We study theoretically the electric dipole transitions of even Ni isotopes at low energies, using the self-consistent quasiparticle random-phase approximation with the D1S Gogny interaction and a continuum-RPA model with the SLy4 Skyrme force. We analyze isoscalar states, isovector states, and the dipole polarizability. We define a reference value for the polarizability to remove a trivial dependence on the mass number. We compare our results with data and other calculations, with a focus on collective states, shell effects, and threshold transitions. Our results support the presence of a strong isoscalar transition, with little or moderate $E1$ strength, as a universal feature of ordinary nuclei. In moderately neutron-rich Ni isotopes, namely ${}^{68}\mathrm{Ni}$ and neighboring isotopes, this transition is found bimodal due to couplings with surface neutrons. An adequate treatment of the continuum states appears essential for describing suprathreshold $E1$ strength, especially beyond ${}^{68}\mathrm{Ni}$. Very exotic isotopes $\left(N>50\right)$ are found highly polarizable, with practically all their $E1$ strength in the continuum. The dipole polarizability and the neutron-skin thickness are influenced by shell structure in different ways, so they can appear anticorrelated. A comparison with existing results for lighter (Ca) and heavier (Sn) nuclei suggests that the so-called pygmy dipole strength is influenced strongly by shell effects and that, partly for that reason, its isospin structure depends on the mass region.

In order to simulate the relativistic effects of the Dirac-Brueckner-Hartree-Fock approach for finite nuclei, the part of the Urbana three-nucleon (3N) force is considered, which represents the enhancement of the small components of the Dirac spinors for the nucleons in the nuclear medium. This 3N force is included in a Brueckner-Hartree-Fock calculation with rearrangement terms using a realistic model for the NN interaction. The strength of the 3N force is adjusted to reproduce the empirical saturation point of nuclear matter and then used in corresponding studies of the closed shell nuclei ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$. Special attention is paid to a consistent treatment of the spectrum of particle states in the NN propagator of the Bethe-Goldstone equation.

Background: The concept of single-nucleon shells constitutes a basic pillar of our understanding of nuclear structure. Effective single-particle energies (ESPEs) introduced by French [Proceedings of the International School of Physics “Enrico Fermi,” Course XXXVI, Varenna 1965, edited by C. Bloch (Academic Press, New York, 1966)] and Baranger [Nucl. Phys. A 149, 225 (1970)] represent the most appropriate tool to relate many-body observables to a single-nucleon shell structure. As briefly discussed in Duguet and Hagen [Phys. Rev. C 85, 034330 (2012)], the dependence of ESPEs on one-nucleon transfer probability matrices makes them purely theoretical quantities that “run” with the nonobservable resolution scale $\lambda$ employed in the calculation.

Purpose: Given that ESPEs provide a way to interpret the many-body problem in terms of simpler theoretical ingredients, the goal is to specify the terms, i.e., the exact sense and conditions, in which this interpretation can be conducted meaningfully.

Methods: While the nuclear shell structure is both scale and scheme dependent, the present study focuses on the former. A detailed discussion is provided to illustrate the scale (in)dependence of observables and nonobservables and the reasons why ESPEs, i.e., the shell structure, belong to the latter category. State-of-the-art multireference in-medium similarity renormalization group and self-consistent Gorkov Green's function many-body calculations are employed to corroborate the formal analysis. This is done by comparing the behavior of several observables and of nonobservable ESPEs (and spectroscopic factors) under (quasi) unitary similarity renormalization group transformations of the Hamiltonian parametrized by the resolution scale $\lambda$.

Results: The formal proofs are confirmed by the results of ab initio many-body calculations in their current stage of implementation. In practice, the unitarity of the similarity transformations is broken owing to the omission of induced many-body interactions beyond three-body operators and to the nonexact treatment of the many-body Schrödinger equation. The impact of this breaking is first characterized by quantifying the artificial running of observables over a (necessarily) finite interval of $\lambda$ values. Then the genuine running of ESPEs is characterized and shown to be convincingly larger than the one of observables (which would be zero in an exact calculation).

