The thermalization of the particles produced in collisions of small objects can be achieved by quantum entanglement of the partons of the initial state as was analyzed recently in proton-proton collisions. We extend such study to Pb-Pb collisions and to different multiplicities of proton-proton collisions. We observe that, in all cases, the effective temperature is approximately proportional to the hard scale of the collision. We show that such a relation between the thermalization temperature and the hard scale can be explained as a consequence of the clustering of the color sources. The fluctuations of the number of parton states decrease with multiplicity in Pb-Pb collisions as long as the width of the transverse-momentum distribution decreases, contrary to the $p\text{−}p$ case. We relate these fluctuations to the temperature fluctuations by means of a Langevin equation for the white stochastic noise. We show that the multiplicity parton distribution for events with at least one hard parton collision is a $\mathrm{\Gamma }$ distribution. We use this result to compute the entanglement entropy, showing that the leading term is the logarithm of the number of partons, meaning that the $n$ microstates are equally probable and the entropy is maximal. There is another contribution related to the inverse of the normalized parton number fluctuation, which at very high energy changes the behavior from $lnn$ to $ln\sqrt{n}$.

The lattice QCD analysis of the HAL QCD Collaboration has recently derived $\mathrm{\Omega }N$ and $\mathrm{\Omega }\mathrm{\Omega }$ interacting potentials with nearly physical quark masses ($m_{\pi }\simeq 146$ MeV and $m_K\simeq 525$ MeV). They found an attractive interaction in the $\mathrm{\Omega }N{}^{5}S_2$ channel which supports a bound state with a central binding energy of 1.54 MeV. The $\mathrm{\Omega }\mathrm{\Omega }{}^{1}S_0$ channel shows an overall attraction with a bound state with a central binding energy of 1.6 MeV. In this paper we looked closely at the $\mathrm{\Omega }\mathit{NN}$ and $\mathrm{\Omega }\mathrm{\Omega }N$ three-body systems making use of the latest HAL QCD Collaboration $\mathrm{\Omega }N$ and $\mathrm{\Omega }\mathrm{\Omega }$ interactions. Our results show that the $\mathrm{\Omega }d$ system in the state with maximal spin $\left(I\right)J^P=\left(0\right)5/2^{+}$ is bound with a binding energy of about 20 MeV. The $\left(I\right)J^P=\left(1\right)3/2^{+}\mathrm{\Omega }nn$ state presents a resonance decaying to $\mathrm{\Lambda }\mathrm{\Xi }n$ and $\mathrm{\Sigma }\mathrm{\Xi }n$, with a separation energy of $\sim 1$ MeV. The $\left(I\right)J^P=(1/2)1/2^{+}\mathrm{\Omega }\mathrm{\Omega }N$ state also exhibits a resonance decaying to $\mathrm{\Lambda }\mathrm{\Xi }\mathrm{\Omega }$ and $\mathrm{\Sigma }\mathrm{\Xi }\mathrm{\Omega }$ with a separation energy of $\sim 4.6$ MeV. We have calculated the contribution of the Coulomb potential to differentiate among the different charged states.

The canonical single-particle energies and wave functions are obtained by diagonalizing the density matrix on a spatial mesh in continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the exotic nucleus ${}^{66}\mathrm{Ca}$ as an illustrative example, the canonical energies and wave functions are compared with those obtained by the box-discretized method. Most of the results are consistent except for $s_{1/2}$ orbitals with positive energies, which have large spatial extension. By examining the canonical energies and wave functions with different box sizes, it is shown that the Green's function method can obtain the convergent canonical energy within a box size smaller than that of the box-discretized method, due to the correct asymptotic behaviors of the canonical wave functions.

The nature of low-lying $3^{-}$ levels in ${}^{144}\mathrm{Nd}$ was investigated in the ${}^{143}\mathrm{Nd}(n,\gamma \gamma )$ cold neutron-capture reaction. The combination of the high neutron flux from the research reactor at the Institut Laue-Langevin and the high $\gamma$-ray detection efficiency of the EXILL setup allowed the recording of $\gamma \gamma$ coincidences. From the coincidence data precise branching ratios were extracted. Furthermore, the octagonal symmetry of the setup allowed angular-distribution measurements to determine multipole-mixing ratios. Additionally, in a second measurement the ultra-high resolution spectrometer GAMS6 was employed to conduct lifetime measurements using the gamma-ray induced Doppler-shift technique (GRID). The confirmed strong $M1$ component in the $3_3^{-}\to 3_1^{-}$ decay strongly supports the assignment of the $3_3^{-}$ level at $2779\mathrm{keV}$ as low-lying isovector octupole excitation. Microscopic calculations within the quasiparticle phonon model confirm an isovector component in the wave function of the $3_3^{-}$ level, firmly establishing this fundamental mode of nuclear excitation in near-spherical nuclei.

