In this work, new recursion relations for the number of spin-$J$ states for identical particles in a single-$j$ shell are presented. Such relations are obtained using the generating-function technique, which enables one to exhibit an odd-even staggering in the spin distribution of an even number of fermions in a single-$j$ shell: the number of states with an even value of $J$ is larger than the number of states with an odd value of $J$. An analytical expression of the excess of states with an even value of $J$ is provided, and its asymptotic behavior for large values of $j$ is discussed.

We study the evolution of hydrodynamic and nonhydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e., of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from nonhydrodynamic modes coupling into the entropy evolution, which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.

We investigate the transport dynamics of partons in proton-proton collisions at the CERN Large Hadron Collider using a Boltzmann transport approach, the Parton Cascade Model (PCM). The calculations include semihard perturbative quantum chromodynamics interaction of partons populating the nucleons and provide a space-time description of the collision in terms of cascading partons undergoing scatterings and fragmentations. Parton production and number of collisions rise rapidly with an increase in the center of mass energy of the collision. For a given center of mass energy, the number of parton interactions is seen to rise stronger than linear with decreasing impact parameter before saturating for very central collisions. The strangeness enhancement factor ${\gamma }_s$ for the semihard processes is found to rise rapidly and saturate towards the highest collision energies. Overall, our study indicates a significant amount of partonic interactions in proton-proton collisions, which supports the observation of fluid-like behavior for high multiplicity proton-proton collisions observed in the experiments.

We present a detailed measurement of charged two-pion correlation functions in 0–30% centrality $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from Lévy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the Lévy index of stability $\alpha$, and the Lévy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same Lévy-stable source functions. The $\lambda \left(m_T\right)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The Lévy length scale parameter $R\left(m_T\right)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the Lévy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha =2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.

Quantum-statistical (Bose-Einstein) two-particle correlations are measured in $pp$ collisions at $\sqrt{s}=0.9$, 2.76, and 7 TeV, as well as in $p\mathrm{Pb}$ and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the Large Hadron Collider. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum ($k_{\mathrm{T}}$) and the charged-particle multiplicity in the event. For all systems, the extracted correlation radii steadily increase with the event multiplicity, and decrease with increasing $k_{\mathrm{T}}$. The radii are in the range 1–5 fm, the largest values corresponding to very high multiplicity $p\mathrm{Pb}$ interactions and to peripheral PbPb collisions with multiplicities similar to those seen in $p\mathrm{Pb}$ data. It is also observed that the dependencies of the radii on multiplicity and $k_{\mathrm{T}}$ largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.

Background: ${}^{31}\mathrm{Cl}$ is a neutron-deficient isotope with a half-life of $T_{1/2}=190\left(1\right)$ ms. The nuclear structure of its daughter, ${}^{31}\mathrm{S}$, is important for the determination of the thermonuclear ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate, which affects the final isotopic abundances of the ejecta from classical oxygen-neon novae.

Purpose: We aim to determine the $\beta$ feedings, $\gamma$-decay branchings, and excitation energies of states populated in ${}^{31}\mathrm{S}$ and create a comprehensive decay scheme for comparison with predictions based on the shell model.

Methods: Using a ${}^{31}\mathrm{Cl}$ rare istope beam implanted into a plastic scintillator and an array of high-purity Ge detectors, $\gamma$ rays from the ${}^{31}\mathrm{Cl}\left(\beta \gamma \right){}^{31}\mathrm{S}$ decay sequence were measured. Shell-model calculations using the USDB and the recently-developed USDE interactions were performed for comparison.

Results: A ${}^{31}\mathrm{Cl} \beta$-decay scheme was constructed from the experimental data and compared to the USDB and USDE shell-model calculations based on the $\beta$ feeding and $\gamma$-decay branches of each observed state. 33 new $\gamma$-ray transitions and ten new $\beta$ decay branches were observed. The $\beta$ feeding and $\gamma$-decay branches of each observed state were compared to those from the USDB and USDE shell-model calculations. For every allowed transition predicted by the USD calculations up to an excitation energy of 6.4 MeV in ${}^{31}\mathrm{S}$, an analogous transition was found in the experimental data, enabling a one-to-one comparison with the shell model. Using these identifications, spin and parity arguments were made for observed states.

