For the linear σ model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high density. In the latter solution, the formation of droplets of massless quarks is realized even at low density.

A large body of data for pion-induced neutral pion continuum spectra spanning outgoing energies near 180 MeV shows no dip there that might be ascribed to internal strong absorption processes involving the formation of Δ’s. This is the same observation previously made for the charged pion continuum spectra. Calculations in an intranuclear cascade model or a cascade exciton model with free-space parameters predict such a dip for both neutral and charged pions. We explore several medium modifications to the interactions of pions with internal nucleons that are able to reproduce the data for nuclei from ${}^7\mathrm{Li}$ through Bi.

We investigate the interplay of collective and chaotic motion in a classical self-bound N-body system with two-body interactions. This system displays a hierarchy of three well-separated time scales that govern the onset of chaos, damping of collective motion and equilibration. Comparison with a mean-field problem shows that damping is mainly due to dephasing. The Lyapunov exponent, damping, and equilibration rates depend mildly on the system size N.

The influence of multiboson effects on pion multiplicities, single-pion spectra, and two-pion correlation functions is discussed in terms of an analytically solvable model. The applicability of its basic factorization assumption is clarified. An approximate scaling of the basic observables with the phase space density is demonstrated in the low density (gas) limit. This scaling and also its violation at high densities due to the condensate formation is described by approximate analytical formulas which allow, in principle, for the identification of the multiboson effects among others. For moderate densities indicated by the experimental data, a fast saturation of multiboson effects with the number of contributing cumulants is obtained, allowing for the account of these effects in realistic transport code simulations. At high densities, the spectra are mainly determined by the universal condensate term and the initially narrow Poisson multiplicity distribution approaches a wide Bose-Einstein one. As a result, the intercepts of the inclusive and fixed-$n$ correlation functions (properly normalized to 1 at large relative momenta) approach 2 and 1, respectively, and their widths logarithmically increase with the increasing phase space density. It is shown that the neglect of energy-momentum constraints in the model is justified except near a multipion threshold, where these constraints practically exclude the possibility of a very cold condensate production. It is argued that spectacular multiboson effects are likely to be observed only in the rare events containing sufficiently high density (speckle) fluctuations.

We continue our studies of a relativistic quark model that features chiral symmetry, covariance, and confinement. In this work we apply our model to the study of scalar-isoscalar mesons. Several of the parameters of the model have been determined in our earlier work, so that only two new parameters are needed for our analysis. We find a good fit to the spectrum of the $f_0$ mesons, if we add a glueball with energy of about 1700 MeV. In this model we are rather close to “ideal mixing,” with the $f_0\mathrm{}\left(980\right)\mathrm{}$ having the largest $s\overline{s}$ mixture of 10%. The $f_0\mathrm{}\left(1370\right)\mathrm{}$ is the nodeless $s\overline{s}$ state, while the $f_0\mathrm{}\left(1500\right)\mathrm{}$ is a $n\mathrm{n̄}=(uū+d\overline{d})/\sqrt{2}$ state with a single node. [The presence of that node accounts for the small width of the $f_0\mathrm{}\left(1500\right).]$ The next state is a $n\mathrm{n̄}$ state with two nodes at 1843 MeV. Thus, we identify the $f_0\mathrm{}\left(1770\right)\mathrm{}$ as the state with the largest glueball component. It was found that the vacuum polarization functions that describe coupling to the two-meson and other continuum meson channels play an important role in achieving a good fit to the experimentally determined spectrum. In this work we use a Gaussian regulator in all our calculations of meson decay amplitudes. In the first part of our study we multiply the Gaussian regulator by a $P^2$-dependent factor that was chosen so as to modify the threshold behavior of our polarization functions. With that factor in place, we can study the spectrum of $f_0$ states without introducing the imaginary parts of the polarization functions that describe decay to the two-meson continuum. When we do introduce the imaginary parts, we use the vacuum polarization functions with unmodified threshold behavior. The use of the $P^2$-dependent factor helps to clarify the nature of the $f_0(400\mathrm{}–1200),$ which is seen, in part, to have its origin as a rather complex threshold effect associated with the rapid increase of the amplitudes for decay to the ππ and $K\overline{K}$ channels. [For a full understanding of the $f_0(400\mathrm{}–1200)$ one needs to also consider the role of t-channel ρ exchange.] The model used in this work is based upon weak quarkonium-glueball coupling. However, the four-pion decay of the $f_0\mathrm{}\left(1370\right)\mathrm{}$ and the $f_0\mathrm{}\left(1500\right)\mathrm{}$ suggests that these states may be strongly mixed with the glueball, which may have a large four-pion decay width. It is also possible that mixing of these states with the $f_0\mathrm{}\left(980\right)\mathrm{}$ may be important for understanding the four-pion decay widths. We provide a short discussion of quarkonium-glueball mixing in a schematic model. There is not enough information presently available to treat that problem in an unambiguous manner.

