In the framework of the Glauber multiple scattering theory, the complete expansion (which contains $2^{A\times B}-1$ terms) of the Glauber amplitude of elastic scattering between two nuclei A, $B>~4$ is obtained. Using double Gaussian density consistent with the electron-scattering experiments, the differential cross section $(\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}+\mathrm{C}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{o}\mathrm{m}\mathrm{b})$ is calculated and compared with the experimental data. It is shown that, in general, higher order terms give a substantial improvement in comparison with the previous optical limit results at relatively large scattering angles. The effect of invoking a phase-variation in the nucleon-nucleon (NN) amplitude is examined. We found that the presence of the phase variation improves our results, especially at the minima of the diffraction pattern.

A systematic study of the spectra and yields of $K^{+}$ and $K^{-}$ is reported by experiment E866 as a function of centrality in Au+Au collisions at $11.6A\hspace{0.5em}\mathrm{GeV}/c.\mathrm{}$ The invariant transverse spectra for both kaon species are well described by exponentials in $m_t,$ with inverse slope parameters that are largest at midrapidity and which increase with centrality. The inverse slopes of the $K^{+}$ spectra are slightly larger than the inverse slopes of the $K^{-}$ spectra. The kaon rapidity density peaks at midrapidity with the $K^{+}$ distribution wider in rapidity than $K^{-}.$ The integrated total yields of $K^{+}$ and $K^{-}$ increase nonlinearly and steadily with the number of projectile participants. The yield per participant for kaons is two to three times larger than the yield from $N-N$ collisions. This enhancement suggests that the majority of kaons in central Au+Au reactions are produced in secondary hadronic collisions. There is no evidence for an onset of additional kaon production from a possible small volume of baryon-rich quark-gluon plasma. The differences between $K^{+}$ and $K^{-}$ rapidity distributions and transverse spectra are consistent with a lower phase space for $K^{-}$ production due to a higher energy threshold. These differences also exclude simple thermal models that assume emission from a common equilibrated system.

We report the measurement of secondary charge and isotopic fragmentation cross sections in a liquid hydrogen target from 30 incident beams of relativistic nuclei ranging from ${}^{10}\mathrm{B}$ to ${}^{55}\mathrm{Mn}.$ These individual beams were obtained by initially accelerating 580 MeV/nucleon ${}^{40}\mathrm{Ar}$ and 630 MeV/nucleon ${}^{56}\mathrm{Fe}$ nuclei and letting these nuclei interact in a thin ${\mathrm{CH}}_2$ target in the beam line. The fragments of these interactions were then focused according to their $A/Z$ ratios onto a hydrogen target and the charge and isotopic composition of the fragmentation in this target was measured using our standard cosmic ray telescope. Several of these nuclei have had their cross sections measured previously and a comparison with earlier data confirms the estimated precision ∼5% of the new cross section data. The 30 nuclei for which the cross sections were measured doubles the previously reported data for 15 nuclei from several experiments in the charge range from Li to Ni. The systematics of these new cross sections are discussed both with respect to the charge changing and isotopic cross sections. These systematics will lead to improvements in the productive capability of the formulas used to describe the unmeasured cross sections. It should be noted, however, that from the point of view of the propagation of galactic cosmic rays through the interstellar medium, which is one of the main goals of this experiment, the fragmentation cross sections have now been measured at at least one energy for over 98% of the arriving particles with $Z=3\mathrm{}–28.$

The multifractal nature of target residues in ${}^{16}\mathrm{O}-\mathrm{A}\mathrm{g}\mathrm{B}\mathrm{r}$ interactions at $60A\mathrm{GeV}$ and ${}^{32}\mathrm{S}-\mathrm{A}\mathrm{g}\mathrm{B}\mathrm{r}$ interactions at $200A\mathrm{GeV}$ has been observed using the $〈G_q〉$-moment and T-moment (Takagi’s) methods.

