Based on recent experimental results at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), the $\langle p_T\rangle$ dependence of identified light flavor charged hadrons on $\sqrt{\left(\frac{dN}{dy}\right)/S_{\perp }\phantom{{}^2}}$, the relevant scale in the gluon saturation picture, is studied from $\sqrt{s_{\mathit{NN}}}=7.7$ GeV up to 5.02 TeV. This study is extended to the slopes of the $\langle p_T\rangle$ dependence on the particle mass and the $\langle {\beta }_T\rangle$ parameter from Boltzmann-Gibbs blast wave (BGBW) fits of the $p_T$ spectra. A systematic decrease of the slope of the $\langle p_T\rangle$ dependence on $\sqrt{\left(\frac{dN}{dy}\right)/S_{\perp }\phantom{{}^2}}$ from Beam Energy Scan (BES) to LHC energies is evidenced. While, for the RHIC energies, within the experimental errors, $\langle p_T\rangle /\sqrt{\left(\frac{dN}{dy}\right)/S_{\perp }\phantom{{}^2}}$ does not depend on centrality, at the LHC energies a deviation from a linear behavior is observed towards the most central collisions. The influence of the corona contribution on the observed trends is discussed. The slopes of the $\langle p_T\rangle$ particle mass dependence and the $\langle {\beta }_T\rangle$ parameter from BGBW fits scale well with $\sqrt{\left(\frac{dN}{dy}\right)/S_{\perp }\phantom{{}^2}}$. Similar systematic trends for $pp$ at $\sqrt{s}=7$ TeV are in a good agreement with the ones corresponding to Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ and 5.02 TeV, pointing to a system-size-independent behavior.

We discuss several misleading statements made in the article by Eccles et al. [Phys. Rev. C 96, 054611 (2017)]. In particular, contrary to what is claimed in that paper, the analysis of the borders of Kramers formula applicability as a function of temperature using the mean first-passage time formula was performed earlier in the paper by Gontchar et al. [Phys. Rev. C 82, 064606 (2010)].

In this Reply, we address the issues raised by Gontchar and Chushnyakova in the preceding Comment [Gontchar and Chushnyakova, Phys. Rev. C 98, 029801 (2018)] with respect to the relation between the Eccles-Roy-Gray-Zaccone (ERGZ) analytical model of nuclear fission lifetime and previous models based on the mean-first passage time approach. We clarify that the originality of the ERGZ approach lies in the ability to provide closed-form expressions for the lifetime valid across the entire range of nuclear temperature.

The possible existence of shape-coexisting nuclear configurations with tetrahedral symmetry is receiving increasing attention due to unprecedented nuclear structure properties, in particular, in terms of the exotic fourfold nucleonic level degeneracies and the expected long lifetimes, which may become a new decisive argument in the exotic nuclei research programs. The present article addresses the rotational structure properties of the tetrahedrally symmetric even-even core configurations coupled with a single valence nucleon. We focus on the properties of the associated Coriolis-coupling Hamiltonian proposing the solutions based on the explicit construction of the bases of the irreducible representations of the tetrahedral point-group on the one-hand side and the microscopic angular-momentum and parity projection nuclear mean-field approach on the other. It is shown that for one particle occupying an orbital belonging to the $E_{1/2}$ or $E_{5/2}$ irreducible representation, the rotational spectrum splits into two sequences, the structures analogous to those of the $K=1/2$ rotational bands in the axially symmetric nuclei. Although the spectrum is generally more complicated for one-particle occupying a fourfold degenerate orbital belonging to the $G_{3/2}$ representation, an appearance of the correlated double-sequence structures persists. The spectra of the doubly-magic tetrahedral core plus one-particle systems can be well interpreted using the analytical solutions of the first order Coriolis-coupling Hamiltonian. We introduce the notion of the generalized decoupling parameters, which determine the size of the energy-splitting between the double-sequence structures.

