Background: The study of the nuclear equation of state (EOS) and the behavior of nuclear matter under extreme conditions is crucial to our understanding of many nuclear and astrophysical phenomena. Nuclear reactions serve as one of the means for studying the EOS.

Purpose: It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities [A. B. Balantekin et al., Mod. Phys. Lett. A 29, 1430010 (2014)]. In practice, we focus on ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ fusion.

Method: We employ three different approaches to calculate fusion cross sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties.

Results: The folding-potential model provides a reasonable first estimate of cross sections. DC-TDHF, which includes dynamical polarization, reduces the fusion barriers and delivers much better cross sections. Full TDHF near the barrier agrees nicely with DC-TDHF. Most of the Skyrme forces which we used deliver, on the average, fusion cross sections in good agreement with the data. Trying to read off a trend in the results, we find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$ MeV that corresponds to a neutron-skin thickness of ${}^{48}\mathrm{Ca}$ of $R_{\mathrm{skin}}=(0.180–0.210)$ fm.

Conclusions: Fusion reactions in the barrier and sub-barrier region can be a tool to study the EOS and the neutron skin of nuclei. The success of the approach will depend on reduced experimental uncertainties of fusion data as well as the development of fusion theories that closely couple to the microscopic structure and dynamics.

The production of charmonium in heavy ion collisions is investigated based on the Boltzmann-type transport model for charmonium evolution and the Langevin equation for charm quark evolution. Charmonium suppression and regeneration in both quark-gluon plasma (QGP) and hadron phase are considered. Charm quarks are far from thermalization, and regeneration of charmonium in QGP and hadron gas is negligible at the Super Proton Synchrotron (SPS) and the Facility for Antiproton and Ion Research (FAIR). At peripheral collisions, charmonium suppression with hadron gas explains the experimental data well. But at central collisions, additional suppression from deconfined matter (QGP) is necessary for the data. This means there should be QGP produced at central collisions, and no QGP produced at peripheral collisions at SPS energy. Predictions are also made at FAIR $\sqrt{s_{NN}}=7.7$ GeV Au+Au collisions.

We consider that most of the long-range forward-backward multiplicity (FB) correlations in high energy $A\text{−}A$ collisions are caused by the centrality fluctuation, and this phenomenon interferes with the measurement of the dynamical correlations greatly. We investigate the relationship between FB correlation strength and centrality by a Monte Carlo simulation and a derivation which are tested by A MultiPhases Transport (AMPT) model in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV. We compare the FB correlation strengths of AMPT model with the results of the derivation at $\sqrt{s_{\mathrm{NN}}}$ $=$ $7.7$ to 200 GeV. A comparison between the default AMPT model and string melting AMPT model with different partonic scattering sections is made. As a result, we consider that the FB correlation strengths may be dominated by the mixing of different centrality events, and the short-range correlation may be overwhelmed for the most central collisions.

In off-central heavy-ion collisions, quark-gluon plasma (QGP) is exposed to the strongest magnetic fields ever created in the universe. Because of the paramagnetic nature of the QGP at high temperatures, the spatially inhomogeneous magnetic field configuration exerts an anisotropic force density that competes with the pressure gradients resulting from purely geometric effects. In this paper, we simulate (3+1)-dimensional ideal hydrodynamics with external magnetic fields to estimate the effect of this force density on the anisotropic expansion of the QGP in collisions at the Relativistic Heavy Ion Collider and at the Large Hadron Collider (LHC). While negligible for quickly decaying magnetic fields, we find that long-lived fields generate a substantial force density that suppresses the momentum anisotropy of the plasma by up to $20\%$ at the LHC energy and also leaves its imprint on the elliptic flow $v_2$ of charged pions.

States in the $N=28$ nucleus ${}^{46}\mathrm{Ar}$ have been studied by a two-neutron transfer reaction at REX-ISOLDE (CERN). A beam of radioactive ${}^{44}\mathrm{Ar}$ at an energy of 2.16 AMeV and a tritium-loaded titanium target were used to populate ${}^{46}\mathrm{Ar}$ by the ${}^3\text{H}({}^{44}\mathrm{Ar},p)$ two-neutron transfer reaction. Protons emitted from the target were identified in the T-REX silicon detector array. The excitation energies of states in ${}^{46}\mathrm{Ar}$ have been reconstructed from the measured angles and energies of recoil protons. Angular distributions for three final states were measured and based on the shape of the differential cross section an excited state at 3695 keV was identified as $J^{\pi }=0^{+}$. The angular differential cross section for the population of different states are compared to calculations using a reaction model employing both sequential and direct transfer of two neutrons. Results are compared to shell-model calculations using state-of-the-art effective interactions.

