The cross sections for the glueball candidates in quasireal photon-photon collisions and on central diffraction processes (i.e., double Pomeron exchange) in heavy-ion interactions at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) are computed. The rates for these distinct production channels are compared, and they may be a fruitful approach to the investigation of glueballs.

We discuss low-mass dilepton rates ($⩽1$ GeV) from the deconfined phase of QCD using both perturbative and nonperturbative models and compare them with those from lattice gauge theory and in-medium hadron gas. Our analysis suggests that the rate at very low invariant mass ($M⩽200$ MeV) using the nonperturbative gluon condensate in a semiempirical way within the Green function approach dominates over the Born rate, independent of any uncertainty associated with the choice of the strong coupling in perturbation theory. On the other hand, the rate from $\rho$-$q$ interaction in the deconfined phase is important at $200$ MeV $⩽M⩽$ $1$ GeV as it is almost of same order as the Born rate as well as the in-medium hadron gas rate. Also, the higher order perturbative rate, leaving aside its various uncertainties, from the hard-thermal-loop approximation becomes reliable at $M⩾200$ MeV and also becomes comparable with the Born rate and the lattice rate for $M⩾500$ MeV, constraining on the broad resonance structures in the dilepton rate at large invariant mass. We also discuss the lattice constraints on the low-mass dilepton rate. Furthermore, we discuss a realistic way to advocate the quark-hadron duality hypothesis based on the dilepton rates from quark-gluon plasma and hadron gas.

For $\pi {}^0\eta$ photoproduction on the nucleon formal expressions are developed for the fivefold differential cross section and the recoil polarization including beam and target polarizations. The polarization observables are described by various beam, target, and beam-target asymmetries for polarized photons and/or polarized nucleons. They are given as bilinear Hermitian forms in the reaction matrix elements divided by the unpolarized cross section. Numerical results for the linear and circular beam asymmetries for $\gamma p\to \pi {}^0\eta p$ are obtained within an isobar model and are compared with existing data. Predictions are also given for the target asymmetry $T_{11}$, and the beam-target asymmetries $T_{10}^c$ and $T_{11}^c$ for circularly polarized photons.

Using, for the first time, configuration-constrained potential-energy-surface calculations with the inclusion of ${\beta }_6$ deformation, we find remarkable effects of the high-order deformation on the high-$K$ isomers in ${}^{254}\mathrm{No}$, the focus of recent spectroscopy experiments on superheavy nuclei. For shapes with multipolarity six, the isomers are more tightly bound and, microscopically, have enhanced deformed shell gaps at $N=152$ and $Z=100$. The inclusion of ${\beta }_6$ deformation significantly improves the description of the very heavy high-$K$ isomers.

Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order $Q^3$ from the empirical ${}^1{P}_1$ phase shift. The one divergence that arises can be renormalized using an order-$Q^2$ counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.

A theoretical framework for the calculation of shear and bulk viscosities of hadronic matter at finite temperature is presented. The framework is based on the quasiparticle picture. It allows for an arbitrary number of hadron species with pointlike interactions, and allows for both elastic and inelastic collisions. Detailed balance is ensured. The particles have temperature-dependent masses arising from mean-field or potential effects, which maintains self-consistency between the equation of state and the transport coefficients. As an example, we calculate the shear and bulk viscosity in the linear $\sigma$ model. The ratio of shear viscosity to entropy density shows a minimum in the vicinity of a rapid crossover transition, whereas the ratio of bulk viscosity to entropy density shows a maximum.

We show that the dominant Gamow-Teller part, $M_{\mathrm{GT}}^{0\nu }$, of the nuclear matrix element governing the neutrinoless $\beta \beta$ decay is related to the matrix element $M_{\mathrm{cl}}^{2\nu }$ governing the allowed two-neutrino $\beta \beta$ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance $r$ between the pair of neutrons that are transformed into a pair of protons in the $\beta \beta$ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when $A$ and $Z$ is changed; while $M_{\mathrm{GT}}^{0\nu }$ changes slowly and smoothly, $M^{2\nu }$ has pronounced shell effects. We also discuss the possibility of phenomenological determination of the $M_{\mathrm{cl}}^{2\nu }$ and from them of the $M_{\mathrm{GT}}^{0\nu }$values from the experimental study of the ${\beta }^{\pm }$ strength functions.

