We derive expressions for various correlators of the gauge field and find the propagators in Hamiltonian dynamics which employs a new gauge $A^{\tau }=0.\mathrm{}$ This gauge is a part of the wedge form of relativistic dynamics suggested earlier as a tool for the study of quantum dynamics in ultrarelativistic heavy ion collisions. We prove that the gauge is completely fixed. The gauge field is quantized and the field of radiation and the longitudinal fields are unambiguously separated. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid factorization.

Using the framework of wedge dynamics, we compute the effective transverse mass of a soft quark mode propagating in the expanding background of hard quarks and gluons created at the earliest time of the collision. We discover that the wedge dynamics does not require any external infrared or collinear cutoff. The effective mass is produced mainly due to the forward quark-quark scattering mediated by the longitudinal (in the sense of Gauss law) magnetic fields. Contribution of the radiation field is parametrically suppressed.

A mean-field equation of state for a hot and dense hadron gas developed earlier, which incorporates excluded volume repulsive interaction between a pair of baryons and the Kaplan-Nelson chiral Lagrangian term for kaon-baryon interactions is used to study the production of strange particle ratios, e.g., $K^{+}/{\pi }^{+},$ $K^{-}/{\pi }^{-},$ and $K^{+}{/K}^{-}.$ We find that the strange particle production is considerably enhanced due to the medium modification of their masses in the hadron gas and, therefore, it gives a hint for a partial restoration of chiral symmetry in a dense and hot medium.

We have evaluated the differential cross section for ${}^{11}\mathrm{Li}$ scattering from protons at 800 MeV/nucleon using the single-scattering approximation to Kerman-McManus-Thaler multiple-scattering expansion of the optical potential, and also the multiple-scattering expansion of the total T matrix. Using the same projectile density distributions and nucleon-nucleon transition amplitudes as inputs, we show that the two scattering frameworks produce significantly different elastic-scattering observables. We also show that the predictions from the two approaches differ because of core recoil and virtual breakup of the valence halo neutrons, which tend to produce opposite effects.

The ${\beta }^{+}$-decay half-lives of the neutron-deficient odd-odd $N=Z$ nuclei ${}^{74}\mathrm{Rb},$ ${}^{78}\mathrm{Y},$ ${}^{82}\mathrm{Nb},$ and ${}^{86}\mathrm{Tc}$ have been measured following the fragmentation of a primary ${}^{92}\mathrm{Mo}$ beam at an energy of 60 MeV per nucleon at the GANIL laboratory, France. This was achieved by correlating ${\beta }^{+}$ decays with the implantation of unambiguously identified fragments at the final focus of the LISE3 separator. The deduced ${\log }_{10}{\mathrm{ft}}_{1/2}$ values are consistent with $0^{+}\to 0^{+},$ Fermi superallowed transitions, which together with the measured ${\beta }^{+}$-detection efficiencies, suggest $T=1,$ $I^{\pi }{=0\mathrm{}}^{+}$ ground states for these odd-odd $N=Z$ nuclei. These data represent the heaviest $N=Z$ systems for which Fermi superallowed decays have been established.

The dynamic deformation theory with the pairing plus quadrupole interaction is applied to study the multiphonon band structure in ${}^{168}\mathrm{Er}.$ Three $K^{\pi }{=0\mathrm{}}^{+},$ two $K^{\pi }{=2\mathrm{}}^{+},$ and $K^{\pi }{=4\mathrm{}}^{+}$ bands have been analyzed. The lower four bands are also analyzed in the interacting boson model. The nature of the $K^{\pi }{=0\mathrm{}}_2$ and $0_3$ and $K^{\pi }{=4\mathrm{}}^{+}$ bands is discussed.