The results of a study of the $\beta$ decays of three proton-rich nuclei with $T_z=-2$, namely ${}^{48}\mathrm{Fe},{}^{52}\mathrm{Ni}$, and ${}^{56}\mathrm{Zn}$, produced in an experiment carried out at GANIL, are reported. In all three cases we have extracted the half-lives and the total $\beta$-delayed proton emission branching ratios. We have measured the individual $\beta$-delayed protons and $\beta$-delayed $\gamma$ rays and the branching ratios of the corresponding levels. Decay schemes have been determined for the three nuclei, and new energy levels are identified in the daughter nuclei. Competition between $\beta$-delayed protons and $\gamma$ rays is observed in the de-excitation of the $T=2$ isobaric analog states in all three cases. Absolute Fermi and Gamow-Teller transition strengths have been determined. The mass excesses of the nuclei under study have been deduced. In addition, we discuss in detail the data analysis taking as a test case ${}^{56}\mathrm{Zn}$, where the exotic $\beta$-delayed $\gamma$-proton decay has been observed.

The appearance and disappearance of shells and subshells are determined using a previously introduced method of structural analysis. This work extends the approach and applies it to protons, in addition to neutrons, in an attempt to provide a more complete understanding of shell structure in nuclei. Experimental observables including the mean-square charge radius, as well as other spectroscopic and mass related quantities are analyzed for extrema. This analysis also uses differential observables among adjacent even-even nuclei to serve as the derivatives for these quantities of interest. Local extrema in these quantities indicate shell structure and the lack of local extrema indicate missing shell closures. The shell structure of low-mass nuclei is inconsistent likely as a consequence of the single-particle structure. Additionally, multiple shell features occurring in midshell regions are determined by combining information from two or more observables. Our results near stability complement previous observations further out.

The discovery of pulsars as heavy as 2 solar masses has led astrophysicists to rethink the core compositions of neutron stars, ruling out many models for the nuclear equations of state (EoS). We explore the hybrid stars that occur when hadronic matter is treated in a relativistic mean-field approximation and quark matter is modeled by three-flavor local and nonlocal Nambu–Jona-Lasinio (NJL) models with repulsive vector interactions. The NJL models typically yield equations of state that feature a first-order transition to quark matter. Assuming that the quark-hadron surface tension is high enough to disfavor mixed phases and restricting to EoSs that allow stars to reach 2 solar masses, we find that the appearance of the quark-matter core either destabilizes the star immediately (this is typical for nonlocal NJL models) or leads to a very short hybrid star branch in the mass-radius relation (this is typical for local NJL models). Using the constant-sound-speed parametrization we can see that the reason for the near absence of hybrid stars is that the transition pressure is fairly high and the transition is strongly first order.

Empirical formulas for the second inverse moment of the photoabsorption cross sections in nuclei are discussed by Orce [Phys. Rev. C 91, 064602 (2015)]. In this Comment I point out that the experimental values used are systematically too small in heavy nuclei by about 5–10% because of the neglection of the $E1$ strength below the neutron threshold. Furthermore, combining recently deduced values of the polarizability in heavy and total photoabsorption data in light nuclei, it is demonstrated that the mass number dependence of ${\sigma }_{-2}$ is sensitive to the volume and surface coefficients of the symmetry energy and parameters different to the ones chosen by Orce may be better suited.

I reply to the preceding Comment.

In this article we present an extension of our recent Rapid Communication [Phys. Rev. C 90, 051301(R) (2014)] where we calculate the nuclear matrix elements for neutrinoless double-$\beta$ decay of ${}^{76}\mathrm{Ge}$. For the calculations we use a novel method that has perfect convergence properties and allows one to obtain the nonclosure nuclear matrix elements for ${}^{76}\mathrm{Ge}$ with a 1% accuracy. We present a new way to calculate the optimal closure energy; using this energy with the closure approximation provides the most accurate closure nuclear matrix elements. In addition, we present a new analysis of the heavy-neutrino-exchange nuclear matrix elements, and we compare occupation probabilities and Gamow-Teller strength with experimental data.

Four-dimensional Langevin equations have been suggested for the dynamical simulation of neutron-induced fission at low and medium excitation energies. The mass distribution of the fission fragments, the neutron multiplicity, and the fission cross section for the thermal and fast neutron-induced fission of ${}^{233}\mathrm{U},{}^{235}\mathrm{U}$, and ${}^{238}\mathrm{U}$ is studied by considering energy dissipation of the compound nucleus through the fission using four-dimensional Langevin equations combined with a Monte Carlo simulation approach. The calculated results using this approach indicate reasonable agreement with available experimental data.