Conclusions: The new ${}^{31}\mathrm{Cl} \gamma$-decay scheme presented in this work is the most complete and precise one for this nucleus constructed to date, incorporating statistics over an order of magnitude higher than previous work on ${}^{31}\mathrm{Cl} \beta$-delayed $\gamma$ decay. Of particular interest is the discovery of a 6390-keV state that mixes with the isobaric analog state and affects the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate. Other states observed in the decay are not expected to strongly affect the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate, but the comprehensive comparison to the shell model helps to clarify spin and parity assignments of resonances that might affect the rate.

We present a study on the isoscalar quadrupole strength in tin nuclei, focusing mainly on the low-energy region. The calculations are performed using the Skyrme-type energy density functionals within the fully self-consistent quasiparticle random phase approximation, allowing for a good description of the experimental data for the first $2^{+}$ state and the isoscalar giant quadrupole resonance. It is found that the first $2^{+}$ state and the low-energy quadrupole states between 3 and 6 MeV display an opposite behavior with increasing neutron number. While the strength of the first $2^{+}$ state decreases, some excited states start to accumulate between 3 and 6 MeV, and increase their strength with increasing neutron number. This low-energy region between 3 and 6 MeV is quite sensitive to the changes in the shell structure with increasing neutron number. In particular, between ${}^{116}\mathrm{Sn}$ and ${}^{132}\mathrm{Sn}$, the filling of the neutron orbitals with large values of $j$, has an important impact on the low-energy region. Our analysis shows that the low-energy states have a noncollective character, except the first $2^{+}$ state. In addition, the states in the low-energy region above 5 MeV display an interesting pattern: with the increase of the neutron number, their strength increases and their nature changes, namely they switch from proton excitations to neutron-dominated one. We conclude that the low-energy quadrupole states between 3 and 6 MeV can provide information about the shell evolution in open-shell nuclei.

The effect of correlations between the slope and the curvature of the symmetry energy on ground-state nuclear observables is studied within the extended Thomas-Fermi approximation. We consider different isovector probes of the symmetry energy, with a special focus on the neutron skin thickness of ${}^{208}\mathrm{Pb}$. We use a recently proposed metamodeling technique to generate a large number of equation of state models, where the empirical parameters are independently varied. The results are compared to a set of calculations using 17 different Skyrme interactions. We show that the curvature parameter plays a non-negligible role on the neutron skin, while the effect is reduced in Skyrme functionals because of the correlation with the slope parameter.

Lifetimes of several short-lived excited states in ${}^{138}\mathrm{Nd}$ were measured with the ROSPHERE array at IFIN-HH, Bucharest, using the recoil-distance Doppler shift technique following the ${}^{123}\mathrm{Sb}({}^{19}\mathrm{F},4n$) reaction. The resulting electromagnetic transition probabilities are compared to large-scale shell model calculations and to constrained Hartree-Fock-Bogoliubov calculations with the Gogny D1S interaction, configuration mixing, and a five-dimensional collective Hamiltonian formalism. The onset of collectivity in Nd isotopes below the $N=82$ shell closure and the deformation induced by the alignment of protons and neutron holes in the $h_{11/2}$ orbitals are discussed.

An unusually large value of the ${}^{22}\mathrm{C}$ matter radius, extracted by Tanaka et al. [Phys. Rev. Lett. 104, 062701 (2010)] from measured reaction cross sections, attracted great attention of scientific community. Since that time, several experimental works related to the ${}^{22}\mathrm{C}$ nucleus have appeared in the literature. Some of the experimental data, measured with high accuracy, allow us to fix ${}^{22}\mathrm{C}$ structure more reliably. Two limiting models reproducing ${}^{22}\mathrm{C}$ nuclear structure within the three-body cluster approach, that allow us to describe all existing experimental data, are presented. The ${}^{22}\mathrm{C}$ ground state, continuum structure, and geometry are obtained. With fixed ${}^{22}\mathrm{C}$ wave function, the prediction for the soft dipole mode in ${}^{22}\mathrm{C}$, which is studied in the process of Coulomb fragmentation, is performed.