Conclusions: The nonobservable nature of the nuclear shell structure, i.e., the fact that it constitutes an intrinsically theoretical object with no counterpart in the empirical world, must be recognized and assimilated. Indeed, the shell structure cannot be determined uniquely from experimental data and cannot be talked about in an absolute sense as it depends on the nonobservable resolution scale employed in the theoretical calculation. It is only at the price of fixing arbitrarily (but conveniently) such a scale that one can establish correlations between observables and the shell structure. To some extent, fixing the resolution scale provides ESPEs (and spectroscopic factors) with a quasi-observable character. Eventually, practitioners can refer to nuclear shells and spectroscopic factors in their analyses of nuclear phenomena if, and only if, they use consistent structure and reaction theoretical schemes based on a fixed resolution scale they have agreed on prior to performing their analysis and comparisons.

In the search for the fully aligned ${27}^{-}$ state in ${}^{140}\mathrm{Nd}$ predicted by cranked Nilsson-Strutinsky calculations, new close-to-spherical high-spin states have been discovered. Both the close-to-spherical and the triaxial calculated states are in good agreement with the experimental results, supporting the existence of shape coexistence up to very high spins. Shell-model calculations using a newly developed effective interaction for the $50\le N,Z\le 82$ mass region are in good agreement with the observed spherical states. The comparison between the experimental and calculated level energies allowed the relative energy to be established between several proton and neutron orbitals at high energy and spins.

The isotopic yield distributions and kinematic properties of fragments produced in the transfer-induced fission of ${}^{240}\mathrm{Pu}$ and fusion-induced fission of ${}^{250}\mathrm{Cf}$, with 9 MeV and 45 MeV excitation energy, respectively, were measured in inverse kinematics with the spectrometer VAMOS. The kinematics of identified fission fragments allow to derive properties of the scission configuration such as the distance between fragments, the total kinetic energy, the neutron multiplicity, the total excitation energy, and, for the first time, the proton- and neutron-number sharing during the emergence of the fragments. These properties of the scission point are studied as functions of the fragment atomic number. The correlation between these observables, gathered in one single experiment and for two different fissioning systems at different excitation energies, give valuable information for the understanding and modeling of the fission process.

Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of a few intermediate-mass fragments (IMFs) can also be observed. We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions. We find that the formation of few IMFs can be confused with asymmetric fission when relying on yield observables, but it cannot be ascribed to the statistical decay of a compound nucleus when analyzing the dynamics and kinematic observables; it can be described as a fragmentation process initiated by phase-space fluctuations, and successively frustrated by the mean-field resilience. As an extreme situation, which corresponds to non-negligible probability, the number of fragments in the exit channel reduces to two, so that fission-like events are obtained by re-aggregation processes. This interpretation, inspired by nuclear-spallation experiments, can be generalized to heavy-ion collisions from Fermi to relativistic energies, for situations when the system is closely approaching the fragmentation threshold.

The Glauber model analysis of the elastic ${}^{6,8}\mathrm{He}+p$ scattering data at energies around 700 MeV/nucleon, measured in two separate experiments at GSI-Darmstadt, has been carried out using several phenomenological parametrizations of the nuclear matter density. By taking into account the new data points measured at high-momentum transfer, the nuclear matter radii of ${}^{6,8}\text{He}$ have been accurately determined from the Glauber model analysis of the data, with the spin-orbital interaction explicitly taken into account. The well-known geometry for the core and dineutron halo has been used with the new parametrizations of the ${}^6\text{He}$ density to extract the detailed information on the structure of ${}^6\text{He}$ in terms of the core and dineutron halo radii. An enhanced sensitivity of the data measured at high-momentum transfer to the core part of the ${}^{6,8}\text{He}$ densities has been found.

Correlations between the elliptic or triangular flow coefficients $v_m$ ($m=2$ or 3) and other flow harmonics $v_n$ ($n=2$ to 5) are measured using $\sqrt{s_{{}_{NN}}}=2.76$ TeV $\mathrm{Pb}+\mathrm{Pb}$ collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of $7 \mu {\mathrm{b}}^{-1}$. The $v_m\text{−}{v}_n$ correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, $v_3$ is found to be anticorrelated with $v_2$ and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities, ${\epsilon }_2$ and ${\epsilon }_3$. However, it is observed that $v_4$ increases strongly with $v_2$, and $v_5$ increases strongly with both $v_2$ and $v_3$. The trend and strength of the $v_m\text{−}{v}_n$ correlations for $n=4$ and 5 are found to disagree with ${\epsilon }_m\text{−}{\epsilon }_n$ correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to $v_n$ and a nonlinear term that is a function of $v_2^2$ or of $v_2{v}_3$, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to $v_4$ and $v_5$ are found to be consistent with previously measured event-plane correlations.