The low-energy spectra and $B\left(E2\mathrm{}\right)\mathrm{}$ electromagnetic transition strengths of ${}^{159}\mathrm{Eu},$ ${}^{159}\mathrm{Tb},$ and ${}^{159}\mathrm{Dy}$ are described using the pseudo SU(3) model. Normal parity bands are built as linear combinations of SU(3) states, which are the direct product of SU(3) proton and neutron states with pseudospin zero (for even number of nucleons) and pseudospin 1/2 (for odd number of nucleons). Each of the many-particle states has a well-defined particle number and total angular momentum. The Hamiltonian includes spherical Nilsson single-particle energies, the quadrupole-quadrupole and pairing interactions, as well as three rotor terms which are diagonal in the SU(3) basis. The pseudo SU(3) model is shown to be a powerful tool to describe odd-mass heavy deformed nuclei.

A comparison of calculated and experimental $Q_{\alpha }$ values of superheavy even-even nuclei and a few selected odd-$N$ nuclei is presented in the framework of the relativistic mean-field model with the parametrization NL-Z2. Blocking effects are found to be important for a proper description of $Q_{\alpha }$ of odd mass nuclei. The model gives a good overall description of the available experimental data. The mass and charge assignment of the recently measured decay chains from Dubna and Berkeley is in agreement with the predictions of the model. The analysis of the new data does not allow a final conclusion about the location of the expected island of spherical doubly magic superheavy nuclei.

The measured $K^{+}/{\pi }^{+}$ ratios from heavy-ion reactions are compared with the $K^{+}/{\pi }^{+}$ ratios from $p+p$ reactions over the energy range $2-160A\hspace{0.5em}\mathrm{GeV}.$ The $K/\pi$ enhancement in heavy-ion reactions is largest at the lower energies, consistent with strangeness production in secondary scattering becoming relatively more important than initial collisions near the kaon production threshold. The enhancement decreases steadily from 4 to $160A\hspace{0.5em}\mathrm{GeV},$ suggesting that the same enhancement mechanism of hadronic rescattering and decay of strings may be applicable over this full energy range. Based on existing data, the midrapidity $K^{+}/{\pi }^{+}$ ratio is predicted to be $0.25\pm 0.02$ for the forthcoming Pb+Pb reactions at $40A\hspace{0.5em}\mathrm{GeV}/c.\mathrm{}$

Production of $J/\psi$ from nucleus-nucleus reactions depends sensitively on the dissociation cross section with light hadrons. Effective Lagrangian methods are used to describe the hadronic degrees of freedom, including strangeness and charm. Cross sections with pions, rho mesons, kaons, and nucleons having magnitudes 4–8 mb are found, and with steep thresholds. This, folded with thermal momentum distributions for the scattering partners, suggests a mean dissociation lifetime $\simeq 20\mathrm{fm}/c.\mathrm{}$ Therefore, the “abnormal” $J/\psi$ suppression seen in recent $\mathrm{Pb}+\mathrm{Pb}$ experiments seems to owe a debt to expected hadron kinetics.

We investigate the production of the $\phi$ meson and the $\Omega$ baryon which interact relatively weakly with hot hadronic matter, their spectra thus reflecting the early stage of the heavy ion collisions. Our analysis shows that the hadronization temperature, $T_{\mathrm{had}},$ and the transverse flow, $v_T^0,$ of the initial deconfined phase are strongly correlated: $T_{\mathrm{had}}+a\cdot {(v}_T^0{)}^2=0.25\mathrm{}$ GeV, where $a=0.37\mathrm{}$ GeV in the Pb+Pb collision at $158A$ $\mathrm{GeV}/c.\mathrm{}$ When choosing appropriate initial values of $T_{\mathrm{had}}$ and $v_T^0$ from the temperature region $T_{\mathrm{had}}=175\mathrm{}\pm 15$ MeV, the measured $\rho$ meson spectra was reproduced surprisingly well by the MICOR model. We have found weak influence of final state hadronic interactions on the transverse hadron spectra at $m_T-m_i>0.3\mathrm{}\mathrm{GeV}.\mathrm{}$

Multiparticle boson states, proposed recently for “independently” emitted pions in heavy-ion collisions, are reconsidered in standard second quantized formalism and shown to emerge from a simplistic chaotic current dynamics. Compact equations relate the density operator, the generating functional of multiparticle counts, and the correlator of the external current to each other. “Bose-Einstein condensation” is related to the external pulse. A quantum master equation is advocated for future Monte Carlo simulations.