The regular systematic behavior of $Q_{\mathrm{p}}$ values is analyzed to provide a basis for estimating $Q$ values for as yet unknown proton and $\alpha$ decays. These estimates are used in predicting partial half-lives for proton and $\alpha$-particle emission from states in Ta, Re, Ir, and Au nuclei beyond the proton drip line. The implications of these predictions for further experimental study in this region are discussed.

The ${\beta }^{+}$ decay of very neutron-deficient ${}^{43}\mathrm{Cr}$ was studied by means of an imaging time projection chamber that allowed recording tracks of charged particles. Events of $\beta$-delayed emission of one, two, and three protons were clearly identified. The absolute branching ratios for these channels were determined to be ($81\pm 4$)%, ($7.1\pm 0.4$)%, and ($0.08\pm 0.03$)%, respectively. ${}^{43}\mathrm{Cr}$ is thus established as the second case in which the $\beta$-3$p$ decay occurs. Although the feeding to the proton-bound states in ${}^{43}\mathrm{V}$ is expected to be negligible, the large branching ratio of ($12\pm 4$)% for decays without proton emission is found.

Recent studies show that for systems with four identical fermions in the $j=9/2$ shell, two special states, which have seniority $v=4$ and total spins $I=4$ and 6, are eigenstates of any two-body interaction. These states have good seniority for an arbitrary interaction. In this work, an analytic proof is given to this peculiar occurrence of partial conservation of seniority, which is the consequence of the special property of certain coefficients of fractional parentage. Further calculations did not reveal its existence in systems with other $n$ and/or $I$ for shells with $j⩽15/2$.

Parity-violating effects for low-energy elastic neutron deuteron scattering are calculated for Desplanques, Donoghue, and Holstein (DDH) and effective field theory types of weak potentials in a distorted-wave Born approximation, using realistic hadronic strong interaction wave functions, obtained by solving three-body Faddeev equations in configuration space. The resulting relation between physical observables and low-energy constants can be used to fix low-energy constants from experiments. Potential model dependencies of parity-violating effects are discussed.

The spectroscopic quadrupole moment of the $T_{1/2}=9.4(5)$ ns isomer in ${}^{193}\mathrm{Pb}$ at an excitation energy $E_{\mathrm{ex}}=(2585+x)$ keV is measured by the time-differential perturbed angular distribution method as $\left|Q_s\right|=2.6(3)$ $e$ b. Spin and parity $I^{\pi }=27/2^{-}$ are assigned to it based on angular distribution measurements. This state is the band head of a magnetic-rotational band, described by the $1i_{13/2}$ subshell with the $(3s_{1/2}^{-2}1h_{9/2}1i_{13/2}){}_{{11}^{-}}$ proton excitation. The pairing-plus-quadrupole tilted-axis cranking calculations reproduce the measured quadrupole moment with a moderate oblate deformation ${\epsilon }_2=-0.11$, similar to that of the ${11}^{-}$proton intruder states, which nuclei in the region. This is the first direct measurement of a quadrupole moment and thus of the deformation of a magnetic-rotational band head.

We analytically calculate the contribution of transverse momentum conservation to the azimuthal correlations that have been proposed as signals for possible local strong parity violation and recently have been measured in heavy ion collisions. These corrections are on the order of the inverse of the total final-state particle multiplicity and, thus, are on the same order as the observed signal. The corrections contribute with the same sign to both like-sign and opposite-sign pair correlations. Their dependence on the momentum is in qualitative agreement with the measurements by the solenoidal tracker at the BNL Relativistic Heavy Ion Collider Collaboration, while the pseudorapidity dependence differs from the data.

