Within the framework of the dinuclear system model, the evaporation residue (ER) cross sections of superheavy nuclei in ${}^{48}\mathrm{Ca}$-induced hot fusion reactions with different entrance orientations are investigated. The production cross sections are obtained by calculating the average ER cross sections for different orientations of deformed colliding nuclei. The average results are in good agreement with the experimental data. The orientation effects on ER cross sections are investigated through studying the orientation dependence of the capture cross sections and the fusion probability. It is found that the fusion probabilities with the polar orientation of the target are higher than those with the equatorial orientation at lower incident energies, while the opposite behavior can be seen at high incident energy regions. The production cross sections for synthesizing $Z=119$ and 120 by fusion reactions of ${}^{48}\mathrm{Ca}$ with actinide targets are predicted.

A paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) model is presented, which employs the same method to calculate the liquid-drop energy and moment of inertia as the unpaired cranked Nilsson-Strutinsky (CNS) model. In the CNSB model, the energy minimization is carried out in the mesh of pairing gaps $\Delta$ and Fermi levels $\lambda$ as well as deformation parameters. The high spin states in ${}^{161}\mathrm{Lu}$ are then investigated with the CNSB and CNS models. The terminating structure shows a striking similarity with these two models. Combining the CNSB and CNS models, a complete understanding of high spin structures, including the normal deformed (ND) and triaxial strongly deformed (TSD) bands and observed side bands in ${}^{161}\mathrm{Lu}$, is achieved. It appears that the only important paired crossings are the first $i_{13/2}$ neutron crossing and the first $h_{11/2}$ proton crossing. For the description of the unpaired high spin crossings, it is important to be able to distinguish between the pseudospin partners in the proton $\mathcal{N}=4$ shell, $(d_{5/2}$,$g_{7/2}$) and $(d_{3/2}$,$s_{1/2}$). The yrast bands are predicted to terminate, which explains the structure of a TSD-like band X2. A band crossing at $I\approx 36.5$ for the TSD band in ${}^{161}\mathrm{Lu}$, unique within the chain of even-$N$ Lu isotopes, is well described by the CNSB model.

The magnetic dipole moments and changes in mean-square charge radii of the neutron-rich ${}^{218m,219,229,231}\mathrm{Fr}$ isotopes were measured with the newly installed Collinear Resonance Ionization Spectroscopy (CRIS) beam line at the On-Line Isotope Mass Separator (ISOLDE), CERN, probing the $7s^2{S}_{1/2}$ to $8p^2{P}_{3/2}$ atomic transition. The $\delta {\langle r^2\rangle }^{A,221}$ values for ${}^{218m,219}\mathrm{Fr}$ and ${}^{229,231}\mathrm{Fr}$ follow the observed increasing slope of the charge radii beyond $N=126$. The charge radii odd-even staggering in this neutron-rich region is discussed, showing that ${}^{220}\mathrm{Fr}$ has a weakly inverted odd-even staggering while ${}^{228}\mathrm{Fr}$ has normal staggering. This suggests that both isotopes reside at the borders of a region of inverted staggering, which has been associated with reflection-asymmetric shapes. The $g{(}^{219}\mathrm{Fr})=+0.69\left(1\right)$ value supports a $\pi 1h_{9/2}$ shell-model configuration for the ground state. The $g{(}^{229,231}\mathrm{Fr})$ values support the tentative $I^{\pi }{(}^{229,231}\mathrm{Fr})=(1/2^{+})$ spin and point to a $\pi s_{1/2}^{-1}$ intruder ground-state configuration.

A new intense superthermal source for ultracold neutrons (UCN) was installed at a dedicated beam line at the Institut Laue-Langevin. Incident neutrons with a wavelength of 0.89 nm are converted to UCN in a 5-liter volume filled with superfluid ${}^4\mathrm{He}$ at a temperature of about 0.7 K. The UCN can be extracted to room temperature experiments. We present the cryogenic setup of the source, a characterization of the cold neutron beam, and UCN production measurements, where a UCN density in the production volume of at least 55 per ${\mathrm{cm}}^3$ was determined.