The vast knowledge regarding the strong influence of quadrupole deformation ${\beta }_2$ of colliding nuclei in heavy-ion sub-barrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as ${\beta }_4$ and ${\beta }_6$ deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of ${\beta }_4$ of the projectile nucleus in the fusion of the ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ system. We demonstrated that the fusion barrier distribution is sensitive to the sign and value of the ${\beta }_4$ parameter of the projectile, ${}^{28}\mathrm{Si}$, and confirmed that the ${}^{28}\mathrm{Si}$ nucleus has a large positive ${\beta }_4$. This study opens an indirect way to estimate deformation parameters of radioactive nuclei using fusion reactions, which is otherwise difficult because of experimental constraints.

I develop an extension of the continuum-discretized coupled-channels (CDCC) method to reactions where both nuclei present a low breakup threshold. This leads to a four-body model, where the only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. Once these potentials are chosen, the model does not contain any additional parameter. First I briefly discuss the general formalism, and emphasize the need for dealing with large coupled-channel systems. The method is tested with existing benchmarks on $4\alpha$ bound states with the Ali-Bodmer potential. Then I apply the four-body CDCC to the ${}^{11}\mathrm{Be}+d$ system, where I consider the ${}^{10}\mathrm{Be}(0^{+},2^{+})+n$ configuration for ${}^{11}\mathrm{Be}$. I show that breakup channels are crucial to reproduce the elastic cross section, but that core excitation plays a weak role. The ${}^7\mathrm{Li}+d$ system is investigated with an $\alpha +t$ cluster model for ${}^7\mathrm{Li}$. I show that breakup channels significantly improve the agreement with the experimental cross section, but an additional imaginary term, simulating missing transfer channels, is necessary. The full CDCC results can be interpreted by equivalent potentials. For both systems, the real part is weakly affected by breakup channels, but the imaginary part is strongly modified. I suggest that the present wave functions could be used in future DWBA calculations.

The influence of the pion-nucleon potential on the pion dynamics in ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at 1.5 GeV/nucleon for different centrality intervals is investigated in the framework of the isospin-dependent quantum molecular dynamics model. It is found that the observables related to pions, such as the rapidity distributions, the rapidity dependencies of the directed flow and the elliptic flow, the centrality dependencies of the directed flow and the elliptic flow, and the transverse momentum distribution of the strength function of the azimuthal anisotropy are sensitive to the pion-nucleon potential. The pion multiplicity and the polar-angle distributions of pions are less affected by the pion-nucleon potential. The comparisons to the experimental data, in particular to the rapidity distributions of the directed flow and the elliptic flow, favor the stronger pion-nucleon potential derived from the phenomenological ansatz proposed by Gale and Kapusta [C. Gale and J. Kapusta, Phys. Rev. C 35, 2107 (1987)].

The production of neutron-rich superheavy nuclei with $Z=105–118$ in neutron evaporation channels is investigated within the dinuclear system model. The different stable and radioactive beam-induced hot fusion reactions are studied systematically. The prospect for synthesizing neutron-rich superheavy nuclei using radioactive beams is evaluated quantitatively based on the beam intensities proposed by Argonne Tandem Linac Accelerator System [B. B. Back and C. L. Jiang, Argonne National Laboratory Report No. ANL-06/55, 2006 (unpublished)]. All possible combinations (with projectiles of $Z=16–22$ and half-lives longer than 1 ms; with targets of half-lives longer than 30 days), which can be performed in available experimental equipment, for producing several unknown neutron-rich superheavy nuclei in neutron evaporation channels are investigated and the most promising reactions are predicted. It is found that the stable beams still show great advantages for producing most of superheavy nuclei. The calculated results are also compared with production cross sections in the $\mathrm{p}xn$ and $\alpha xn$ evaporation channels [Hong et al., Phys. Lett. B 764, 42 (2017)]. We find that the radioactive beam-induced reactions are comparable to the stable beam-induced reactions in charged particle evaporation channels. To obtain more experimental achievements, the beam intensities of modern radioactive beam facilities need to be further improved in the future.