The neutron-unbound isotope ${}^{13}\mathrm{Be}$ has been studied in several experiments using different reactions, different projectile energies, and different experimental setups. There is, however, no real consensus in the interpretation of the data, in particular concerning the structure of the low-lying excited states. Gathering new experimental information, which may reveal the ${}^{13}\mathrm{Be}$ structure, is a challenge, particularly in light of its bridging role between ${}^{12}\mathrm{Be}$, where the $N=8$ neutron shell breaks down, and the Borromean halo nucleus ${}^{14}\mathrm{Be}$. The purpose of the present study is to investigate the role of bound excited states in the reaction product ${}^{12}\mathrm{Be}$ after proton knockout from ${}^{14}\mathrm{B}$, by measuring coincidences between ${}^{12}\mathrm{Be}$, neutrons, and $\gamma$ rays originating from de-excitation of states fed by neutron decay of ${}^{13}\mathrm{Be}$. The ${}^{13}\mathrm{Be}$ isotopes were produced in proton knockout from a 400 MeV/nucleon ${}^{14}\mathrm{B}$ beam impinging on a ${\mathrm{CH}}_2$ target. The ${}^{12}\mathrm{Be}\text{−}n$ relative-energy spectrum $d\sigma /d{E}_{fn}$ was obtained from coincidences between ${}^{12}\mathrm{Be}$(g.s.) and a neutron, and also as threefold coincidences by adding $\gamma$ rays, from the de-excitation of excited states in ${}^{12}\mathrm{Be}$. Neutron decay from the first $5/2^{+}$ state in ${}^{13}\mathrm{Be}$ to the $2^{+}$ state in ${}^{12}\mathrm{Be}$  at 2.11 MeV is confirmed. An energy independence of the proton-knockout mechanism is found from a comparison with data taken with a 35 MeV/nucleon ${}^{14}\mathrm{B}$ beam. A low-lying $p$-wave resonance in ${}^{13}\mathrm{Be}\left(1/2^{-}\right)$ is confirmed by comparing proton- and neutron-knockout data from ${}^{14}\mathrm{B}$ and ${}^{14}\mathrm{Be}$.

The prescission particle multiplicities suggest a lifetime of $\approx {10}^{-20}$ s for nuclear fission to occur which is in contrast to the fission lifetime $\approx {10}^{-18}$ s as predicted by an atomic probe. This long-standing ambiguity, arising due to the orders of magnitude differences among the fission lifetimes measured from the nuclear and atomic probes, has been addressed within a dynamical model which includes the contributions from the nuclear shell effects. We show that at lower excitation energies, these two probes decouple as the fissioning system survives for a long time without any particle evaporation. We also consider a wide range of reactions to study the impact of the excitation energy of the compound nucleus on the fission dynamics in general. Prescission neutron multiplicity is found to be an inappropriate probe to measure fission lifetime at low excitation energy. In addition, our model predicts the average fission lifetime of the superheavy nucleus ${}^{302}120$ to be more than ${10}^{-18}$ s, which is in reasonable agreement with recent experiments.

We report in situ neutron background measurements at the Kuo-Sheng Reactor Neutrino Laboratory (KSNL) by a hybrid neutron detector (HND) with a data size of 33.8 days under shielding configurations identical to those used during the neutrino physics data taking. The HND consists of BC-501A liquid and BC-702 phosphor powder scintillation neutron detectors, which are sensitive to both fast and thermal neutrons, respectively. Neutron-induced events for the two channels are identified and differentiated by pulse shape analysis, such that the backgrounds of both are simultaneously measured. The fast neutron fluxes are derived by an iterative unfolding algorithm. Neutron-induced backgrounds in the germanium detector under the same fluxes, due to both cosmic rays and ambient radioactivity, are derived and compared with the measurements. The results are valuable to background understanding of the neutrino data at the KSNL. In particular, neutron-induced background events due to ambient radioactivity as well as from reactor operation are negligible compared to intrinsic cosmogenic activity and ambient $\gamma$ activity. The detector concept and analysis procedures are applicable to neutron background characterization in similar rare-event experiments.