The longitudinal quark spin polarization along the beam direction in noncentral relativistic heavy ion collisions is studied in the chiral kinetic approach. Its azimuthal angle dependence in the transverse plane of the collision is found to have a quadrupole structure as in studies from hydrodynamic and transport models based on the relativistic spin-vorticity coupling in a thermodynamically equilibrated hadronic matter at kinetic freeze-out. The direction of the quark longitudinal spin polarization is, however, opposite to that from these models, and this is due to the axial charge current induced by the transverse component of the vorticity field in the chiral kinetic approach. Our finding is consistent with the azimuthal angle dependence of the longitudinal spin polarization of $\mathrm{\Lambda }$ hyperons, which is mainly determined by that of the strange quark, recently measured in the experiments by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider.

The low-lying, low-spin levels of ${}^{76}\mathrm{Se}$ were studied with the $(n,n^{\prime }\gamma )$ reaction. Gamma-ray excitation function measurements were performed at incident neutron energies from 2.0 to 3.5 MeV, and $\gamma$-ray angular distributions were measured at neutron energies of 2.4, 3.0, and 3.7 MeV. From these measurements, level spins, level lifetimes, branching ratios, and multipole mixing ratios were determined. We established the $0_2^{+}$ band, which supports the shape coexistence in ${}^{76}\mathrm{Se}$ predicted by large-scale shell model calculations and the interacting boson model.

Background: Study of competition between compound nucleus fission and quasifission in heavy-ion-induced reactions and its dependence on the reaction entrance channel are important for picking up the right target-projectile combination for the synthesis of superheavy elements.

Purpose: We investigate the decrease of fusion probability in the ${}^{52}\mathrm{Cr}+{}^{232}\mathrm{Th}$ reaction in comparison with that in the reactions ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$ and ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$. All reactions lead to the formation of composite systems with $Z=114$.

Methods: Mass-energy distributions of binary fragments formed in the reaction ${}^{52}\mathrm{Cr}+{}^{232}\mathrm{Th}$ leading to the ${}^{284}\mathrm{Fl}$ composite system at energies of 265, 288, 302, and 320 MeV have been measured using the double-arm time-of-flight spectrometer CORSET. To study the properties and entrance channel dependence of quasifission in more detail, the mass and energy distributions of fragments formed in the ${}^{86}\mathrm{Kr}+{}^{198}\mathrm{Pt}$ reaction, leading to the same composite system ${}^{284}\mathrm{Fl}$, have also been measured.

Results: The contribution of symmetric fragments in all fissionlike events is nearly the same for both the reactions ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ and ${}^{52}\mathrm{Cr}+{}^{232}\mathrm{Th}$ at energies above the barrier, while it is greater for ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$. The analysis of total kinetic energy distribution of symmetric fragments formed in the reaction ${}^{52}\mathrm{Cr}+{}^{232}\mathrm{Th}$ shows that at an energy 15% over the Bass barrier the contribution of compound nucleus fission in the capture cross section is less than 0.4%.

Conclusions: The fusion probability drops down by about a factor of 4 at the transition from the ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$ reaction to ${}^{48}\mathrm{Ti}+{}^{238}\mathrm{U}$ and about a factor of 25 at the transition to ${}^{52}\mathrm{Cr}+{}^{232}\mathrm{Th}$ at energies above the barrier. It agrees with the trend of fusion probability to decrease exponentially with increasing the mean fissility parameter of the composite system.

Isomeric yield ratios for the odd-$A$ isotopes of ${}^{119–127}\mathrm{Cd}$ and ${}^{119–127}\mathrm{In}$ from 25-MeV proton-induced fission on natural uranium have been measured at the JYFLTRAP double Penning trap, by employing the phase-imaging ion-cyclotron-resonance technique. With the significantly improved mass resolution of this novel method isomeric states separated by 140 keV from the ground state, and with half-lives of the order of 500 ms, could be resolved. This opens the door for obtaining new information on low-lying isomers, which are important for nuclear structure, fission, and astrophysics. In the present work the experimental isomeric yield ratios are used for the estimation of the root-mean-square angular momentum $J_{\mathrm{rms}}$ of the primary fragments. The results show a dependency on the number of unpaired protons and neutrons, where the odd-$Z$ In isotopes carry larger angular momenta. The deduced values of $J_{\mathrm{rms}}$ display a linear relationship when compared with the electric quadrupole moments of the fission products.

