Excited states in the odd-$A\hspace{0.5em}{}^{71,73,75,77}\mathrm{Ga}$ nuclei have been populated in deep-inelastic reactions of a ${}^{76}\mathrm{Ge}$ beam at 530 MeV with a thick ${}^{238}\mathrm{U}$ target. High-spin sequences built upon the $9/2^{+}$, $5/2^{-}$, and $3/2^{-}$ states were identified in all four isotopes. A comparison of the observed structures with the yrast positive-parity states in the neighboring even-even Zn cores indicates that the newly identified levels may be regarded as arising from the relatively weak coupling of the odd proton to the core states. However, significant contributions from broken pairs are expected to be present in this region of excitation energy. The present data set also provides clarification of previously reported decay paths of the low-energy levels in ${}^{71,73,75,77}\mathrm{Ga}$.

The electromagnetic transition between the almost degenerate $5/2^{+}$ and $3/2^{+}$ states in ${}^{229}\mathrm{Th}$ is deemed to be very sensitive to potential changes in the fine structure constant $\alpha$. State of the art Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the difference in Coulomb energies of the two states that determines the sensitivity of the transition frequency ν on variations in $\alpha$. The kinetic energies are also calculated that reflect a possible variation in the nucleon or quark masses. As the two states differ mainly in the orbit occupied by the last unpaired neutron the Coulomb energy difference results from a change in the nuclear polarization of the proton distribution. This effect turns out to be rather small and to depend on the nuclear model. The sensitivity $q_s$ of the frequency shift $\delta \nu$ on $\delta \alpha /\alpha (\delta \nu =q_s\delta \alpha /\alpha )$ varies for the different models between about $+{10}^{20}\hspace{0.5em}\mathrm{Hz}$ and $-{10}^{20}\hspace{0.5em}\mathrm{Hz}$. Therefore, much more effort must be put into the improvement of the nuclear models before one can draw conclusions from a measured drift in the transition frequency on the size of a temporal drift of $\alpha$.

Precise measurements of the reaction cross sections ($\sigma {}_{\mathrm{R}}$) for ${}^{12}\mathrm{C}$ on Be, C, and Al targets and ${}^{11}\mathrm{Be}$ on Be targets were performed in the energy range between 30 and 400 MeV/nucleon. The energy dependencies of $\sigma {}_{\mathrm{R}}$ for ${}^{12}\mathrm{C}$, ${}^{11}\mathrm{Be}$, and ${}^8\mathrm{B}$ were compared to Glauber-type calculations performed using reliable nucleon-density distributions that are supported by experimental data. It was found that the Glauber-type calculations, which include the higher-order multiple scattering effect, the finite-range effect, and the Fermi-motion effect of nucleons in the nucleus, seem to provide a good prescription relating $\sigma {}_R$ at intermediate energies to a proper nucleon-density distribution. This method provides a powerful tool with which to study the nuclear surface structure through the $\sigma {}_{\mathrm{R}}$ measurements.

We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random-Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited $2^{+}$ states for the chain of Sn isotopes with $Z=50$ and the chain of isotones with $N=82$ isotones are calculated in RQRPA together with the $3^{-}$ states of Sn isotopes. By comparing our results with experimental data and with the results of the original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.

Nuclear thermodynamic observables such as temperature, freeze-out volume, and specific heat as obtained from isotopic ratios in hot disassembled nuclear matter are examined in the light of the $S$-matrix approach to the nuclear equation of state. The values of the observables, as extracted without inclusion of scattering effects, are found to be modified appreciably in some cases when scattering between the fragment species is taken care of.

Excitation spectra usually reveal important features of the many-body systems. The vibrational excitations can be studied through the well-known linear response theory. This theory is realized, in the nuclear case, by means of the random-phase approximation (RPA); the generalization in the case in which one deals with open shells, and the pairing force is active, is the quasiparticle RPA (QRPA). It is useful to have at one's disposal theorems that provide information on, e.g., the sum rules and mean excitation energies associated with given external operators acting on the system. This article focuses on such theorems in the case of self-consistent QRPA based on Hartree-Fock-Bogoliubov (HFB). In particular, the so-called dielectric theorem that provides the value of the inverse-energy-weighted sum rule based on the simple knowledge of the ground state is demonstrated. This theorem is applied to the case of constrained calculations of the average excitation energy of the monopole resonance combined with the Thouless theorem. The pairing correlations are shown to have the effect of increasing the polarizability $m_{-1}$. The detailed analysis of the profile of the strength functions by mean of QRPA reveals that the decrease of the average monopole excitation energies in some isotopes is associated with neutron states that emerge at an energy that is lower than the main giant resonance peak.