The impact of jet quenching on $Z^0$-tagged jets in relativistic heavy-ion collisions at the CERN Large Hadron Collider is investigated. We employ the sherpa Monte Carlo program that combines next-to-leading-order matrix elements with matched resummation of parton shower to compute the initial $Z^0$+jet production. The linear Boltzmann transport (LBT) model is then used to simulate the propagation, energy attenuation of, and medium response induced by jet partons in the quark-gluon plasma. With both higher-order corrections and matched soft and collinear radiation as well as a sophisticated treatment of parton energy loss and medium response in LBT, our numerical calculations can provide the best description so far of all available observables of $Z^0$+jet simultaneously in both proton + proton and Pb+Pb collisions, in particular, the shift of the distribution in transverse momentum asymmetry $x_{\mathrm{jZ}}=p_T^{\mathrm{jet}}/p_T^Z$, the modification of azimuthal angle correlation in $\mathrm{\Delta }{\varphi }_{\mathrm{j}\mathrm{Z}}=|{\varphi }_{\mathrm{jet}}-{\varphi }_Z|$, and the overall suppression of average number of $Z^0$-tagged jets per boson $R_{\mathrm{jZ}}$ at $\sqrt{s}=5.02$ TeV as measured by the Compact Muon Solenoid experiment. We also show that higher-order corrections to $Z^0$+jet production play an indispensable role in understanding $Z^0$+jet azimuthal angle correlation at small and intermediate $\mathrm{\Delta }{\varphi }_{\mathrm{jZ}}$, and momentum imbalance at small $x_{\mathrm{jZ}}$. Jet quenching of the subleading jets is shown to lead to suppression of the $Z^0$+jet correlation at small azimuthal angle difference $\mathrm{\Delta }{\varphi }_{\mathrm{jZ}}$ and at small $x_{\mathrm{jZ}}$.

Nuclear level density at low excitation energies is proposed as an indicator of the first order phase transitions in nuclei. The new signature, a maximum value of the level density at the critical point, appears to be sensitive to the detailed way the phase transition takes place in different nuclear regions: it is consistent with phase coexistence in the $N=90$ region, and with a rapid crossing of the two phases, without their coexistence/mixing at the critical point in the $N=60$ region, respectively. Candidates for critical point nuclei are proposed for odd-mass and odd-odd nuclei, using correlations between relative excitation energies, and their ratios, for structures (bands) based on unique-parity orbitals.

A multiparticle spin-trap isomeric state having a half-life of 179(4) ns and lying 2601 keV above the yrast ${10}^{+}$ state in ${}^{156}\mathrm{Lu}$ has been discovered. The ${}^{156}\mathrm{Lu}$ nuclei were produced by bombarding isotopically enriched ${}^{106}\mathrm{Cd}$ targets with beams of ${}^{58}\mathrm{Ni}$ ions, separated in flight using the gas-filled separator RITU and their decays were measured using the GREAT spectrometer. Analysis of the main decay path that populates yrast states observed previously suggests a spin-parity assignment of ${19}^{-}$ for the isomeric state, which is consistent with isomeric states identified in the $N$ = 85 isotones. Comparison with other decay paths in ${}^{156}\mathrm{Lu}$ indicates that the $[\pi h_{11/2}^{-1}\otimes \nu h_{9/2}]{10}^{+}$ state at the bottom of the yrast sequence is likely to be the $\alpha$-decaying isomeric state, with the $[\pi h_{11/2}^{-1}\otimes \nu f_{7/2}]9^{+}$ state lying 62 keV above it. The relative ordering of the lowest-lying $9^{+}$ and ${10}^{+}$ states is inverted in ${}^{156}\mathrm{Lu}$ compared with its odd-odd isotones.

A simple expression for the fission width of excited nuclei with the fission barrier dependent on excitation energy is obtained. This fission width is larger than the one obtained with the help of the energy-independent fission barrier. The ratio of fission widths evaluated with and without the energy-dependent fission barrier has the maximum at excitation energy close to $\approx 40\mathrm{MeV}$. The dependence of the fission barrier on the excitation energy is discussed.

Production of large transverse momentum ${\rho }^0$ meson in high-energy nuclear collisions is investigated for the first time at next to leading order (NLO) in the QCD improved parton model. The ${\rho }^0$ fragmentation functions (FFs) in vacuum at any scale $Q$ are obtained, by evolving a newly developed initial parametrization of ${\rho }^0$ FFs at a scale $Q_0^2=1.5{\mathrm{GeV}}^2$ from a broken SU(3) model through NLO Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equations. The numerical simulations of $p_{\mathrm{T}}$ spectra of ${\rho }^0$ meson in the elementary $p+p$ collisions at NLO give a decent description of STAR $p+p$ data. In $A+A$ reactions the jet quenching effect is taken into account with the higher-twist approach by the medium-modified parton FFs due to gluon radiation in the quark-gluon plasma, whose space-time evolution is described by a (3+1D) hydrodynamical model. The nuclear modification factors for ${\rho }^0$ meson and its double ratio with ${\pi }^{\pm }$ nuclear modification in central $\mathrm{Au}+\mathrm{Au}$ collisions at the BNL Relativistic Heavy Ion Collider are calculated and found to be in good agreement with the STAR measurement. Predictions of ${\rho }^0$ nuclear modification and the yield ratio ${\rho }^0/{\pi }^0$ in central Pb+Pb at the CERN Large Hadron Collider are also presented. It is shown that the ratio ${\rho }^0/{\pi }^0$ in central Pb+Pb will approach to that in $p+p$ reactions when $p_{\mathrm{T}}>12$ GeV.