The dynamics of induced fission of ${}^{226}\mathrm{Th}$ is investigated in a theoretical framework based on the finite-temperature time-dependent generator coordinate method (TDGCM) in the Gaussian overlap approximation (GOA). The thermodynamical collective potential and inertia tensor at temperatures in the interval $T=0–1.25$ MeV are calculated using the self-consistent multidimensionally constrained relativistic mean-field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Constrained RMF+BCS calculations are carried out in the collective space of axially symmetric quadrupole and octupole deformations for the asymmetric fissioning nucleus ${}^{226}\mathrm{Th}$. The collective Hamiltonian is determined by the temperature-dependent free energy surface and perturbative cranking inertia tensor, and the TDGCM+GOA is used to propagate the initial collective state in time. The resulting charge and mass fragment distributions are analyzed as functions of the internal excitation energy. The model can qualitatively reproduce the empirical triple-humped structure of the fission charge and mass distributions already at $T=0$, but the precise experimental position of the asymmetric peaks and the symmetric-fission yield can only be accurately reproduced when the potential and inertia tensor of the collective Hamiltonian are determined at finite temperature, in this particular case between $T=0.75$ MeV and $T=1$ MeV.

The ${}^3\mathrm{H}(d,n){}^4\mathrm{He}$ reaction has a large low-energy cross section and will likely be utilized in future commercial fusion reactors. This reaction also takes place during Big Bang nucleosynthesis. Studies of both scenarios require accurate and precise fusion rates. To this end, we implement a one-level, two-channel $R$-matrix approximation into a Bayesian model. Our main goals are to predict reliable astrophysical $S$-factors and to estimate $R$-matrix parameters using the Bayesian approach. All relevant parameters are sampled in our study, including the channel radii, boundary condition parameters, and data set normalization factors. In addition, we take uncertainties in both measured bombarding energies and $S$-factors rigorously into account. Thermonuclear rates and reactivities of the ${}^3\mathrm{H}(d,n){}^4\mathrm{He}$ reaction are derived by numerically integrating the Bayesian $S$-factor samples. The present reaction rate uncertainties at temperatures between 1.0 MK and 1.0 GK are in the range of 0.2% to 0.6%. Our reaction rates differ from previous results by 2.9% near 1.0 GK. Our reactivities are smaller than previous results, with a maximum deviation of 2.9% near a thermal energy of 4 keV. The present rate or reactivity uncertainties are more reliable compared to previous studies that did not include the channel radii, boundary condition parameters, and data set normalization factors in the fitting. Finally, we investigate previous claims of electron screening effects in the published ${}^3\mathrm{H}(d,n){}^4\mathrm{He}$ data. No such effects are evident and only an upper limit for the electron screening potential can be obtained.

The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an electron-ion collider. We introduce the mcdijet Monte Carlo generator to sample quark-antiquark dijet configurations based on leading-order parton level cross sections with WW gluon distributions that solve the nonlinear small-$x$ QCD evolution equations. These configurations are fragmented to hadrons using PYTHIA, and final-state jets are reconstructed. We report on background studies and on the effect of kinematic cuts introduced to remove beam jet remnants. We estimate that with an integrated luminosity of 20 ${\mathrm{fb}}^{-1}/\mathrm{nucleon}$ one can determine the distribution of linearly polarized gluons with a statistical accuracy of approximately 5%.

New data for the elastic scattering of ${}^9\mathrm{Be}$ from protons were obtained and analyzed together with data from the literature in a coherent coupled-reaction-channels approach. The new measurements were performed in inverse kinematics at 15, 22 and 51 MeV (1.67, 2.44, and 5.67 MeV/nucleon) by detecting the heavy ejectile in the MAGNEX spectrometer. This enabled an almost full angular distribution to be obtained, extending the results to forward angles where calculated values coincide and give the opportunity of proper normalization. Previous inconsistencies in absolute normalization between different data sets are removed. Standard collective model form factors fail to reproduce the inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$, suggesting that a more sophisticated approach based on the cluster structure of ${}^9\mathrm{Be}$ is required to describe this process.

The hot and dense matter generated in heavy-ion collisions contains intricate vortical structure in which the local fluid vorticity can be very large. Such vorticity can polarize the spin of the produced particles. We study the event-by-event generation of the so-called thermal vorticity in Au+Au collisions at energy region $\sqrt{s}=7.7–200$ GeV and calculate its time evolution, spatial distribution, etc., in a multiphase transport model. We then compute the spin polarization of the $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons as a function of $\sqrt{s}$, transverse momentum $p_T$, rapidity, and azimuthal angle. Furthermore, we study the harmonic flow of the spin, in a manner analogous to the harmonic flow of the particle number. The measurement of the spin harmonic flow may provide a way to probe the vortical structure in heavy-ion collisions. We also discuss the spin polarization of ${\mathrm{\Xi }}^0$ and ${\mathrm{\Omega }}^{-}$ hyperons, which may provide further information about the spin polarization mechanism of hadrons.

