We employ recently published cross sections for $D$ mesons with hadrons and calculate the drag and diffusion coefficients of $D$ mesons in hadronic matter as a function of the momentum of $D$ mesons as well as of the temperature of the medium. Calculating in our approach the spatial diffusion coefficient, $D_x$, at zero chemical potential we see a very smooth transition between our calculations for the hadron gas and the lattice QCD calculations. Applying the results for the transport coefficients of $D$ mesons in a Fokker-Planck equation, which describes the evolution of $D$ mesons during the expansion of a hadron gas created in ultrarelativistic heavy-ion collisions, we find that the value of $R_{AA}$ is little influenced by hadronic rescattering, whereas in the elliptic flow the effects are stronger. We extend our calculations to the finite chemical potentials and calculate the spatial diffusion coefficients of $D$ mesons propagating through the hadronic medium following isentropic trajectories, appropriate at future FAIR (Facility for Antiproton and Ion Research, Darmstadt) and NICA (Nuclotron-Based Ion Collider Facility, Dubna) heavy-ion experiments. For the isentropic trajectory with $s/{\rho }_B^{\mathrm{net}}=20$ we find a perfect matching of results for $D$ mesons in hadronic matter and for charm quarks in partonic matter treated within the dynamical quasiparticle model approach.

We present a study of in-medium cross sections and (off-shell) transition rates for the most relevant binary reactions for strange pseudoscalar meson production close to threshold in heavy-ion collisions at energies available at the Facility for Antiproton and Ion Research. Our results rely on a chiral unitary approach in coupled channels which incorporates the $s$ and $p$ waves of the kaon-nucleon interaction. The formalism, which is modified in the hot and dense medium to account for Pauli blocking effects, mean-field binding on baryons, and pion and kaon self-energies, has been improved to implement unitarization and self-consistency for both the $s$- and the $p$-wave interactions at finite temperature and density. This gives access to in-medium amplitudes in several elastic and inelastic coupled channels with strangeness content $S=-1$. The obtained total cross sections mostly reflect the fate of the $\Lambda \left(1405\right)$ resonance, which melts in the nuclear environment, whereas the off-shell transition probabilities are also sensitive to the in-medium properties of the hyperons excited in the $p$-wave amplitudes $[\Lambda ,\Sigma$, and ${\Sigma }^{*}\left(1385\right)]$. The single-particle potentials of these hyperons at finite momentum, density, and temperature are also discussed in connection with the pertinent scattering amplitudes. Our results are the basis for future implementations in microscopic transport approaches accounting for off-shell dynamics of strangeness production in nucleus-nucleus collisions.

Background: The neutron emission rates in thermal excited nuclei are conventionally described by statistical models with a phenomenological level density parameter that depends on excitation energies, deformations, and mass regions. In the microscopic view of hot nuclei, the neutron emission rates can be determined by the external neutron gas densities without any free parameters. Therefore a microscopic description of thermal neutron emissions is desirable that can aid in understanding such properties as the survival probabilities of superheavy compound nuclei and neutron emissivity in reactors.

Purpose: To describe neutron emission rates in deformed compound nuclei, the external thermal neutron gases are self-consistently obtained based on the finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) approach.

Methods: The Skyrme FT-HFB equation is solved by the HFB-AX solver in deformed coordinate spaces. Based on the FT-HFB approach, the thermal properties and external neutron gases are properly described with the self-consistent gas substraction procedure. Then neutron emission rates can be obtained with the densities of external neutron gases. The results are compared with the statistical model to explore the connections between the FT-HFB approach and the statistical model.

Results: The thermal statistical properties of ${}^{238}\mathrm{U}$ and ${}^{258}\mathrm{U}$ are studied in detail in terms of excitation energies. The thermal neutron emission rates in ${}^{238,258}\mathrm{U}$ and superheavy compound nuclei ${}_{112}{}^{278}\mathrm{Cn}$ and ${}_{114}{}^{292}\mathrm{Fl}$ are calculated, which agree well with the statistical model by adopting variables from FT-HFB.

Conclusions: The coordinate-space FT-HFB approach can provide reliable microscopic descriptions of neutron emission rates in hot nuclei, as well as microscopic constraints on the excitation energy dependence of level density parameters for statistical models.