Inelastic excitation of ${}^{170}\mathrm{Er}$ by a ${}^{238}\mathrm{U}$ beam, studied at near-barrier energies, has led to the observation of unusual features in rotational bands built on low-lying vibrations. The population of the high-spin members of the $K^{\pi }{=0\mathrm{}}^{+},$ $\beta$-vibrational band is enhanced due to mixing with the $K^{\pi }{=2\mathrm{}}^{+},$ $\gamma$-vibrational band at spin $4^{+}.$ Strong mixing of the $K^{\pi }{=0\mathrm{}}^{+}$ band with a rotationally aligned 2 qp band results in this band losing its $\beta$-vibrational character and in a rapid gain in spin alignment leading to a crossing with the ground-state band between spins ${20}^{+}$ and ${22}^{+}.$ The low-lying $K^{\pi }{=3\mathrm{}}^{+}$ band also is populated. It subsequently decays to both the $\gamma$-vibrational and the ground-state bands. The occurrence of appreciable K-forbidden $E2\mathrm{}$ transitions from the $K^{\pi }{=3\mathrm{}}^{+}$ to the ground-state band is attributed to mixing with the $K^{\pi }{=2\mathrm{}}^{+}$ band, caused by the interaction between the quadrupole $\gamma$-vibrational and the hexadecapole vibrational motions.

The existence and importance of collective vibrational quadrupole bands on top of two-particle excitations in spherical even-even nuclei is investigated on the example of Te isotopes. Three types of structures are suggested in the framework of the quasiparticle-phonon model and are compared to experimental data systematized from the literature and confirmed by recent experiments. It is suggested that complex structures of the type $[2\mathrm{QP}\otimes n$ phonons] play an important role in the structure of the $8^{+}$ and ${10}^{+}$ states below 4.5 MeV in the Te isotopes.

In three-body models of halo nuclei such as ${}^6\mathrm{He},$ Pauli blocking is needed to remove components of the halo wave function that would disappear under full antisymmetrization. We compare a full projection-operator method with two others presently used for the purpose. A range of differences is found, small for bound states and resonances but larger for nonresonant continuum states. We indicate discriminating characteristics sensitive to the off-shell behavior.

Data for the scattering of ${}^6\mathrm{He},$ ${}^8\mathrm{He},$ ${}^9\mathrm{Li},$ and ${}^{11}\mathrm{Li}$ from hydrogen are analyzed within a fully microscopic folding model of proton-nucleus scattering. Current data suggest that of these only ${}^{11}\mathrm{Li}$ has a noticeable halo. For ${}^6\mathrm{He},$ we have also analyzed the complementary reaction ${}^6\mathrm{Li}(\gamma ,{\pi }^{+}{)}^6{\mathrm{He}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}.$ The available data for that reaction support the hypothesis that ${}^6\mathrm{He}$ may not be a halo nucleus. However, those data are scarce and there is clearly a need for more to elicit the microscopic structure of ${}^6\mathrm{He}.$

In a detailed investigation of giant dipole resonance (GDR) γ-ray yield from the ${}^{16}{\mathrm{O}+}^{208}\mathrm{Pb}$ system, the absolute γ-ray/fission multiplicities are extracted and reported over a wide range of excitation energy and angular momentum. The enhanced yield of GDR decay γ rays from the compound system has been analyzed within the framework of a modified statistical model containing the nuclear viscosity as a free parameter. The nuclear viscosity parameter γ has been studied over a much wider range of excitation energy and angular momentum than in earlier works. The measured γ-ray multiplicities as well as known neutron multiplicities and evaporation residue cross sections indicate a strongly damped fission motion. The systematics of the extracted dissipation coefficient is fitted equally well with either temperature or a deformation-dependent nuclear viscosity.

The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, (1+1)-dimensional bag model, three-dimensional harmonic oscillator and the Hulthén potential. The latter provide simplified versions of momentum distributions and form factors of relevance to experiments. In particular, the relativistic correction to the mean square radius of a nucleus is shown to be very small. Solving these simple examples suggests another more general approach—the use of tilted light front coordinates. The simple examples are made even simpler.

Proton decay from ${}^{151}\mathrm{Lu}$ is analyzed in the perspective of decay from a deformed nucleus. The experimental values of the half-life for decay from the ground state and the recently found isomeric state are very well described as decay from a ${K=5/2\mathrm{}}^{-}$ ground state and a ${K=3/2\mathrm{}}^{+}$ isomeric state with an oblate deformation -0.18<β<-0.14. With this deformation one is able to describe consistently both decays, using the correct spectroscopic factors, which is not possible in a spherical interpretation.

The asymptotic behavior of three-body scattering wave functions in configuration space is studied by considering a model equation that has the same asymptotic form as the Faddeev equations. Boundary conditions for the wave function are derived, and their validity is verified by numerical calculations. It is shown that these boundary conditions for the partial differential equation can be used to obtain accurate numerical solutions for the wave function.