the nucleon OP.

The symmetry energy at sub- and supra-saturation densities has great importance for understanding the exact nature of asymmetric nuclear matter as well as neutron stars, but it is poorly known, especially at supra-saturation densities. We will demonstrate here whether or not the neutron-to-proton ratios from different kinds of fragments can determine the supra-saturation behavior of the symmetry energy. For this purpose, a series of Sn isotopes were simulated at different incident energies using the isospin quantum molecular dynamics (IQMD) model with either a soft or a stiff symmetry energy. It is found that the single neutron-to-proton ratio from free nucleons as well as Light Charged Particles (LCPs) is sensitive to the symmetry energy, incident energy, and isospin asymmetry of the system. However, with the double neutron-to-proton ratio, this is true only for the free nucleons. It is possible to study the high-density behavior of symmetry energy by using the neutron-to-proton ratio from free nucleons.

The projectile fragmentation reactions of ${}^{40}$Ar at 57 MeV/nucleon on ${}^9$Be and ${}^{181}$Ta targets have been studied by the Radioactive Ion Beam Line in Lanzhou (RIBLL) at the Heavy-Ion Research Facility in Lanzhou (HIRFL). The momentum distributions of fragments have been measured and the competition between different mechanisms are observed. The production cross sections have been obtained and compared with the empirical parametrization of fragmentation cross section (EPAX), abrasion-ablation (AA), and heavy-ion phase space exploration (HIPSE) models, and the target dependence of fragment cross sections has also been discussed.