From empirically determined values of some of the characteristic constants associated with homogeneous nuclear matter at saturation and subsaturation densities, within the framework of a Skyrme-inspired energy density functional, we construct an equation of state (EoS) of nuclear matter. This EoS is then used to predict values of density slope parameters of symmetry energy $L\left(\rho \right)$, isoscalar incompressibility $K\left(\rho \right)$, and a few related quantities. The close consonance of our predicted values with the currently available ones for the density dependence of symmetry energy and incompressibility gleaned from diverse approaches offers the possibility that our method may help in settling their values in tighter bounds. Extrapolation of our EoS at supranormal densities shows that it is in good harmony with the one extracted from experimental data.

Within the two-center shell model parameterization we defined the optimal shape that fissioning nuclei attain just before the scission and calculated the total deformation energy (liquid-drop part plus the shell correction) as a function of the mass asymmetry and elongation at the scission point. The three minima corresponding to one mass-symmetric and two mass-asymmetric peaks in the mass distribution of fission fragments are found in the deformation energy at the scission point. The calculated deformation energy is used in a quasistatic approximation for the estimation of the total kinetic and excitation energies of fission fragments and the total number of emitted prompt neutrons. The calculated results reproduce rather well the experimental data on the position of the peaks in the mass distribution of fission fragments, and the total kinetic and excitation energies of fission fragments. The calculated value of neutron multiplicity is somewhat larger than experimental results.

We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at ${\sqrt{s}}_{NN}=2.76$ TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of posthadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the urqmd model, we are able to obtain a significant improvement in the statistical model fit quality and to reconstruct the primordial chemical equilibrium configuration. This is characterized by a nearly constant temperature of about 164 MeV, which we interpret as the actual hadronization temperature.

We investigate the effects of next-to-next-to leading order (NNLO) chiral three-nucleon force (3NF) on nucleus-nucleus elastic scattering, using a standard prescription based on the Brueckner-Hartree-Fock method and the $g$-matrix folding model. The $g$-matrix calculated in nuclear matter from the next-to-next-to-next-to leading order $\left({\mathrm{N}}^3\text{LO}\right)$ chiral two-nucleon forces (2NF) is close to that from the Bonn-B 2NF. Since the Melbourne group has already developed a practical $g$-matrix interaction by localizing the nonlocal $g$-matrix calculated from the Bonn-B 2NF, as this first attempt we consider the effects of chiral 3NF by modifying the local Melbourne $g$ matrix according to the difference between the $g$ matrices of the chiral 2NF and 2NF+3NF. For nucleus-nucleus elastic scattering, the 3NF corrections make the folding potential less attractive and more absorptive. The latter effect is due to the enhanced tensor correlations in triplet channels. These changes reduce the differential cross section at middle and large angles and improve the agreement with the experimental data for ${}^{16}\mathrm{O}\text{−}{}^{16}\mathrm{O}$ scattering at 70 MeV/nucleon and ${}^{12}\mathrm{C}\text{−}{}^{12}\mathrm{C}$ scattering at 85 MeV/nucleon.

Background: The relativistic three-body problem has a long tradition in few-nucleon physics. Calculations of the triton binding energy based on the solution of the relativistic Faddeev equation, in general, lead to a weaker binding than the corresponding nonrelativistic calculation.

Purpose: In this work we solve for the three-body binding energy as well as the wave function and its momentum distribution. The effect of the different relativistic ingredients is studied in detail.

Method: Relativistic invariance is incorporated within the framework of Poincaré invariant quantum mechanics. The relativistic momentum-space Faddeev equation is formulated and directly solved in terms of momentum vectors without employing a partial-wave decomposition.

Results: The relativistic calculation gives a three-body binding energy which is about 3% smaller than its nonrelativistic counterpart. In the wave function, relativistic effects are manifested in the Fermi motion of the spectator particle.

Conclusions: Our calculations show that though the overall relativistic effects in the three-body bound state are small, individual effects by themselves are not necessarily small and must be taken into account consistently.