The parton-hadron string dynamics (PHSD) transport model is used to study the impact of the choice of initial degrees of freedom on the final hadronic and electromagnetic observables in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. We find that a nonperturbative system of massive gluons (scenario I) and a system dominated by quarks and antiquarks (scenario II) lead to different hadronic observables when imposing the same initial energy-momentum tensor $T_{\mu \nu }\left(x\right)$ just after the passage of the impinging nuclei. In case of the gluonic initial condition the formation of $s,\overline{s}$ pairs in the quark-gluon plasma (QGP) proceeds rather slowly, such that the antistrange quarks and accordingly the $K^{+}$ mesons do not achieve chemical equilibrium even in central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. Accordingly, the $K^{+}$ rapidity distribution is suppressed in the gluonic scenario, and is in conflict with the data from the BRAHMS Collaboration. The proton and antiproton rapidity distributions also disfavor scenario I. Furthermore, a clear suppression of direct photon and dilepton production is found for the pure gluonic initial conditions, which is not so clearly seen in the present photon and dilepton spectra from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV due to a large contribution from other channels. It is argued that dilepton spectra in the invariant mass range $1.2 <M<$ 3 GeV will provide a definitive answer once the background from correlated $D$-meson decays is subtracted experimentally.

The proton-capture reaction ${}^{26}\mathrm{Si}\left(\mathrm{p},\gamma \right){}^{27}\mathrm{P}$ was studied via Coulomb dissociation (CD) of ${}^{27}\mathrm{P}$ at an incident energy of about 500 MeV/u. The three lowest-lying resonances in ${}^{27}\mathrm{P}$ have been populated and their resonance strengths have been measured. In addition, a nonresonant direct-capture component was clearly identified and its astrophysical $S$ factor measured. The experimental results are compared to Monte Carlo simulations of the CD process using a semiclassical model. Our thermonuclear reaction rates show good agreement with the rates from a recent compilation. With respect to the nuclear structure of ${}^{27}\mathrm{P}$ we have found evidence for a negative-parity intruder state at 2.88-MeV excitation energy.

Three-dimensional cutoff regulators are frequently employed in multinucleon calculations, but they violate chiral symmetry and Lorentz invariance. A cutoff regularization scheme is proposed to compensate systematically at subleading orders for these symmetry violations caused by regulator artifacts. This is especially helpful when a soft momentum cutoff has to be used for technical reasons. It is also shown that dimensional regularization can still be used for some Feynman (sub)diagrams while cutoff regulators are used for the rest.

The sensitivity of nuclear symmetry energy elements at the saturation density to the binding energies of ultra-neutron-rich nuclei (neutron-to-proton ratio $\sim 2$) and the maximum mass of a neutron star is explored within a relativistic mean field model. Values of the interaction parameters governing the isovector strengths and the symmetry elements are determined in tighter bounds. Assessments based on the sensitivity matrix reveal that the properties of extreme neutron-rich systems play a predominant role in narrowing down the uncertainties in the various symmetry energy parameters. The calculations are extended over a wide range of nuclear matter density, and the results are discussed.

The influence of the medium polarization on the effective nuclear interaction of asymmetric nuclear matter is calculated in the framework of the induced interaction theory. The strong isospin dependence of the density and spin-density fluctuations is studied as it is driven by the interplay between the neutron and proton medium polarizations. Going from symmetric nuclear matter to pure neutron matter, the crossover of the induced interaction from attractive to repulsive in the spin-singlet state is determined as a function of the isospin imbalance. The density range in which the crossover occurs is also determined. For the spin-triplet state the induced interaction turns out to be always repulsive. The implications of the results for neutron star superfluid phases are briefly discussed.

The $\gamma$ decay from the high-lying states of ${}^{140}\mathrm{Ce}$ excited via inelastic scattering of ${}^{17}\mathrm{O}$ at a bombarding energy of 340 MeV was measured using the high-resolution AGATA-demonstrator array in coincidence with scattered ions detected in two segmented $\mathrm{\Delta }E-E$ silicon detectors. Angular distributions of scattered ions and emitted $\gamma$ rays were measured, as well as their differential cross sections. The excitation of $1^{-}$ states below the neutron separation energy is similar to the one obtained in reactions with the $\alpha$ isoscalar probe. The comparison between the experimental differential cross sections and the corresponding predictions using the distorted-wave Born approximation allowed us to extract the isoscalar component of identified $1^{-}$ pygmy states. For this analysis the form factor obtained by folding microscopically calculated transition densities and optical potentials was used.

We study the convergence of bound-state quadrupole moments in finite harmonic oscillator spaces. We derive an expression for the infrared extrapolation for the quadrupole moment of a nucleus and benchmark our results using different model interactions for the deuteron. We find good agreement between the analytically derived and numerically obtained convergence behavior. We also derive an extrapolation formula for electric quadrupole transitions and find good agreement with the numerical calculation of a simple system.

We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to ${}^{132}\mathrm{Sn}$ converge fast for the ground-state energies and radii in feasible model spaces.