Excitation functions for the 11 evaporation residues populated through complete and/or incomplete fusion in ${}^{16}\mathrm{O}+{}^{124}\mathrm{Sn}$ system at low projectile energies $\approx 3-7\mathrm{MeV}/\mathrm{nucleon}$ have been measured. Recoil catcher activation technique followed by offline $\gamma$-ray spectrometry has been employed. Some of the evaporation residues are found to have contributions from precursor decays. The precursor contributions have been separated out from the measured cumulative cross-sections of evaporation residues. Independent cross-sections are compared with statistical model code PACE-4 predictions. The evaporation residues produced through $xn$ and pxn channels are found to be well reproduced with the PACE-4 predictions after subtraction of precursor decay contributions. A substantial enhancement in the measured excitation functions over their theoretical predictions for the evaporation residues produced in $\alpha$-emitting channels has been observed, which is attributed to the presence of incomplete fusion of projectile with target at these low energies. The present study shows that the incomplete fusion and the break-up probability of the incident ${}^{16}\mathrm{O}$ into $\alpha$ clusters (i.e., break-up of ${}^{16}\mathrm{O}$ into ${}^{12}\mathrm{C}+\alpha$ and/or ${}^8\mathrm{Be}+{}^8\mathrm{Be}$) increases with projectile energy. The present data suggests that the deformation of target is highlighting the important role to affect the ICF reactions independently with different projectiles. The comparison of the present study with literature data also shows that the ICF probability depends on various entrance channel parameters, namely, projectile energy, entrance channel mass-asymmetry, $\alpha \text{−}Q$ value, Coulomb factor $\left(Z_{\mathrm{P}}{Z}_{\mathrm{T}}\right)$, deformation parameter (${\beta }_2$), and their combinations. Moreover, the combined parameters $Z_{\mathrm{P}}{Z}_{\mathrm{T}}·{\beta }_2$ and ${\mu }_{\mathrm{EC}}^{\mathrm{AS}}·{\beta }_2$ are not found suitable to explain whole ICF characteristics, particularly for spherical and slightly deformed targets. On the other hand, the combined parameter $Z_{\mathrm{P}}{Z}_{\mathrm{T}}·{\mu }_{\mathrm{EC}}^{\mathrm{AS}}$ has been found to explain more precisely the ICF dynamics as compared to other single and combined entrance channel parameters.

We present measurements of the transverse-momentum dependence of elliptic flow $v_2$ for identified pions and (anti)protons at midrapidity ($\left|\eta \right|<0.35$), in 0%–5% central $p+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. When taken together with previously published measurements in $d+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, the results cover a broad range of small-collision-system multiplicities and intrinsic initial geometries. We observe a clear mass-dependent splitting of $v_2\left(p_T\right)$ in $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions, just as in large nucleus-nucleus ($A+A$) collisions, and a smaller splitting in $p+\mathrm{Au}$ collisions. Both hydrodynamic and transport model calculations successfully describe the data at low $p_T$ ($<1.5\mathrm{GeV}/c$), but fail to describe various features at higher $p_T$. In all systems, the $v_2$ values follow an approximate quark-number scaling as a function of the hadron transverse kinetic energy per constituent quark $(K{E}_T/n_q$), which was also seen previously in $A+A$ collisions.