The polarization observables for elastic 400 and 700 MeV deuteron scattering from ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ nuclei have been analyzed in the framework of the multiple diffraction scattering theory and the $\alpha$-cluster model with dispersion. The rigid projectile approximation with “effective” $d$-$\alpha$ scattering amplitude as well as the three-body $n+p+A$ model, which uses nucleon-$A$ scattering amplitudes and the deuteron ground-state wave function with both $S$ and $D$ waves, are applied for the calculations. Both approaches are compared with each other and with the available experimental data.

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasiparticles (qp's). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qp's. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the projected shell model is expanded to include 6-qp states for both positive and negative parities. Taking ${}^{166}\mathrm{Hf}$ as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I\approx 34\hslash$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in ${}^{176}\mathrm{Hf}$ are analyzed as another example.

The nuclear level density, an important input to Hauser-Feshbach calculations, depends not only on excitation energy but also on angular momentum $J$. The $J$ dependence of the level density at fixed excitation energy $E_x$ is usually parametrized via the spin-cutoff factor $\sigma$. We carefully test the statistical accuracy of this parametrization for a large number of spectra computed using semirealistic interactions in the interacting shell model, with a nonlinear least-squares fit of $\sigma$ and finding the error bar in $\sigma$. The spin-cutoff parametrization works well as long as there are enough states to be statistical. In turn, the spin-cutoff factor can be related to the average value of $J^2$ at a fixed excitation energy, and we briefly investigate extracting $\langle {\widehat{J}}^2\left(E_x\right)\rangle$ from a thermal calculation such as one might do via a Monte Carlo method.

Within an isospin- and momentum-dependent transport model (IBUU11) using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study the influence of the uncertainty of the neutron skin thickness on the ${\pi }^{-}/{\pi }^{+}$ ratio in both central and peripheral Pb + Pb collisions at beam energies of 400 MeV/nucleon and 1000 MeV/nucleon. Within the current experimental uncertainty range of neutron skin in ${}^{208}\mathrm{Pb}$, while the neutron skin effect on the ${\pi }^{-}/{\pi }^{+}$ ratio is negligible in central reactions at both energies, it increases gradually with increasing impact parameter and becomes comparable with or even larger than the symmetry energy effect in peripheral collisions especially at 400 MeV/nucleon. Moreover, we find that while the ${\pi }^{-}/{\pi }^{+}$ ratio is larger with a softer $E_{\mathrm{sym}}\left(\rho \right)$ in central collisions, above certain impact parameters depending on the size of the neutron skin, a stiffer $E_{\mathrm{sym}}\left(\rho \right)$ can lead to a larger ${\pi }^{-}/{\pi }^{+}$ ratio as most of the pions are produced at densities below the saturation density in these peripheral reactions. Therefore, a clear impact parameter selection is important to extract reliable information about the $E_{\mathrm{sym}}\left(\rho \right)$ at suprasaturation densities (size of neutron skin) from the ${\pi }^{-}/{\pi }^{+}$ ratio in central (peripheral) heavy-ion collisions.

A chemical nonequilibrium version of the statistical hadronization model combined with a single-freeze-out scenario is used to analyze the transverse-momentum spectra of pions, kaons, and protons produced in heavy-ion collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. With the statistical parameters found in earlier studies of hadronic ratios and two new geometric parameters determined by the absolute normalization and slopes of the spectra, we obtain a very good agreement between the data and the model predictions. In particular, the enhancement of pions observed at the very low transverse momenta is very well reproduced. In the chemical nonequilibrium approach, this effect may be naturally interpreted as the onset of pion condensation in heavy-ion collisions. We further stress that the chemical nonequilibrium explains not only the proton yield but the proton spectra up to $p_T=$ 3 GeV/$c$ as well.

Background: In our previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014)] we have calculated the capture (fusion) excitation functions for several reactions with ${}^{16}\mathrm{O},{}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$ nuclei as the projectiles and ${}^{92}\mathrm{Zr},{}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ nuclei as the targets. These calculations were performed by using our fluctuation-dissipation trajectory model based on the double-folding approach with the density-dependent M3Y NN forces that include the finite range exchange part. For the nuclear matter density the Hartree-Fock approach with the SKP coefficient set that includes the tensor interaction was applied. It was found that for most of the reactions induced by ${}^{16}\mathrm{O}$ the calculated cross sections cannot be brought into agreement with the data. This suggested that the deviation in the calculated nuclear density for ${}^{16}\mathrm{O}$ from the experimental one was crucial.