The primary $\gamma$-ray spectra of ${}^{166}\mathrm{Er}$ and ${}^{167}\mathrm{Er}$ are deduced from the ${(}^3\mathrm{He},\alpha \gamma )$ reaction and the ${(}^3\mathrm{He}{,}^3{\mathrm{He}}^{\prime }\gamma )$ reaction, respectively, enabling a simultaneous extraction of the level density and the $\gamma$-ray-strength function. Entropy, temperature, and heat capacity are deduced from the level density within the microcanonical and canonical ensembles, displaying signals of a phaselike transition from the pair-correlated ground state to an uncorrelated state at $T_c\sim 0.5$ MeV. The $\gamma$-ray-strength function displays a bump around $E_{\gamma }\sim 3$ MeV, interpreted as the pygmy resonance.

The role of final state interactions (FSIs) in the inclusive quasielastic disintegration of the deuteron is investigated treating the two-nucleon final state within the exact continuum solutions of the nonrelativistic Schrödinger equation, as well as within the Glauber multiple-scattering approach. It is shown that for values of the Bjorken scaling variable $x_{\mathrm{Bj}}\simeq 1$ both approaches provide similar results, except for the case $x_{\mathrm{Bj}}\gtrsim 1,$ where they appreciably disagree. It is demonstrated that present experimental data, which are mostly limited to a region of four-momentum transfer $[Q^2\lesssim 4\hspace{0.5em}(\mathrm{GeV}{/c)}^2]$ where the center-of-mass energy of the final state is below the pion threshold production, can be satisfactorily reproduced by an approach based on an exact solution of the Schrödinger equation and not by the Glauber approach.

Contributions of nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ correlations, meson exchange currents, and the residual final state interactions (FSIs) on exclusive two-nucleon knockout reactions induced by electron scattering are investigated. All contributions are derived from the same realistic meson exchange model for the $\mathrm{NN}$ interaction. Effects of correlations and FSIs are determined in a consistent way by solving the $\mathrm{NN}$ scattering equation, the Bethe-Goldstone equation, for two nucleons in nuclear matter. One finds that the FSI rescattering terms are non-negligible even if the two nucleons are emitted back to back.

The quantum mechanical formula for Mayer’s second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The proper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second cluster integral for the pion gas is calculated in quantum mechanical approach accounting for both attractive and hard-core repulsive interactions. It is shown that, in the second cluster approximation, the repulsive $\pi \pi$-interactions as well as the finite width of resonances give important but almost canceling contributions. In contrast, an appreciable deviation from the ideal gas of pions and pion resonances is observed beyond the second cluster approximation in the framework of the Van der Waals excluded-volume model.

We discuss the fact that yrast levels in vibrational-like even-even nuclei do not follow the simple first-order anharmonic relation if $6^{+}$ and $8^{+}$ states are taken into account. The interpretation in terms of the vibrator model with three-phonon interactions is in contrast to the earlier description using the $U\left(5\right)\mathrm{}$ limit of the interacting boson model-1 with an anomalous energy of the $2_1^{+}$ state. The recently discovered peak in the statistical distribution of the $4_1^{+}$ to $2_1^{+}$ energy ratio at $R_{4/2}\approx 2.3,$ supports the latter viewpoint.

We propose a collective Hamiltonian which incorporates quadrupole terms, octupole terms classified according to the irreducible representations of the octahedron group, a quadrupole-octupole interaction, as well as a term for the bandhead energy linear in K (the projection of angular momentum on the body-fixed z axis). The energy is subsequently minimized with respect to K for each given value of the angular momentum I, resulting in K values increasing with I within each band, even in the case in which K is restricted to a set of microscopically plausible values. We demonstrate that this Hamiltonian is able to reproduce a variety of “beat” patterns observed recently for the odd-even staggering in octupole bands of light actinides.

A spherical-deformed shape coexistence for semimagic pf-shell nuclei is investigated. Deformed states can arise by breaking the $f_{7/2}$ submagic shell, and coexist with spherical yrast states for ${}^{54}\mathrm{Fe}.$ These states are shown to be primarily two-particle two-hole excitations on top of the respective correlated ground states. In addition to these modes, a four-particle–four-hole excitation can be found for ${}^{54}\mathrm{Fe},$ which is related to the deformed band of doubly magic ${}^{56}\mathrm{Ni}.$ To investigate this shape coexistence, we use the conventional shell-model diagonalization, constrained Hartree-Fock, generator coordinate, variation-after-projection, and Monte Carlo shell-model methods.