Background: The precision of nuclear Hartree-Fock-Bogoliubov (HFB) calculations in coordinate space is limited by box discretization schemes. In particular, for the finite-difference (FD) discretization method, both the resolution and box size determine the calculation error.

Purpose: The current work studies the accuracy of the FD approximation as applied to the three-dimensional (3D) nuclear HFB problem.

Methods: By (1) taking the wave functions solved in the harmonic oscillator (HO) basis and (2) representing the HFB problem in coordinate space using the FD method, the current work carefully evaluates the error due to box discretization by examining the deviation of the resulting HFB matrix, the total energies in the coordinate space, from those calculated with the HO method, the latter of which is free from numerical error within its model configuration. To estimate how the box discretization error accumulates with self-consistent iterations, HF and HFB calculations (with the two-basis method) were carried out for ${}^{40}\mathrm{Ca}$, ${}^{110}\mathrm{Mo}$, and ${}^{132}\mathrm{Sn}$. The resulting energies were compared with those from the HO basis, and 3D coordinate space calculations in the literature.

Results: The analysis shows that for a grid spacing of $\le 0.6$ fm, the off-diagonal elements of the HFB matrix are extremely small ($<1\mathrm{keV}$). The calculated quasiparticle spectra differ from those of HO calculations by a few keV. Self-consistent HF and HFB calculations within the current FD method, with the box discretization schemes suggested in the above analysis, give results similar to those using the HO basis. For the HFB calculations, the FD and HO methods predict different single-particle spectra, making an exact comparison difficult. This makes the analysis of precision at a certain iteration useful.

Conclusions: With the described FD approximation to the differential operators, together with the way various densities and the Hamiltonian are constructed, it can be concluded that for a box grid spacing of $\le 0.7$ fm, the accuracy of each calculated energy contribution is on the order of a few tens of keV. The box size needs to be large enough for the normal densities to be smaller than ${10}^{-8}{\mathrm{fm}}^{-3}$ at the edge of the box. With this discretization scheme, the number of the calculated matrix elements differs from that of the HO calculation by $\le 10\%$ of the total number of the HFB matrix elements. For the single- and quasiparticle energies, the accuracy is on the order of a few keV. The above conclusions have been verified by performing self-consistent HF and HFB calculations.

This paper reports on an investigation on the level structure of the odd-mass ${}^{29}\mathrm{Al}$ nucleus populated via heavy-ion induced fusion evaporation reaction. Rotational sequences with fast magnetic dipole transitions have been identified. These sequences exhibit the essential characteristic features of magnetic-rotation-like behavior, which has been corroborated through lifetime measurements using the Doppler shift attenuation method. The sequences also show features exhibited by axially deformed nuclei. Thus, the level structure presents the possibility of existence of multifaceted excitation modes in ${}^{29}\mathrm{Al}$, which are believed to be the first of its kind observed in the $A\approx$ 30 region. Shell model calculations, carried out within the $sd$-model space, qualitatively reproduce the experimental observations.