Method: The SKX parameter set is used to obtain the nuclear densities. Reactions with ${}^{12}\mathrm{C}$ and ${}^{36}\mathrm{S}$ as the projectiles and ${}^{204}\mathrm{Pb}$ as the target are included in the analysis in addition to those of the previous paper. Only data that correspond to the collision energy $E_{\mathrm{c}.\mathrm{m}.}>1.1U_{B0}$ $(U_{B0}$ is the $s$-wave fusion barrier height) are included in the analysis. The radial friction strength $K_R$ is used as the individual adjustable parameter for each reaction.

Results: For all 13 reactions (91 points) it is possible to reach an agreement with the experimental fusion cross sections within 10%. Only at ten points does the deviation exceed 5%. The value of $K_R$, which provides the best agreement with the data in general, decreases as the system gets heavier in accord with the previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014)]. A universal analytical approximation for the dependence of $K_R$ upon the Coulomb barrier height is found.

Conclusions: The developed model is able to reproduce the above-barrier portion of the fusion excitation function within 5% with a probability of 90%. Only one fitting parameter per excitation function $K_R$ is used. The model can be used to predict the results of relevant measurements. The universal analytical approximation of the $K_R$ dependence upon the Coulomb barrier height helps to find the starting value of $K_R$ for a more accurate description.

We investigate selected static and transition properties of ${}^{12}\mathrm{C}$ using ab initio no-core shell model (NCSM) methods with chiral two- and three-nucleon interactions. We adopt the similarity renormalization group (SRG) to assist convergence including up to three-nucleon ($3N$) contributions. We examine the dependencies of the ${}^{12}$C observables on the SRG evolution scale and on the model-space parameters. We obtain nearly converged low-lying excitation spectra. We compare results of the full NCSM with the importance truncated NCSM in large model spaces for benchmarking purposes. We highlight the effects of the chiral $3N$ interaction on several spectroscopic observables. The agreement of some observables with experiment is improved significantly by the inclusion of $3N$ interactions, e.g., the $B\left(M1\right)$ from the first $J^{\pi }T=1^{+}1$ state to the ground state. However, in some cases the agreement deteriorates, e.g., for the excitation energy of the first $1^{+}0$ state, leaving room for improved next-generation chiral Hamiltonians.

General expressions for the breakup cross sections in the laboratory frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The $\mathcal{S}$ matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe $1+2$ processes, there are particular configurations in the breakup channel (for example, those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations.

A new measurement of the dynamical dipole emission was performed in the system ${}^{16}\mathrm{O}+{}^{116}\mathrm{Sn}$ at 12 MeV/nucleon. These data, together with those measured at 8.1 MeV/nucleon and 15.6 MeV/nucleon on the same system, provide the dependence of the dynamical dipole total emission yield on the beam energy. The energy removed by preequilibrium charged particles emission was directly measured and this made possible the direct estimation of the compound nucleus excitation energy. The experimental results show a weak increase of the dynamical dipole total yield with beam energy and they are in agreement both in trend and in absolute values with the predictions of the theoretical model based on the Boltzmann-Nordheim-Vlasov approach. The measured γ-ray angular distribution has a dipole character but with a strong quenching probably owing to the rotation of the dipolar axis during the fusion and thermalization processes.

Based on the nuclear equation of state, the curvature correction term to the surface tension coefficient is calculated. Tolman's $\delta$ correction is shown to be sensitive to the Skyrme force parametrization. The temperature dependence of the Tolman length, important in heavy ion collision experiments, is derived. In the present approach the curvature term is related to the bulk properties of the nuclear matter through the equation of state. The results are compared with the existing theoretical calculations based on the Gibbs-Tolman formalism and with the theoretical predictions concerning its dependence on the interparticle distance.