Relativistic mean-field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus ${}^{132}\mathrm{Sn}$ and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in ${}^{132}\mathrm{Sn}$ as well as the Nilsson spin-orbit parameter $C$ and orbit-orbit parameter $D$ thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.

A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in $\beta$ and a steep harmonic oscillator in $\gamma$, centered around $\gamma =\pi /6$, is developed. Analytical expressions for spectra and$B(E2)$ transition rates ranging from a triaxial vibrator to the rigid triaxial rotator are obtained and compared to experimental results. Using a variational procedure, we point out that the $Z(5)$ solution, in which an infinite square well potential in $\beta$ is used, corresponds to the critical point of the shape phase transition from a triaxial vibrator to the rigid triaxial rotator.

We investigate the reaction path followed by heavy ion collisions with exotic nuclear beams at low energies. We focus on the interplay between reaction mechanisms, fusion vs. breakup (fast-fission, deep-inelastic), that in exotic systems is expected to be influenced by the symmetry energy term at densities around the normal value. The evolution of the system is described by a stochastic mean-field transport equation, where two parametrizations for the density dependence of symmetry energy (Asysoft and Asystiff) are implemented, allowing one to explore the sensitivity of the results to this ingredient of the nuclear interaction. The method described here, based on the event-by-event evolution of phase-space quadrupole collective modes, nicely allows us to extract the fusion probability at relatively early times, when the transport results are reliable. Fusion probabilities for reactions induced by ${}^{132}\mathrm{Sn}$ on ${}^{64,58}\mathrm{Ni}$ targets at 10 $A$ MeV are evaluated. We obtain larger fusion cross sections for the more $n$-rich composite system, and, for a given reaction, in the Asysoft choice. Finally a collective charge equilibration mechanism (the dynamical dipole) is revealed in both fusion and breakup events, depending on the stiffnsess of the symmetry term just below saturation.

In this work the investigation of the space-time scales of the hadronization process in the framework of a string model is continued. The average formation lengths of several widely used species of baryons (antibaryons) such as $p(\mathrm{p̄}$), $n(\mathrm{n̄}$), $\Delta (\mathrm{\Delta ̄}$), $\Lambda (\mathrm{\Lambda ̄}$), and $\Sigma (\mathrm{\Sigma ̄}$) are studied. It is shown that they depend on electrical charges or, more precisely, on the quark contents of the hadrons. In particular, the average formation lengths of positively charged hadrons, for example, protons, are considerably larger than those of their negatively charged antiparticles, antiprotons. This statement for all nuclear targets and any values of the Bjorken scaling variable $x_{\mathrm{Bj}}$ is fulfilled. The main mechanism is direct production. Additional production mechanism as a result of the decay of resonances gives small contribution. It is shown that the average formation lengths of protons (antiprotons) are slowly increasing (decreasing) functions of $x_{\mathrm{Bj}}$, whereas the ones of neutrons and antineutrons are slowly decreasing functions of $x_{\mathrm{Bj}}$. The shape and behavior of average formation lengths for baryons qualitatively coincide with the ones for pseudoscalar mesons obtained earlier.

Two nonrelativistic quark models, a chiral quark model and a quark delocalization color screening model, are employed to calculate the baryon-baryon scattering phase shifts to look for dibaryon resonances with strangeness by means of the resonating group method. The two models predict similar-strangeness dibaryon resonance states. No resonance appears in the octet-octet channels, but resonance did exist in the octet-decuplet and decuplet-decuplet channels. These resonances were distributed in the energy region 2400–2800 MeV. The widths are generally smaller than 10 MeV but increased to tens of MeV after taking into account the off-shell widths of decuplet baryons. These resonances all appear in the $D$-wave nucleon-hyperon and hyperon-hyperon scatterings and can be searched for through hyperon-nucleon scatterings with hyperon beams and hyperon-hyperon vertex and masses reconstruction with the data collected by relativistic heavy ion collisions.