A comparative decay analysis of ${}^{80}\mathrm{Zr}^{*}$, ${}^{80}\mathrm{Sr}^{*}$, and ${}^{80}\mathrm{Kr}^{*}$ isobaric nuclear systems formed in ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$, ${}^{16}\mathrm{O}+{}^{64}\mathrm{Zn}$, and ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ reactions, respectively, has been conducted to investigate the $N/Z$ dependence of different decay modes within a dynamical cluster-decay model based on the collective clusterization approach of quantum mechanical fragmentation theory. The comparative contributions of the emission of light particles (LPs), intermediate mass fragments (IMFs), and symmetric mass fragments (SMFs) in the total fusion cross-sections, ${\sigma }_{\mathrm{fusion}}$, have been calculated. The results show that LPs have a major contribution to ${\sigma }_{\mathrm{fusion}}$ in the decay of all three compound nuclei (CN). The percentage contribution of LPs is larger for CN with higher $N/Z$ ratio. The IMFs and SMFs cross-section are comparatively low in the total ${\sigma }_{\mathrm{fusion}}$ but their emissions are in competition in the decay process. The results show that the shape of mass distribution evolves from symmetric to asymmetric with increasing $N/Z$ ratio. The yield around SMFs is greater for the system having the lowest $N/Z$ ratio. This may be attributed to higher $P_0$ for the symmetric exit channel, particularly at higher $\ell$ values. The calculated fusion cross-sections for all three CN are in good agreement with the experimental data.

Background: In recent years, there has been increasing interest in multinucleon transfer processes in low-energy deep inelastic (damped) collisions of heavy ions. Partly, it was provoked by a possibility of using them as a method of production of heavy neutron-enriched nuclei. Possible promising projectile-target combinations include nuclei deformed in the ground state (e.g., actinides). Mutual orientations of such nuclei in the entrance channel of a reaction may significantly influence the reaction dynamics.

Purpose: The major aim of the work is to implement a possibility of modeling collisions of statically deformed heavy nuclei within a multidimensional dynamical model based on the Langevin equations. Another purpose of the paper is to study the influence of mutual orientations of statically deformed nuclei on their collision dynamics. Finally, production yields of heavy transuranium nuclei in collisions of actinides are examined.

Method: An analysis has been performed within a multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations [Phys. Rev. C 96 024618 (2017)]. In the present paper, the model has been improved to describe collisions of statically deformed heavy nuclei with different mutual orientations.

Results: The available experimental data on multinucleon transfer reactions with statically deformed as well as spherical heavy nuclei ${}^{144}\mathrm{Sm}+{}^{144}\mathrm{Sm}$, ${}^{154}\mathrm{Sm}+{}^{154}\mathrm{Sm}$, ${}^{160}\mathrm{Gd}+{}^{186}\mathrm{W}$, and ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb},{}^{238}\mathrm{U}$ have been analyzed within the developed model. A good agreement of the calculated quantities with the corresponding experimental data has been reached. Special attention in the paper is paid to analyzing the possibility of producing neutron-enriched isotopes of heavy and superheavy elements in multinucleon transfer processes in ${}^{238}\mathrm{U}+{}^{238}\mathrm{U},{}^{248}\mathrm{Cm},{}^{254}\mathrm{Es}$ collisions.

Conclusions: Mutual orientation of colliding statically deformed nuclei in the entrance channel strongly affects the energy, angular, mass, and charge characteristics of multinucleon transfer reaction products at near-barrier energies. These orientational effects disappear with increasing collision energy well above the Coulomb barrier. An exponential drop in the isotopic distributions of the above-target products formed in the collisions of actinides with an increasing atomic number does not allow one to synthesize new isotopes of superheavy nuclei with experimentally reachable cross sections. However, there is a possibility to produce a number of neutron-enriched isotopes of heavy actinides with cross sections exceeding 1 $\mu \mathrm{b}$.

We compare anisotropic hydrodynamics (aHydro) results obtained using the relaxation-time approximation (RTA) and leading-order (LO) scalar $\lambda {\varphi }^4$ collisional kernels. We extend previous work by explicitly enforcing number conservation through the incorporation of a dynamical chemical potential (fugacity) in the underlying aHydro distribution function. We focus on the case of a transversally homogenous and boost-invariant system obeying classical statistics and compare the relevant moments of the two collisional kernels. We then compare the time evolution of the aHydro microscopic parameters and components of the energy-momentum tensor. We also determine the nonequilibrium attractor using both the RTA and LO massless $\lambda {\varphi }^4$ number-conserving kernels. We find that the aHydro dynamics receives quantitatively important corrections when enforcing number conservation; however, the aHydro attractor itself is not modified substantially.