The proton radioactivity half-lives of spherical proton emitters are investigated theoretically. The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM) including the proximity effects between nuclei in a neck and the mass and charge asymmetry. The penetrability is calculated with the WKB approximation. The spectroscopic factor has been taken into account in half-life calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the BCS method with the force NL3. The half-lives within the GLDM are compared with the experimental data and other theoretical values. The GLDM works quite well for spherical proton emitters when the spectroscopic factors are considered, indicating the necessity of introducing the spectroscopic factor and the success of the GLDM for proton emission. Finally, we present two formulas for proton emission half-life calculation similar to the Viola-Seaborg formulas and Royer's formulas of $\alpha$ decay.

We present a shell-model calculation for the $\beta$ decay of ${}^{14}\mathrm{C}$ to the ${}^{14}\mathrm{N}$ ground state, treating the relevant nuclear states as two $0p$ holes in an ${}^{16}\mathrm{O}$ core. Employing the universal low-momentum nucleon-nucleon potential $V_{\mathrm{low}\hspace{0.5em}k}$ only, one finds that the Gamow-Teller matrix element is too large to describe the known (very long) lifetime of ${}^{14}\mathrm{C}$. As a novel approach to this problem, we invoke the chiral three-nucleon force (3NF) at leading order and derive from it a density-dependent in-medium $\mathit{NN}$ interaction. By including this effective in-medium $\mathit{NN}$ interaction, the Gamow-Teller matrix element vanishes for a nuclear density close to that of saturated nuclear matter, ${\rho }_0=0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$. The genuine short-range part of the three-nucleon interaction plays a particularly important role in this context, since the medium modifications to the pion propagator and pion-nucleon vertex (owing to the long-range 3NF) tend to cancel out in the relevant observable. We discuss also uncertainties related to the off-shell extrapolation of the in-medium $\mathit{NN}$ interaction. Using the off-shell behavior of $V_{\mathrm{low}\hspace{0.5em}k}$ as a guide, we find that these uncertainties are rather small.

The high spin states in the ${}^{139}\mathrm{Ce}$ nucleus have been studied by in-beam $\gamma$-spectroscopic techniques using the reaction ${}^{130}\mathrm{Te}({}^{12}\mathrm{C},3n){}^{139}\mathrm{Ce}$ at $E_{\mathrm{beam}}=65$ MeV. A gamma detector array, consisting of five Compton-suppressed Clover detectors was used for coincidence measurements. 15 new levels have been proposed and 28 new $\gamma$ transitions have been assigned to ${}^{139}\mathrm{Ce}$ on the basis of $\gamma \gamma$ coincidence data. The level scheme of ${}^{139}\mathrm{Ce}$ has been extended above the known 70 ns ${\frac{19}{2}}^{-}$ isomer up to $~6.1$ MeV in excitation energy and $\frac{35}{2}\hslash$ in spin. The spin-parity assignments for most of the newly proposed levels have been made using the deduced Directional Correlation from Oriented states of nuclei (DCO ratio) and the Polarization Directional Correlation from Oriented states (PDCO ratio) for the de-exciting transitions. The observed level structure has been compared with a large basis shell model calculation and also with the predictions from cranked Nilsson-Strutinsky (CNS) calculations. A general consistency has been observed between these two different theoretical approaches.

We study, within a semiclassical coupled-channels approach, the possible effects of anharmonicities and non linearities on the excitation of the so-called pygmy resonances in several Sn isotopes and using two different Skyrme interactions. In the energy region of the pygmy resonances, there are a few low-lying multiphonon states. The question is whether they may contribute to the observed peak. Calculations show that the inelastic cross sections in the relevant energy region have an increase that varies from 3% to 21% depending on the isotope and on the kind of Skyrme force used. At the same time, we have studied the nature of the pygmy resonance state by means of a new criterion to establish whether this state can be considered as a collective one.

The $R$-matrix simulation of three-body decays is investigated as function of available $Q$ value and the energy and width of the intermediate two-body resonance. We use three $\alpha$-decaying unnatural parity states of ${}^{12}\mathrm{C}$ for illustration. The energy distributions are shown to be sensitive to the parameters when the two-body energy is significantly smaller than $Q$ and the width is smaller than about 0.5 MeV. The sequential decay inherent in the $R$-matrix formalism can then be distinguished from direct decay. We provide conditions for the validity of $R$-matrix analyses. We compare with full three-body computations of the same energy distributions where we also attempt to distinguish between sequential and direct decays. The results give a good reproduction of available experimental data and are consistent with the conclusions from $R$-matrix analyses. Nodes in the momentum distributions arise from angular momentum and parity conservation. Combined with symmetry requirements this constrains the momentum distributions significantly in some cases. Effects of interactions and decay mechanisms can only be seen in the remaining behavior as, e.g., additional nodes related to nodes in the coordinate wave function at large distance.