Based on a particle groups correlation function, a new type of inferring collectivity of collective flow is proposed in this paper. Using this method, the particle group correlations arising from collective flow are analyzed for collisions of $1.2A\mathrm{GeV}$ ${\mathrm{A}\mathrm{r}+\mathrm{B}\mathrm{a}\mathrm{I}}_2$ and $2.1A\mathrm{GeV}$ $\mathrm{N}\mathrm{e}+\mathrm{N}\mathrm{a}\mathrm{F}$ in the Bevalac streamer chamber. The results have been compared with Monte Carlo simulation, which show that the collectivities are between 80 and 95 % for the experimental events in collisions of ${\mathrm{A}\mathrm{r}+\mathrm{B}\mathrm{a}\mathrm{I}}_2,$ and between 75 and 95 % for the experimental events in collisions of $\mathrm{N}\mathrm{e}+\mathrm{N}\mathrm{a}\mathrm{F}.$

Dimuonium (the bound system of two muons, the ${\mu }^{+}{\mu }^{-}$-atom system) has not been observed yet. In this paper we discuss the electromagnetic production of dimuonium at RHIC and LHC in relativistic heavy ion collisions. The production of parastates is analyzed in the equivalent photon approximation. For the treatment of orthostates, we develop a three-photon formalism. We determine the production rates at RHIC and LHC with an accuracy of a few percent and discuss problems related to the observation of dimuonium.

A two phase cascade is presented for ultrahigh energy ion-ion collisions from $\sqrt{s}=17\mathrm{}–200\mathrm{GeV}.$ First a high-energy cascade is performed, in which original baryons and any freed hard partons collide. This stage ignores energy loss from soft processes. In this first version no hard processes, aside from Drell-Yan production, are included. The space-time history of the hard cascade is used to reconstruct the soft energy loss. Soft meson production is treated as coherent over groups of interacting nucleons. Two body data, though, are used to guide this reconstruction. A second, low-energy cascade is then carried out. The model selected to describe elementary hadron-hadron collisions in the soft cascade incorporates generic mesons and baryons as the agents for rescattering. We imagine a constituent quark model applies, with generic mesons consisting of an excited $q\overline{q}$ pair, and generic baryons constructed from three quarks. The chief result is a reconciliation of the important Drell-Yan measurements, indicating high-mass lepton pairs are produced as if no energy is lost from the nucleons, with the apparent success of a purely hadronic, soft cascade in describing nucleon stopping and meson production in heavy ion experiments at the CERN SPS. The LUCIFER II code may be downloaded under the GNU General Public License from http://bnlnth.phy.bnl.gov/.

A relativistic quantum mechanics of constituents is formulated in which particles are bound states of a mass operator. The point form of relativistic dynamics is used, in which Lorentz transformations are kinematic, and the four-momentum operator carries all the interactions. A general covariant expression for matrix elements of the electromagnetic current operator is given in which the invariant form factors are reduced matrix elements of the Poincaré group. A point form relativistic impulse approximation is formulated, in which invariant form factors of particles are given in terms of their underlying constituents.

Isobar amplitudes for pion-nucleon elastic and production reactions are constructed from a dynamical theory. The framework of point form relativistic quantum mechanics is used to derive a relativistic Lippmann-Schwinger equation linking elastic and production channels. The dynamics is contained in a mass operator which is the sum of a free and interacting mass operator. For a separable interacting mass operator, the Lippmann-Schwinger equations can be solved analytically; the resulting matrix equations have determinants whose zeros give the positions of multiple resonances in the same angular momentum channels. Though varying parameters to fit data is highly nonlinear, procedures are developed for fitting elastic and inelastic data. Fits to data are presented for the $P_{33}$ partial wave channel in pion-nucleon scattering.

To carry out calculations dealing with relativistic multiparticle systems requires making a choice of variables that describe the system. Simultaneously coupled states, wherein n single-particle states are coupled together simultaneously rather than in a stepwise fashion, are defined and the resulting variables compared with stepwise variables. Generalized Racah coefficients that connect stepwise coupled states with simultaneously coupled states are derived for three-particle systems and used to calculate properties of resonances in isobar models. Invariants of simultaneously coupled states include orbital and spin angular momentum variables. It is shown how these variables can be coupled together in exactly the same way as is done nonrelativistically.