Measurements of differential cross sections for $J/\psi$ production in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02$ TeV at the CERN Large Hadron Collider with the ATLAS detector are presented. The data set used corresponds to an integrated luminosity of $28.1 {\mathrm{nb}}^{-1}$. The $J/\psi$ mesons are reconstructed in the dimuon decay channel over the transverse momentum range $8<p_{\mathrm{T}}<30\text{GeV}$ and over the center-of-mass rapidity range $-2.87<y^{*}<1.94$. Prompt $J/\psi$ are separated from $J/\psi$ resulting from $b$-hadron decays through an analysis of the distance between the $J/\psi$ decay vertex and the event primary vertex. The differential cross section for production of nonprompt $J/\psi$ is compared to a FONLL calculation that does not include nuclear effects. Forward-backward production ratios are presented and compared to theoretical predictions. These results complement previously published results by covering a region of higher transverse momentum and more central rapidity. They thus constrain the kinematic dependence of nuclear modifications of charmonium and $b$-quark production in $p+\mathrm{Pb}$ collisions.

The by now well-established scalar-isoscalar resonance $f_0\left(500\right)$ (the $\sigma$ meson) seems potentially relevant in the evaluation of thermodynamic quantities of a hadronic gas since its mass is low. However, we recall that its contribution to isospin-averaged observables is, to a surprising accuracy, canceled by the repulsion from the pion-pion scalar-isotensor channel. As a result, in practice one should not incorporate $f_0\left(500\right)$ in standard hadronic resonance-gas models for studies of isospin-averaged quantities. In our analysis we use the formalism of the virial expansion, which allows one to calculate the thermal properties of an interacting hadron gas in terms of derivatives of the scattering phase shifts, hence in a model-independent way directly from experimentally accessible quantities. A similar cancellation mechanism occurs for the scalar kaonic interactions between the $I=1/2$ channel [containing the alleged $K_0^{*}\left(800\right)$ or the $\kappa$ meson] and the $I=3/2$ channel.

Epos is a Monte Carlo event generator for minimum bias hadronic interactions, used for both heavy ion interactions and cosmic ray air shower simulations. Since the last public release in 2009, the Large Hadron Collider (LHC) experiments have provided a number of very interesting data sets comprising minimum bias $p\text{−}p,p$-Pb, and Pb-Pb interactions. We describe the changes required to the model to reproduce in detail the new data available from the LHC and the consequences in the interpretation of these data. In particular we discuss the effect of the collective hadronization in $p\text{−}p$ scattering. A different parametrization of flow has been introduced in the case of a small volume with high density of thermalized matter (core) reached in $p\text{−}p$ compared to large volume produced in heavy ion collisions. Both parametrizations depend only on the geometry and the amount of secondary particles entering in the core and not on the beam mass or energy. The transition between the two flow regimes can be tested with $p$-Pb data. Epos LHC is able to reproduce all minimum bias results for all particles with transverse momentum from $p_{\mathrm{t}}=0$ to a few GeV/$c$.

Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the shell-model language.

Purpose: We intend to study the importance of configuration mixing in the understanding of the nuclear structure of even-even Po isotopes, where the shape coexistence phenomena are not clear enough.

Method: We study in detail a long chain of polonium isotopes, ${}^{190–208}\mathrm{Po}$, using the interacting boson model with configuration mixing (IBM-CM). We fix the parameters of the Hamiltonians through a least-squares fit to the known energies and absolute $B\left(E2\right)$ transition rates of states up to 3 MeV.

Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, $B\left(E2\right)$'s, electric quadrupole moments, nuclear radii and isotopic shifts, quadrupole shape invariants, wave functions, and deformations.

Conclusions: We obtain a good agreement with the experimental data for all the studied observables and we conclude that shape coexistence phenomenon is hidden in Po isotopes, very much as in the case of the Pt isotopes.