The FOPI Collaboration at the GSI SIS-18 synchrotron measured charged kaons from central and semicentral collisions of Ni+Ni at a beam energy of $1.91A$ GeV. We present the distribution of the $K^{-}/K^{+}$ ratio on the energy vs polar angle plane in the nucleon-nucleon center-of-mass frame, with and without subtraction of the contribution of $\varphi \left(1020\right)$ meson decays to the $K^{-}$ yield. The acceptance of the current experiment is substantially wider compared to the previous measurement of the same colliding system. The ratio of $K^{-}$ to $K^{+}$ energy spectra is expected to be sensitive to the in-medium modifications of basic kaon properties like mass. Recent results obtained by the HADES Collaboration at $1.23A$ and $1.76A$ GeV indicate that after inclusion of the $\varphi$ meson decay contribution to the $K^{-}$ production no difference between the slopes of the $K^{-}$ and $K^{+}$ energy spectra is observed within uncertainties. For our data a linear fit to this ratio obtained after subtraction of the $\varphi$ meson contribution still shows a decrease with kinetic energy, although a constant value cannot be rejected. The contribution of $\mathrm{\Lambda }\left(1520\right)\to p{K}^{-}$ decays estimated from fitting the thermal model to the experimental yields appears to be another factor of moderate relevance.

The nuclear structure of the ${}^{76}\mathrm{Ni}$ nucleus was investigated by ($p,2p$) reaction using a NaI(Tl) array to detect the deexciting prompt $\gamma$ rays. A new transition with an energy of 2227 keV was identified by $\gamma \gamma$ and $\gamma \gamma \gamma$ coincidences. According to these coincidence spectra the observed transition connects a new state at 4147 keV and the previously known $4_1^{+}$ state at 1920 keV. Two weaker transitions were also obtained at 2441 and 2838 keV, which could be tentatively placed to feed the known $2_1^{+}$ state at 990 keV. Our shell-model calculations using the Lenzi, Nowacki, Poves, and Sieja interaction produced good candidates for the experimental proton hole states in the observed energy region, and the theoretical cross sections showed good agreement with the experimental values. Although we could not assign all the experimental states to the theoretical ones unambiguously, the results are consistent with a reasonably large $Z=28$ shell gap for nickel isotopes in accordance with previous studies.

The ${}^{59}\mathrm{Ni}(n,xp)$ reaction cross sections have been measured following the surrogate reaction ratio method in the equivalent neutron energy range of 11.9–15.8 MeV by populating the compound nucleus ${}^{60}\mathrm{Ni}^{*}$ through transfer reaction ${}^{56}\mathrm{Fe}({}^6\mathrm{Li},d)$ at $E_{\text{lab}}=35.9$ MeV. The ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha ){}^{61}\mathrm{Ni}^{*}$ transfer reaction at $E_{\text{lab}}=40.5$ MeV has been used as the reference reaction which is the surrogate of ${}^{60}\mathrm{Ni}(n,xp)$ reaction populating the compound nucleus ${}^{61}\mathrm{Ni}^{*}$. The proton decay probabilities have been determined by measuring evaporated protons at backward angles in coincidence with projectile like fragments (PLFs, either $d$ or $\alpha$) detected around grazing angles. The cross sections for the reference reaction ${}^{60}\mathrm{Ni}(n,xp)$ are taken from jendl-4.0 library, which closely reproduce the available experimental data. The cross sections for the desired ${}^{59}\mathrm{Ni}(n,xp)$ reaction so obtained compare well with the nuclear-reactions-model code talys-1.8 using microscopic level densities. The present experimental data are consistent with the evaluated data library of rosfond-2015 but not with tendl-2015 and endf/b-viii, indicating the need of new evaluations for this reaction of importance to fusion technology.

The ${}^7\mathrm{Be}(n,p)$ cross section was measured with an ion-implanted ${}^7\mathrm{Be}$ target at a thermal neutron beam of the research reactor LVR-15 in Řež. The cross section to the ground state of ${}^7\mathrm{Li}$ is $\sigma (n,p_0)=43800\pm 1400\mathrm{b}$ and the cross section to the first excited state of ${}^7\mathrm{Li}$ is $\sigma (n,p_1)=520\pm 260\mathrm{b}$.