Various models for pion multiplicity distributions produced in relativistic heavy ion collisions are discussed. The models include a relativistic hydrodynamic model, a thermodynamic description, an emitting source pion laser model, and a description which generates a negative binomial description. The approach developed can be used to discuss other cases which will be mentioned. The pion probability distributions for these various cases are compared. Comparison of the pion laser model and Bose-Einstein condensation in a laser trap and with the thermal model are made. The thermal model and hydrodynamic model are also used to illustrate why the number of pions never diverges and why the Bose-Einstein correction effects are relatively small. The pion emission strength $\eta$ of a Poisson emitter and a critical density ${\eta }_c$ are connected in a thermal model by $\eta {/n}_c{=e}^{-m/T}<1,$ and this fact reduces any Bose-Einstein correction effects in the number and number fluctuation of pions. Fluctuations can be much larger than Poisson in the pion laser model and for a negative binomial description. The clan representation of the negative binomial distribution due to Van Hove and Giovannini is discussed using the present description. Applications to CERN/NA44 and CERN/NA49 data are discussed in terms of the relativistic hydrodynamic model.

We extract pole positions for the $N\left(1535\right)\mathrm{}$ and $N\left(1650\right)\mathrm{}$ resonances using two different models. The positions are determined from fits to different subsets of the existing $\pi \overrightarrow{N}\pi N$, $\pi \overrightarrow{N}\eta N,$ and $\gamma \overrightarrow{p}\eta p$ data and found to be $1510\left(10\right)\mathrm{}–i85\mathrm{}\left(15\right)\mathrm{}$MeV and $1660\left(10\right)\mathrm{}–i70\mathrm{}\left(10\right)\mathrm{}$MeV, when the data is described in terms of two poles. Sensitivity to the choice of fitted data is explored. The corresponding $\pi \pi$ and $\eta \eta$ residues of these poles are also extracted.

We calculate quark distribution functions and $F_2$ structure functions for protons and neutrons. The calculation is performed in the light-cone frame. The dressed nucleon is assumed to be a superposition of the bare nucleon plus virtual light-cone Fock states of baryon-meson pairs. The bare nucleon is assumed to be composed of a diquark and a quark. The initial distributions are evolved. The $F_2$ structure functions calculated from the evolved distributions are compared with NMC results. Also, the Gottfried sum rule is calculated and observed to be violated. However, the degree of violation is smaller than observation, an indication that the meson cloud model is not the only source of contribution to the Gottfried sum-rule violation.

We continue our studies of a unified model of meson structure that makes use of a Nambu–Jona-Lasinio (NJL) model that has been generalized to include a relativistic model of confinement. (We use Lorentz-vector confinement, so that the Lagrangian exhibits chiral symmetry in the absence of a quark mass matrix.) Here we study φ-ω and $\eta -{\eta }^{\prime }$ mixing. The latter study requires that we include the ’t Hooft interaction in our model. We study states of $\overline{q}q$ structure for energies $P^2<~3{\mathrm{GeV}}^2.$ The coupled φ-ω system exhibits ideal mixing, such that the ω and its radially-excited states have no strange quark content, while the φ states are pure $s\overline{s}$ configurations. In the case of $\eta -{\eta }^{\prime }$ mixing, the ’t Hooft interaction gives rise to a $P^2$-dependent mixing angle ${\theta }_P{(P}^2).\mathrm{}$ At the energy of the η(547), ${\theta }_P{(m}_{\eta }^2)=-11.5°,$ while at the energy of the ${\eta }^{\prime }\mathrm{}\left(958\right),$ we have ${\theta }_P{(m}_{{\eta }^{\prime }}^2)=-36.3°,$ if we take singlet-octet mixing into account. We obtain a satisfactory fit to experimental values for energies of the radially-excited states of the φ-ω system, as well as for the decay constants of the ω(782) and the φ(1020). The predictions for the radially-excited $\overline{q}q$ states of the η and ${\eta }^{\prime }$ are not as good, if those states are to be identified as the η(1295) and η(1440). [However, we do find a state at 1370 MeV which is halfway between the η(1295) and η(1440). That suggests the presence of a non-$q\overline{q}$ state that could mix with our state at 1370 MeV to produce the two states at 1295 and 1440 MeV. The state at 1370 MeV is found to have very little $s\overline{s}$ component. Thus one might suggest a correspondence with the ω(1420), which is also a $2S$ state.] Further work is needed to understand the spectrum of the $\eta -{\eta }^{\prime }$ system of states above $P^2=1.0\mathrm{}{\mathrm{GeV}}^2,$ where one may encounter low-energy pseudoscalar glueball states. We extend our work on singlet-octet mixing to include pseudoscalar-axialvector mixing. In that case there are two mixing angles and two coupling constants to be calculated. It is found that the spectrum obtained with singlet-octet mixing is largely unchanged upon addition of pseudoscalar-axialvector mixing, if a small value for the strength of the ’t Hooft interaction is used. A small ’t Hooft interaction implies ideal mixing for the $\eta -{\eta }^{\prime }$ pair. It remains to be seen if the wave functions in this case are consistent with experimental decay rates.