I comment on the recent article of M.C. Güçlü [Phys. Rev. C 61, 054903 (2000)] on higher-order effects in pair production in heavy-ion collisions. It is pointed out that the uncritical use of earlier results may lead to wrong results. Various assumptions and statements of the article are confronted with the present status of the theoretical investigations on this field of research.

In this Reply, I will show that including the Coulomb corrections to the lepton-pair production in heavy-ion collisions also violates the unitarity. Therefore, the points stressed by U. Eichmann are not complete and the multipair production problem is still an open question.

We develop a toy model for pion production in nucleon-nucleon collisions that reproduces some of the features of the chiral Lagrangian calculations. We calculate the production amplitude and examine some common approximations.

We have carried out a study of the structure of heavy exotic nuclei and superheavy elements in the framework of the relativistic mean field (RMF) theory, adopting a new relativistic force, (NL-RA1). Pairing correlations, are treated in the Bardeen-Cooper-Schrieffer formalism with a constant gap approximation, adopting a new model for the energy gap, where a Gaussian shape distribution depending on the particle numbers is assumed. This pairing model is found to successfully describe heavy open shell nuclei. The new relativistic force NL-RA1 successfully reproduced the ground state properties of finite nuclei as well as nuclear matter. This force is used to study the structure of Sn and Pb isotopic chains, while considering extreme values of isospin. It is found that the binding energies, neutron and proton rms radii, and neutron skins are fairly described. Furthermore, the charge rms radii, and the anomalous kind in the isotopic shifts of the charge radii of the Pb isotopic chain are also well described by the NL-RA1 force. In comparison with other relativistic forces like, TM1, NL-SH, and NL1 it is found that the TM1 force could describe the binding energy, while it overestimates the charge radii of Pb isotopes. The NL-SH produced larger binding in the lighter side of ${}^{208}\mathrm{Pb}$ and smaller charge radii. The NL1 force shows systematic discrepancies in both the binding energies as well as the charge radii, due to their larger symmetry energies. Other relativistic forces, like NL-Z and NL-Z2, have also been tested and found to largely overestimate the charge radii of Pb isotopes. We also investigated the ground state properties of superheavy elements in the region $Z>~98$ and it is found that the NL-RA1 force fairly described the binding energy. The element ${}_{184}^{298}114$ is predicted to be the next spherically doubly magic superheavy nucleus to ${}^{208}\mathrm{Pb},$ where a large stable two-proton gap for the $Z=114\mathrm{}$ proton shell on the order of 3 MeV, depending on the effective interaction and pairing model, has been predicted. We also found strong evidence of other spherically doubly magic superheavy elements, such as the element ${}_{172}^{292}120.$

Proton and $\alpha$ emission from ${}^{185}\mathrm{Bi}$ have been confirmed and measured with improved statistics. The ${}^{185}\mathrm{Bi}$ nuclei were produced via the ${}^{95}\mathrm{Mo}{(}^{92}\mathrm{Mo},pn)$ reaction at a bombarding energy of 420 MeV. The proton decay energy from the ${1/2}^{+}$ intruder state in ${}^{185}\mathrm{Bi}$ to the ${}^{184}\mathrm{Pb}$ ground state was measured to be 1.598(16) MeV with a proton branching ratio $b_p=0.85\mathrm{}\left(6\right).$ An $\alpha$ decay branch from the same state was measured, $b_{\alpha }=0.15\mathrm{}\left(6\right),$ with an energy of 8.08(3) MeV. The state has a half-life of 50(8) $\mu \mathrm{s}.$ In addition, the $\alpha$ branching ratio of the ground state of ${}^{184}\mathrm{Pb}$ was determined for the first time to be $b_{\alpha }=0.23\mathrm{}\left(14\right).$

An upper limit of 5 keV on the width of the ${}^{12}\mathrm{O}$ ground state due to ${}^2\mathrm{He}$ emission is calculated using R-matrix formulas. This limit is much less than a recently published estimate.