We attempt to calculate the production cross sections of unknown ${}^{280–283}\mathrm{Fl}$ and ${}^{290–292}\mathrm{Fl}$ isotopes by using hot fusion reaction mechanism within the dinuclear system model. The production of unknown neutron-deficient Fl isotopes (${}^{280–283}\mathrm{Fl}$) is studied in the reactions ${}^{44}\mathrm{Ca}+{}^{242}\mathrm{Pu}$ and ${}^{36}\mathrm{S}+{}^{249}\mathrm{Cf}$ with the maximum evaporation residue cross sections values 0.91 pb, 6.17 pb, 36.16 pb, and 2.02 pb, respectively. The use of neutron-rich radioactive beams ${}^{44}\mathrm{Ar}$ and ${}^{46}\mathrm{Ar}$ may help us produce new neutron-rich Fl isotopes via fusion reaction mechanism only if an extremely high beam intensity were to be achieved in the future. The maximum production cross sections of unknown neutron-rich isotopes (${}^{290–292}\mathrm{Fl}$) in the reactions ${}^{46}\mathrm{Ar}+{}^{248}\mathrm{Cm}$ and ${}^{46}\mathrm{Ar}+{}^{250}\mathrm{Cm}$ are predicted to be 4.06 pb, 8.55 pb, and 3.35 pb, respectively. At present, reaction with radioactive ion beams is not a promising method to produce neutron-rich superheavy nuclei and other reaction mechanisms such as transfer reaction need to be developed.

The azimuthal anisotropic flow of identified and unidentified charged particles has been systematically studied in Cu+Au collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV for harmonics $n=1–4$ in the pseudorapidity range $\left|\eta \right|<1$. The directed flow in Cu+Au collisions is compared with the rapidity-odd and, for the first time, the rapidity-even components of charged particle directed flow in Au+Au collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. The slope of the directed flow pseudorapidity dependence in Cu+Au collisions is found to be similar to that in Au+Au collisions, with the intercept shifted toward positive pseudorapidity values, i.e., the Cu-going direction. The mean transverse momentum projected onto the spectator plane $\langle p_x\rangle$ in Cu+Au collision also exhibits approximately linear dependence on pseudorapidity with the intercept at about $\eta \approx -0.4$ (shifted from zero in the Au-going direction), closer to the rapidity of the Cu+Au system center of mass. The observed dependencies find a natural explanation in a picture of the directed flow originating partly due the “tilted source” and partly due to the asymmetry in the initial density distribution. A charge dependence of $\langle p_x\rangle$ was also observed in Cu+Au collisions, consistent with an effect of the initial electric field created by charge difference of the spectator protons in two colliding nuclei. The rapidity-even component of directed flow in Au+Au collisions is close to that in Pb+Pb collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=2.76$ TeV, indicating a similar magnitude of dipolelike fluctuations in the initial-state density distribution. Higher harmonic flow in Cu+Au collisions exhibits similar trends to those observed in Au+Au and Pb+Pb collisions and is qualitatively reproduced by a viscous hydrodynamic model and a multiphase transport model. For all harmonics with $n\ge 2$ we observe an approximate scaling of $v_n$ with the number of constituent quarks; this scaling works as well in Cu+Au collisions as it does in Au+Au collisions.

We calculate the differential scattering rate for thermal neutrinos in a hot and dilute gas of interacting neutrons using linear response theory. The dynamical structure factors for density and spin fluctuations of the strongly interacting neutron matter, expected in the neutrino decoupling regions of supernovae and neutron star mergers, are calculated in the virial expansion for the first time. Correlations due to nucleon-nucleon interactions are taken into account using a pseudopotential that reproduces measured nucleon-nucleon phase shifts, and we find that attractive $s$-wave interactions enhance the density response and suppress the spin response of neutron matter. The net effect of neutron correlations is to strongly suppress backscattering. Moreover, we find nearly exact scaling laws for the response functions, valid for the range $T=5–10$ MeV and $q<30$ MeV, allowing us to obtain analytic results for the dynamic structure factors at second order in the fugacity of the neutron gas. We find that the modification of scattering rates depends on the energy and momentum exchanged. The use of dynamical structure factors can lead to corrections of the scattering rate at the 10–20% level compared to approximations based on static structure factors.

Recently, a new $\mathrm{\Delta }$ method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved, and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Padé approximations using the effective-range function $K_l\left(k^2\right)$ fitting do not work. A typical example is the nucleus vertex $\alpha +{}^{12}\mathrm{C}⟷{}^{16}\mathrm{O}$. Here we apply the $\mathrm{\Delta }$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$, $\alpha \text{−}\alpha$, and $\alpha \text{−}{}^{12}\mathrm{C}$ collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$-matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ($E_0$) and width ($\mathrm{\Gamma }$), which is used to find the ANC uncertainty ($\mathrm{\Delta }\mathrm{ANC}$) through the energy ($\mathrm{\Delta }{E}_0$) and the width ($\mathrm{\Delta }\mathrm{\Gamma }$) uncertainties.