The fission barriers of medium and heavy nuclei are calculated looking for the minimum of liquid drop energy at fixed volume and elongation without using any shape parametrization. The fission barrier heights, obtained within the Lublin-Strasbourg drop model, are approximated by a simple analytical expression as functions of $Z$ and $(N-Z)/A$ only. In addition, using the topological theorem by Myers and Świątecki that allows us to represent the barrier height as the sum of the ground-state microscopic correction (which is calculated and tabulated for all nuclei) and the liquid drop fission barrier, we propose a simple but quite accurate approximation of the fission barrier heights.

A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected (FTBCS1$+$SCQRPA) and Lipkin$+$Nogami projected (FTLN1$+$SCQRPA) theories that include the quasiparticle number fluctuation and coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations are performed for the pairing gap, total energy, heat capacity, entropy, and microcanonical temperature within the doubly folded equidistant multilevel pairing model. The FTLN1$+$SCQRPA predictions agree best with the exact grand-canonical results. In general, all approaches clearly show that the superfluid-normal phase transition is smoothed out in finite systems. A novel formula is suggested for extracting the empirical pairing gap in reasonable agreement with the exact canonical results.

The influence of the medium-dependent finite width of quark gluon plasma (QGP) bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags being heavier than 2 GeV from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown, these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that in addition to the $\sigma T^4$ term the lattice QCD pressure contains $T$-linear and $T^4\ln T$ terms in the range of temperatures between 240 and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at high temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.

We carry out a systematic study of interferometry radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii $R_o$ and $R_s$ as a function of $p_t$ for various values of the Knudsen number, which measures the degree of thermalization in the system. They converge to the hydrodynamical limit much more slowly (by a factor $\simeq 3$) than elliptic flow. This solves most of the HBT puzzle for central collisions: $R_o/R_s$ is in the range 1.1–1.2 for realistic values of the Knudsen number, much closer to experimental data ($\simeq 1$) than the value 1.5 from hydrodynamical calculations. The $p_t$ dependence of $R_o$ and $R_s$, which is usually said to reflect collective flow, also has a very limited sensitivity to the degree of thermalization. We then study the azimuthal oscillations of $R_o$, $R_s$, and $R_{\mathit{os}}$ for noncentral collisions. Their amplitudes depend little on the Knudsen number, and reflect the eccentricity of the overlap area between the two nuclei.

We study coherent and incoherent diffractive hadron production in high-energy quarkonium–heavy nucleus collisions as a probe of the gluon saturation regime of quantum chromodynamics. Taking this process as a model for $\mathit{pA}$ collisions, we argue that the coherent diffractive gluon production, in which the target nucleus stays intact, exhibits a remarkable sensitivity to the energy, rapidity, and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-$x$ dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure of the nuclear effects on diffractive hadron production we introduce a new observable—the diffractive nuclear modification factor. We discuss possible signatures of gluon saturation in diffractive gluon production at the Relativistic Heavy Ion Collider, the Large Hadron Collider, and Electron Ion Collider.

We discuss transport properties of dynamical fluid composed of quasiparticles whose masses depend on temperature and charge chemical potentials. Based on the relativistic kinetic theory formulated under the relaxation time approximation, we derive a general expression for the bulk viscosity in the quasiparticle medium. We show that dynamically generated particle masses imply an essential modification of the fluid compressibility. As an application of our results we consider a class of quasiparticle models with the chiral phase transition belonging to $O(4)$ and $Z(2)$ universality class. Based on the Ginzburg-Landau and the scaling theory we study the critical properties of the bulk viscosity $\zeta$ near the phase transition. We show that extrapolating the results of kinetic theory under the relaxation time approximation near the critical region the $\zeta$ does not show singular behavior near the $O(4)$ and $Z(2)$ critical point through static critical exponents.

We study the correlations between quark-antiquark pairs in different quantum number channels in a deconfined plasma by using an effective model of QCD. Using the three flavor PNJL model, the finite temperature spectral functions for different mesonic states are studied at zero and nonzero quark chemical potentials. It is found that in the $\eta$ channel, resonance structures survive above the chiral transition temperature $T_{\chi }$, while the kaonic states seem to get washed off just above $T_{\chi }$. The sensitivity of the structures to the anomaly term are carefully investigated.

Elastic proton scattering on the ${}^3\mathrm{H}$ nucleus is studied between $p\text{−}{}^3\mathrm{H}$ and $n\text{−}{}^3\mathrm{He}$ thresholds, in the energy region where the first excited state of the $\alpha$ particle is embedded in the continuum. Faddeev-Yakubovski equations are solved in configuration space by fully considering effects from isospin breaking and rigorously treating the Coulomb interaction. Different realistic nuclear Hamiltonians are tested, elucidating open problems in the description of the nuclear interaction.