Background: On the mean-field level, pairing correlations are incorporated through the Bogoliubov-Valatin transformation, whereby the particle degrees of freedom are replaced by quasiparticles. This approach leads to a spontaneous breaking of the particle-number symmetry and mixing of states with different particle numbers. In order to restore the particle number, various methods have been employed, which are based on projection approaches before or after variation. Approximate variation-after-projection (VAP) schemes, utilizing the Lipkin method, have mostly been used within the Lipkin-Nogami prescription.

Purpose: Without employing the Lipkin-Nogami prescription, and using, instead, states rotated in the gauge space, we derive the Lipkin method of particle-number restoration up to sixth order and we test the convergence and accuracy of the obtained expansion.

Methods: We perform self-consistent calculations using the higher-order Lipkin method to restore the particle-number symmetry in the framework of superfluid nuclear energy-density functional theory. We also apply the Lipkin method to a schematic exactly solvable two-level pairing model.

Results: Calculations performed in open-shell tin and lead isotopes show that the Lipkin method converges at fourth order and satisfactorily reproduces the VAP ground-state energies and energy kernels. Near closed shells, the higher-order Lipkin method cannot be applied because of a nonanalytic kink in the ground-state energies as a function of the particle number.

Conclusions: In open-shell nuclei, the higher-order Lipkin method provides a good approximation to the exact VAP energies. The method is computationally inexpensive, making it particularly suitable, for example, for future optimizations of the nuclear energy density functionals and simultaneous restoration of different symmetries.

Excited states in ${}^{120}\mathrm{Sb}$ have been investigated using the ${}^{116}\mathrm{Cd}({}^7\mathrm{Li},3n){}^{120}\mathrm{Sb}$ reaction at a beam energy of 34 MeV. A total of 15 new $\gamma$ rays were added into the level scheme of ${}^{120}\mathrm{Sb}$. Most of the observed single-particle states can be interpreted in terms of weak coupling of the odd proton and odd neutron to an excited ${}^{118}\mathrm{Sn}$ core involving either vibrational states or broken neutron pairs. The previously known strongly coupled rotational band based on the $\pi g_{9/2}^{-1}\otimes \nu h_{11/2}$ configuration has been extended up to the ${(15}^{-})$ state. The configuration-fixed constrained triaxial relativistic mean-field approaches and the particle rotor model are employed to discuss the high-spin isomers and strongly coupled rotational band, respectively.

In the present work, we analyze the effects of an external magnetic field on the chiral critical temperature $T_c$ of strongly interacting matter. In doing this, we can characterize the magnetic properties of the quantum chromodynamics (QCD) strongly interacting matter, the quark-gluon plasma (QGP). We investigate this in the framework of the SU(3) Polyakov linear sigma model (PLSM). To this end, we implement two approaches representing two systems, in which the Polyakov-loop potential added to PLSM is either renormalized or non-normalized. The effects of Landau quantization on the strongly interacting matter are conjectured to reduce the electromagnetic interactions between quarks. In this case, the color interactions will be dominant and increasing, which in turn can be achieved by increasing the Polyakov-loop fields. Obviously, each of them equips us with a different understanding about the critical temperature under the effect of an external magnetic field. In both systems, we obtain a paramagnetic response. In one system, we find that $T_c$ increases with increasing magnetic field. In the other one, $T_c$ significantly decreases with increasing magnetic field.

A self-consistent calculation is performed within an equation of motion method to study the electric dipole response in the neutron rich ${}^{132}\mathrm{Sn}$ with special attention at the low-energy excitations associated with the pygmy dipole resonance. A basis of one- plus two-phonon states is constructed by solving iteratively a set of equations of motion and adopted to bring the nuclear Hamiltonian to diagonal form. The phonons are generated in a Tamm-Dancoff approximation using a Hartree-Fock basis. The Hamiltonian is composed of an intrinsic kinetic term and an optimized two-body chiral potential. If complemented with a weak phenomenological density dependent term, such a potential improves substantially the description of the dipole response as compared to other realistic interactions. The two-phonon states play an important role in determining the fine structure of the giant dipole resonance and in enhancing the fragmentation of the strength at low energy, in fair agreement with the available data. Insights into the nature of the excitations building up the pygmy resonance are gained from the analysis of the phonon composition and shell structure of the states.