Inelastic ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ scattering at $E_{\mathrm{lab}}=250,350,704,\mathrm{and}1120\mathrm{MeV}$ for the transitions to the lowest $2^{+}$ and $3^{-}$ states in the ${}^{16}\mathrm{O}$ nucleus have been analyzed within the coupled-channels mechanism by using the semimicroscopic optical potential and inelastic form factor given by the phenomenological squared Woods-Saxon potential, the full cluster potential, and the M3Y $NN$ effective interaction without density dependence. The obtained real potentials, in conjunction with the phenomenological squared Woods-Saxon imaginary potential, provide a satisfactory agreement with the experimental data for the elastic- and inelastic-scattering angular distributions. The deformation length and the intrinsic quadrupole $\left(Q_{20}\right)$ and octupole $\left(Q_{30}\right)$ moment values were extracted and were compared with the electromagnetic measurement values and those obtained from previous studies.

We present the analysis of the inclusive $K^0$ production in $p+p$ and $p+\mathrm{Nb}$ collisions measured with the HADES detector (GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt) at a beam kinetic energy of 3.5 GeV. Data are compared to the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport model. The data suggest the presence of a repulsive momentum-dependent kaon potential as predicted by the chiral perturbation theory (ChPT). For the kaon at rest and at normal nuclear density, the ChPT potential amounts to $\approx 35$ MeV. A detailed tuning of the kaon production cross sections implemented in the model has been carried out to reproduce the experimental data measured in $p+p$ collisions. The uncertainties in the parameters of the model were examined with respect to the sensitivity of the experimental results from $p+\mathrm{Nb}$ collisions to the in-medium kaon potential.

Within a multichannel formulation of $\pi \pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolve scattering observables from lattice QCD spectra. The asymptotic matching of the well-known Lüscher formalism encodes a unique finite-volume spectrum. Nevertheless, in many practical situations, such as coupled-channels systems, it is advantageous to interpolate isolated lattice spectra in order to extract physical scattering parameters. Here we study the use of the Hamiltonian framework as a parametrization that can be fit directly to lattice spectra. We find that, with a modest amount of lattice data, the scattering parameters can be reproduced rather well, with only a minor degree of model dependence.

The rotational symmetry is broken in mean-field models. The symmetry breaking may lead to significant effects even on the ground states of nuclei. The recent observations of enhanced collectivities in neutron-rich Fe and Cr isotopes are challenging the current calculations of mean-field models. By performing angular-momentum projection on mean-field potential energy surface (PES), we can obtain an angular-momentum-conserved PES at each given spin. With the projected PES, we have investigated the collectivity of neutron-rich Fe and Cr isotopes. The calculations reproduce well the excitation energies and electric quadrupole transitions of the collective excited states of the isotopes, indicating the importance of the restoration of the rotational symmetry.

Measurement of a resonance's integrated cross section using nuclear resonance fluorescence can be a valuable tool for verifying the properties of the resonance because of the clear and unambiguous physical connection to the spin, lifetime, and ground state branching ratio of the level. We demonstrate this idea by measuring the integrated cross section of the 3.004-MeV level in ${}^{27}\mathrm{Al}$ to 4% using the monoenergetic $\gamma$-ray beam at the High Intensity $\gamma$-ray Source. That level was the subject of much debate experimentally in the 1960s, especially its spin, and even now only has a current tentative spin assignment of $J=(9/2)$. The consistency check between this integrated cross section and the known properties of the level indicate that one (or more) of the literature properties is incorrect. Based on the range of extent of each property, a reassignment of spin to a tentative $J=(7/2)$ may be warranted, but this would need to be confirmed with other measurements. This result demonstrates the utility of NRF as a way to verify the properties of states in the literature before undertaking more extensive measurements.

The $\Lambda p\to \Lambda p{\pi }^0$ reaction near threshold is studied within an effective Lagrangian method. The production process is described by single-pion and single-kaon exchange. In addition to the role played by the ${\Sigma }^{*}\left(1385\right)$ resonance of spin-parity $J^P=3/2^{+}$, the effects of a newly proposed ${\Sigma }^{*}$ $\left(J^P=1/2^{-}\right)$ state with mass and width around 1380 MeV and 120 MeV are investigated. We show that our model leads to a good description of the experimental data on the total cross section of the $\Lambda p\to \Lambda p{\pi }^0$ reaction by including the contributions from the possible ${\Sigma }^{*}\left({\frac{1}{2}}^{-}\right)$ state. However, the theoretical calculations by considering only the ${\Sigma }^{*}\left(1385\right)$ resonance fail to reproduce the experimental data, especially for the enhancement close to the reaction threshold. On the other hand, it is found that the single-pion exchange is dominant. Furthermore, we also demonstrate that the angular distributions provide direct information of this reaction, hence could be useful for the investigation of the existence of the ${\Sigma }^{*}\left({\frac{1}{2}}^{-}\right)$ state and may be tested by future experiments.