We propose a novel family of equations of state for symmetric nuclear matter based on the induced surface tension concept for the hard-core repulsion. It is shown that having only four adjustable parameters the suggested equations of state can, simultaneously, reproduce not only the main properties of the nuclear matter ground state, but the proton flow constraint up its maximal particle number densities. Varying the model parameters we carefully examine the range of values of incompressibility constant of normal nuclear matter and its critical temperature, which are consistent with the proton flow constraint. This analysis allows us to show that the physically most justified value of nuclear matter critical temperature is 15.5–18 MeV, the incompressibility constant is 270–315 MeV and the hard-core radius of nucleons is less than 0.4 fm.

A known class of analytic, exact, accelerating solutions of prefect relativistic hydrodynamics with longitudinal acceleration is utilized to describe results on the pseudorapidity distributions for different collision systems. These results include $dN/d\eta$ measured in $p+p$, Cu+Cu, Au+Au, and Pb+Pb collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider, in a broad centrality range. Going beyond the traditional Bjorken model, from the accelerating hydrodynamic description we determine the initial energy density and other thermodynamic quantities in those collisions.

Dileptons are considered as one of the cleanest signals of the quark-gluon plasma (QGP); however, the QGP radiation is masked by many background sources from either hadronic decays or semileptonic decays from correlated charm pairs. In this study, we investigate the relative contribution of these channels in heavy-ion collisions from $\sqrt{s_{\mathit{NN}}}=8$ GeV to 5 TeV with a focus on the competition between the thermal QGP radiation and the semileptonic decays from correlated $D\text{−}\mathrm{meson}$ pairs. As a tool, we employ the parton-hadron-string dynamics (PHSD) transport approach to study dilepton spectra in Pb + Pb (Au + Au) collisions in a wide energy range, incorporating for the first time a fully microscopic treatment of the charm dynamics and their semileptonic decays. We find that the dileptons from correlated $D\text{−}\mathrm{meson}$ decays dominate the thermal radiation from the QGP in central Pb + Pb collisions at the intermediate masses (1.2 GeV $<M<$ 3 GeV) for $\sqrt{s_{\mathit{NN}}}>$ 40 GeV, while for $\sqrt{s_{\mathit{NN}}}=8$ to 20 GeV the contribution from $D,\overline{D}$ decays to the intermediate mass dilepton spectra is subleading such that one should observe a rather clear signal from the QGP radiation. We furthermore study the $p_T$ spectra and the $R_{AA}\left(p_T\right)$ of single electrons at different energies as well as the excitation function of the inverse slope of the $m_T$ spectra for intermediate-mass dileptons from the QGP and from charm decays. We find moderate but characteristic changes in the inverse slope parameter for $\sqrt{s_{\mathit{NN}}}>$ 20 GeV which can be observed experimentally in high statistics data. Additionally, we provide detailed predictions for dilepton spectra from Pb + Pb collisions at $\sqrt{s_{\mathit{NN}}}=$ 5.02 TeV.

We present the first chiral effective theory derivation of the neutrinoless double-$\beta$ decay $nn\to pp$ potential induced by light Majorana neutrino exchange. The effective-field-theory framework has allowed us to identify and parametrize short- and long-range contributions previously missed in the literature. These contributions cannot be absorbed into parametrizations of the single-nucleon form factors. Starting from the quark and gluon level, we perform the matching onto chiral effective field theory and subsequently onto the nuclear potential. To derive the nuclear potential mediating neutrinoless double-$\beta$ decay, the hard, soft, and potential neutrino modes must be integrated out. This is performed through next-to-next-to-leading order in the chiral power counting, in both the Weinberg and pionless schemes. At next-to-next-to-leading order, the amplitude receives additional contributions from the exchange of ultrasoft neutrinos, which can be expressed in terms of nuclear matrix elements of the weak current and excitation energies of the intermediate nucleus. These quantities also control the two-neutrino double-$\beta$ decay amplitude. Finally, we outline strategies to determine the low-energy constants that appear in the potentials, by relating them to electromagnetic couplings and/or by matching to lattice QCD calculations.