The experimental signature in searches for the neutrinoless double-$\beta$ decay of ${}^{76}\mathrm{Ge}$ is a peak near 2039 keV in the spectrum. Given the low probability of the process, it is important that the background in this region be well understood. Inelastic scattering reactions with neutrons from muon-induced interactions and $(\alpha ,n)$ reactions in the surrounding materials or in the detector can provide contributions to the background. We have measured the production cross sections for $\gamma$ rays from the ${}^{76}\mathrm{Ge}(n,n^{\prime }\gamma )$ reaction in the 2039-keV region at incident neutron energies up to 4.9 MeV. In addition to determining that the cross sections of a previously known 2040.7-keV $\gamma$ ray from the 3952-keV level in ${}^{76}\mathrm{Ge}$ are rather small, we find that a larger contribution arises from a 2037.5-keV $\gamma$ ray which is attributed to a newly identified level at 3147 keV in ${}^{76}\mathrm{Ge}$. A third contribution is also possible from another new level at 3577 keV. These results indicate that the 2039-keV region in ${}^{76}\mathrm{Ge}$ neutrinoless double-$\beta$ decay searches is more complex than was previously thought.

As an extension of our previous work, the growth of density fluctuations in the spinodal region of charge asymmetric nuclear matter is investigated in the basis of the stochastic mean-field approach in the nonrelativistic framework. A complete treatment of density correlation functions is presented by including collective modes and noncollective modes.

Background: Whether atomic nuclei can possess triaxial shapes at their ground states is still a subject of ongoing debate. According to theory, good prospects for low-spin triaxiality are in the neutron-rich Mo-Ru region. Recently, transition quadrupole moments in rotational bands of even-mass neutron-rich isotopes of molybdenum and ruthenium nuclei have been measured. The new data have provided a challenge for theoretical descriptions invoking stable triaxial deformations.

Purpose: To understand experimental data on rotational bands in the neutron-rich Mo-Ru region, we carried out theoretical analysis of moments of inertia, shapes, and transition quadrupole moments of neutron-rich even-even nuclei around ${}^{110}\mathrm{Ru}$ using self-consistent mean-field and shell model techniques.

Methods: To describe yrast structures in Mo and Ru isotopes, we use nuclear density functional theory (DFT) with the optimized energy density functional UNEDF0. We also apply triaxial projected shell model (TPSM) to describe yrast and positive-parity, near-yrast band structures.

Results: Our self-consistent DFT calculations predict triaxial ground-state deformations in ${}^{106,108}\mathrm{Mo}$ and ${}^{108,110,112}\mathrm{Ru}$ and reproduce the observed low-frequency behavior of moments of inertia. As the rotational frequency increases, a negative-$\gamma$ structure, associated with the aligned $\nu {\left(h_{11/2}\right)}^2$ pair, becomes energetically favored. The computed transition quadrupole moments vary with angular momentum, which reflects deformation changes with rotation; those variations are consistent with experiment. The TPSM calculations explain the observed band structures assuming stable triaxial shapes.

Conclusions: The structure of neutron-rich even-even nuclei around ${}^{110}\mathrm{Ru}$ is consistent with triaxial shape deformations. Our DFT and TPSM frameworks provide a consistent and complementary description of experimental data.

We investigate the impact of the neutron skin thickness, $\mathrm{\Delta }{R}_{np}$, on the energy difference between the anti-analog giant dipole resonance (AGDR), $E_{\mathrm{AGDR}}$, and the isobaric analog state (IAS), $E_{\mathrm{IAS}}$, in a heavy nucleus such as ${}^{208}\mathrm{Pb}$. For guidance, we first develop a simple and analytic, yet physical, approach based on the droplet model that linearly connects the energy difference $E_{\mathrm{AGDR}}-E_{\mathrm{IAS}}$ with $\mathrm{\Delta }{R}_{np}$. To test this correlation on more fundamental grounds, we employ a family of systematically varied Skyrme energy density functionals where variations on the value of the symmetry energy at saturation density $J$ are explored. The calculations have been performed within the fully self-consistent Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA) framework. We confirm the linear correlation within our microscopic approach and we can compare our results with available experimental data in ${}^{208}\mathrm{Pb}$ in order to extract a preferred value for $\mathrm{\Delta }{R}_{np}$ and, in turn, for the symmetry energy parameters. Averaging the results from two available experimental data, our analysis gives $\mathrm{\Delta }{R}_{np}$ = 0.$236\pm 0.018$ fm, $J$ = 33.$2\pm 1.0$ MeV, and a slope parameter of the symmetry energy at saturation $L$ = 97.$3\pm 11.2$ MeV. The errors include the experimental uncertainties and a lower-limit estimate of model uncertainties. These results are consistent with those extracted from different experimental data albeit $L$ and $\mathrm{\Delta }{R}_{np}$ are somewhat large when compared to previous estimations based on giant resonance studies. Possible hints whether model dependence can explain this difference are provided.