Background: Excitations with mixed proton-neutron symmetry have been previously observed in the $N=52$ isotones. Besides the well-established quadrupole mixed-symmetry states (MSS), octupole and hexadecapole MSS have been recently proposed for the nuclei ${}^{92}\mathrm{Zr}$ and ${}^{94}\mathrm{Mo}$.

Purpose: The heaviest stable $N=52$ isotone ${}^{96}\mathrm{Ru}$ was investigated to study the evolution of octupole and hexadecapole MSS with increasing proton number.

Methods: Two inelastic proton-scattering experiments on ${}^{96}\mathrm{Ru}$ were performed to extract branching ratios, multipole mixing ratios, and level lifetimes. From the combined data, absolute transition strengths were calculated.

Results: Strong $M1$ transitions between the lowest-lying $3^{-}$ and $4^{+}$ states were observed, providing evidence for a one-phonon mixed-symmetry character of the $3_2^{(-)}$ and $4_2^{+}$ states.

Conclusions: $sdg$-IBM-2 calculations were performed for ${}^{96}\mathrm{Ru}$. The results are in excellent agreement with the experimental data, pointing out a one-phonon hexadecapole mixed-symmetry character of the $4_2^{+}$ state. The $\langle 3_1^{-}\left|\right|M1\left|\right|3_2^{(-)}\rangle$ matrix element is found to scale with the $\langle 2_{\mathrm{s}}^{+}\left|\right|M1\left|\right|2_{\mathrm{ms}}^{+}\rangle$ matrix element.

In the framework of a generalized liquid drop model (GLDM), a quasimolecular mechanism is introduced to describe the deformation of a nucleus in the procedure of nuclear fission or fusion. In order to more appropriately evaluate the shell correction on the fission or fusion path, the quasimolecular shape is described in terms of deformation parameters $\beta$ (i.e., so-called $\beta$ parameterized) by a transformation. For symmetric fission it is done analytically, whereas for asymmetric fission it is performed in a pure numerical way. Thereafter, for each quasimolecular shape, the shell correction can be calculated by the Strutinsky method where the single-particle energies are derived from a shell model in an axially deformed Woods–Saxon potential with the $\beta$-parameterized quasimolecular shape. We then use this recipe to predict the half-lives of several spontaneous fission channels for some heavy nuclei, and the results are in agreement with the experimental data.

We generalize the recently developed differential equation model for the reduced quadrupole transition probability $B\left(E2\right)\uparrow$ to include the corresponding excitation energy $E2$ for the transition from the ground state to the first $2^{+}$ state of a given even-even nucleus. Accordingly both these quantities of a given nucleus can satisfy a common differential equation, in which both of them individually can be expressed in terms of their derivatives with respect to the neutron and proton numbers. We use this equation to obtain two recursion relations in both of them connecting in each case three neighboring even-even nuclei from lower- to higher-mass numbers and vice versa. Then we demonstrate their numerical validity using the available $E2$ data throughout the nuclear chart and also explore their possible utility in predicting the unknown $E2$ values. Finally we apply the model to analyze ‘‘the $B\left(E2\right)$ problem in ${}^{46}\mathrm{Ar}$,” which refers to the recent experimental observation of a large $B\left(E2\right)$ value contradicting its prevailing value.

We investigate a novel method of accurate calculation of the neutrinoless double-$\beta$ decay shell-model nuclear matrix elements for the experimentally relevant case of ${}^{76}\mathrm{Ge}$. We demonstrate that with the new method the nuclear matrix elements have perfect convergence properties and, using only the first 100 intermediate states of each spin, the matrix elements can be calculated with better than 1% accuracy. Based on the analysis of neutrinoless double-$\beta$ decays of ${}^{48}\mathrm{Ca},{}^{82}\mathrm{Se}$, and ${}^{76}\mathrm{Ge}$ isotopes, we propose a new method to estimate the optimal values of the average closure energies at which the closure approximation gives the most accurate nuclear matrix elements. We also analyze the nuclear matrix elements for the heavy-neutrino-exchange mechanism, and we show that our method can be used to quench contributions from different intermediate spin states.