As a consequence of dynamical chiral symmetry breaking the pion Bethe-Salpeter amplitude necessarily contains terms proportional to ${\gamma }_5\gamma \cdot P$ and ${\gamma }_5\gamma \cdot k,$ where $k$ is the relative and $P$ the total momentum of the constituents. These terms are essential for the preservation of low-energy theorems, such as the Gell-Mann–Oakes-Renner relation and those describing anomalous decays of the pion, and to obtaining an electromagnetic pion form factor that falls as ${1/q}^2$ for large $q^2,$ up to calculable $\ln q^2$ corrections. In a simple model, which correlates low- and high-energy pion observables, we find $q^2{F}_{\pi }{(q}^2)\sim 0.12–0.19{\mathrm{GeV}}^2$ for $q^2\gtrsim 10{\mathrm{GeV}}^2.$

Octet hyperon charge radii are calculated in a chiral constituent quark model including electromagnetic exchange currents between quarks. In the impulse approximation one observes a decrease of the hyperon charge radii with increasing strangeness. This effect is reduced by exchange currents. Due to exchange currents, the charge radius of the negatively charged hyperons is close to the proton charge radius.

Point form relativistic quantum mechanics, a constituent quark model with an oscillator wave function, and a point form impulse approximation are used to calculate the charge form factor of the pion. The resulting form factor fits available data, and in the ultrarelativistic (infinite binding) limit drops off as ${1/Q}^2$ for high $Q^2.$

We discuss effects in β decays at very low β energies, of the order of the kinetic energies of atomic electrons. As the β energy is lowered the atomic response changes from sudden to adiabatic. As a consequence, the β decay rate increases slightly and the ejection of atomic electrons (shake-off) and subsequent production of x rays is turned off. We estimate the transition energy, and the change in decay rate. The rate increase is largest in heavy atoms, which have a small Q value in their decay. The x-ray switch-off is independent of the Q value.

We studied $\beta$-delayed proton and $\gamma$ emission from ${}^{40}\mathrm{Ti}$ decay. We found $t_{1/2}=52.7\mathrm{}\pm 1.5\hspace{0.5em}\mathrm{ms}$ and observed 28 proton groups that we organized into a ${}^{40}\mathrm{Ti}$ decay scheme with 21 branches. The reduced transition strengths of these decay branches were then used to compute the neutrino detection efficiency of the ICARUS liquid argon time-projection chamber. We found ${}^{40}\mathrm{Ar}(\nu ,e)$ cross sections (for an electron energy threshold $W=5\mathrm{}\hspace{0.5em}\mathrm{MeV}$) of $(14.0\mathrm{}\pm 0.3)\times {10}^{-43}\hspace{0.5em}{\mathrm{cm}}^2,$ $(75.1\mathrm{}\pm 1.8)\times {10}^{-43}\hspace{0.5em}{\mathrm{cm}}^2,$ and $(3.2\mathrm{}\pm 0.1)\times {10}^{-41}\hspace{0.5em}{\mathrm{cm}}^2$ for ${}^8\mathrm{B}$ neutrinos, hep neutrinos, and supernova neutrinos characterized by a temperature of 4.5 MeV.

We determine fully self-consistent single-particle potentials and chemical potentials of nucleons and hyperons in asymmetric nuclear matter, using an extended Brueckner-Hartree-Fock formalism. We carefully analyze the onset of ${\Sigma }^{-}$ and $\Lambda$ formation in $\beta$ stable and charge neutral matter. The role played by the three-body nucleon interaction is widely discussed. The results indicate that formation of hyperons sets in at about (2–3) times normal nuclear matter density, for all the different nucleonic equations of state that are considered.