Effects of the completely unknown symmetry (isovector) potential of the $\mathrm{\Delta }\left(1232\right)$ resonance on the total and differential ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions at beam energies from 100 to 1000 MeV/nucleon are explored within an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. The effects are found to be negligible at beam energies above the pion-production threshold owing to the very short lifetimes of less than 2 fm/$c$ for $\mathrm{\Delta }$ resonances with masses around $m_{\mathrm{\Delta }}=1232$ MeV, leaving the ${\pi }^{-}/{\pi }^{+}$ ratios of especially the energetic pions still a reliable probe of the high-density behavior of nuclear symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$. However, as the beam energy becomes deeply subthreshold for pion production, effects of the $\mathrm{\Delta }$ symmetry potential become appreciable, especially on the ${\pi }^{-}/{\pi }^{+}$ ratio of low-energy pions from the decays of low-mass $\mathrm{\Delta }$ resonances which have lived long enough to be affected by their mean-field potentials, providing a useful tool to study the symmetry potential and spectroscopy of $\mathrm{\Delta }$ resonances in neutron-rich nuclear matter. Interestingly, though, even at the deeply subthreshold beam energies, the differential ${\pi }^{-}/{\pi }^{+}$ ratio of energetic pions remains sensitive to the $E_{\mathrm{sym}}\left(\rho \right)$ at suprasaturation densities with little influence from the uncertain symmetry potential of the $\mathrm{\Delta }$ resonance.

Measurements of the ${}^9\mathrm{Be}\left(\gamma ,n_0\right)$ reaction were performed using nearly 100% linearly polarized, high-intensity, and nearly monoenergetic $\gamma$-ray beams having energies between 5.5 and 15.5 MeV at the High Intensity $\gamma$-ray Source located at Duke University and Triangle Universities Nuclear Laboratory. Eighteen liquid scintillator detectors were used to measure neutron yields parallel and perpendicular to the plane of beam polarization. Polarization asymmetries, which are the differences between yields observed in detectors located in-plane and out-of-plane divided by their sums, were measured for the neutrons which left the residual nucleus $\left({}^8\mathrm{Be}\right)$ in its ground state, termed the $n_0$ group. Asymmetries between 0.4 to 0.7 were discovered over this energy region in addition to a clear trend of increasing asymmetries with increasing beam energy. A prediction of the polarization asymmetry based on a pure $E1$ direct capture model shows good agreement with the experimental measurements. These data and the prediction could be of interest for methods that rely on neutron measurements following photofission to identify the presence of special nuclear material.

The lowest-order constrained variational approach at finite temperature is extended by adding a semiphenomenological three-body force to its formulation. The equation of state (EOS) of hot asymmetric nuclear matter is obtained within the framework of the extended model. The density and temperature dependence of the mentioned three-body force is also discussed. The EOS of the proto-neutron star as well as its mass-radius relation is studied for several values of constant entropy and lepton fraction. We find that the maximum gravitational mass of the proto-neutron star is slightly sensitive to the value of the entropy and lepton fraction.

Reaction-diffusion equations with suitable boundary conditions have special propagating solutions which very closely resemble the moving interfaces in a first-order transition. We show that the dynamics of the chiral order parameter for the chiral symmetry breaking transition in heavy-ion collisions, with dissipative dynamics, is governed by one such equation; specifically, the Newell–Whitehead equation. Furthermore, required boundary conditions are automatically satisfied due to the geometry of the collision. The chiral transition is, therefore, completed by a propagating interface, exactly as for a first-order transition, even though the transition actually is a crossover for relativistic heavy-ion collisions. The same thing also happens when we consider the initial confinement-deconfinement transition with the Polyakov loop order parameter. The resulting equation, again with dissipative dynamics, can then be identified with the reaction-diffusion equation known as the FitzHugh–Nagumo equation which is used in population genetics. Observational constraints imply that the entire phase conversion cannot be achieved by such slow moving fronts, and some alternate faster dynamics needs also to be invoked; for example, involving fluctuations. We discuss the implications of these results for heavy-ion collisions. We also discuss possible extensions for the case of the early universe.