Momentum distributions of particles from nuclear breakup of high-energy three-body halos are calculated incorporating effects of final state interactions. The same two-body interactions between the particles are used to calculate both the ground state structure and the final state of the reaction processes. The ground state wave function reproduces size and energy of the halo nucleus. First we give a general and detailed description of the method. Then we investigate the effect of final state interactions in neutron removal and core breakup reactions for one- and two-dimensional momentum distributions. We compute specifically core and neutron momentum distributions from ${}^{11}$Li fragmentation and compare those with available experimental data. We conclude that 20–30 % of the three-body wave function describing ${}^{11}$Li corresponds to a neutron-core relative $p$ state. The fragmentation data strongly suggest that ${}^{10}$Li has an $s$ state below 200 keV and a $p$ state around 500 keV.

A general statistical ensemble is defined. The statistical weights for each configuration and consequently the mean value of any global observable can be expressed analytically. Since the resulting formulas are not numerically tractable, a statistical method of simulation is proposed. The method, a generalization of Koonin and Randrup’s procedure, provides an exploration of configuration space according to the detailed balance principle. This method is then applied to investigate the nuclear multifragmentation phenomenon. Charge and mass distributions calculated for reactions ${}^{40}$Ar+${}^{45}$Sc at 35–115 MeV/nucleon and ${}^{93}$Nb+${}^9$Be at 11.4 and 30.3 MeV/nucleon are compared with the respective experimental data.

A feature universally employed in the application of the Glauber approximation to the scattering of a projectile by a many-particle target is the assumption that the complex phase shift $\chi \mathrm{}\left(b\right)/2=\delta \left(\mathcal{l}\right)$ itself carries a phase which is independent of the impact parameter $b$. The most common assumption is that $\chi \mathrm{}\left(b\right)=(\alpha +i)g\left(b\right)\mathrm{}$, where $g\left(b\right)\mathrm{}$ is real and $\alpha =\mathrm{Re}\left[f\right(0\mathrm{}°\left)\right]/\mathrm{Im}\left[f\right(0\mathrm{}°\left)\right]$ is the real-to-imaginary ratio of the forward amplitude for elastic scattering of the projectile (or one of its constituents) on the constituents of the target. Since $g\left(b\right)\mathrm{}$ is proportional to an eikonal integral through an effective potential $V+iW$, this form also assumes that $V\left(r\right)=\alpha W\left(r\right)\mathrm{}$, i.e., that the real and imaginary parts of this potential have the same radial shapes. In recent years this approximation has been applied to heavy-ion elastic scattering in the relatively low-energy range below $100$ MeV/nucleon. Phenomenological optical potentials for these same nuclei and energies strongly violate the above condition, although they do approximate it in the surface region responsible for scattering to angles dominated by Fraunhofer oscillations. The Glauber approximation provides a qualitative fit to these oscillations, indicating that it is at least employing the correct nuclear radii. However, it grossly overestimates the absorption at larger angles in cases where these angles are sensitive to the interior of the potential. This failure may provide a sensitive means of assessing the effects of Pauli blocking on in-medium $\mathrm{NN}$ scattering.

Nuclear rainbows, which appear in the elastic scattering angular distributions for certain combinations of lighter heavy ions like ${}^{12}$C${+}^{12}$C and ${}^{16}$O${+}^{16}$O, uniquely determine the major features of the optical potentials for these systems. These features are conveniently summarized by the central depth of the real part of the potential, $V(r=0\mathrm{})\mathrm{}\sim 100-300$ MeV, and by the ratio of imaginary to real parts of the potential, $W\left(r\right)/V\left(r\right)\mathrm{}$, found to be $\ll 1$ for both small and large $r$ (internal and far-tail transparency), but $\approx 1$ in the surface region. The resulting maximum in $W/V$, which is found over the entire energy range 6 MeV $\lesssim E_L/A\lesssim 100$ MeV, appears to correlate with the peripheral reactions that occur in this energy range. At higher energies the data available indicate that the far-surface region is no longer transparent. Rather, $W\approx V$ there, suggesting the dominance of nuclear knockout reactions in the far tail. The knockout mode of inelasticity is the one described by the double-Glauber approximation, and $W\left(r\right)\mathrm{}\approx V\left(r\right)\mathrm{}$ agrees with the Glauber prediction in the high-energy range. This suggests that the double-Glauber prediction begins to be accurate in the low-density tail of the $A_1{+A}_2$ interaction around $E_L/A\approx 100$ MeV and that its failure for the higher-density interior may provide a means of investigating the density dependence of Pauli blocking on $\mathrm{NN}$ scattering in the nuclear medium. By way of contrast, systems like ${}^{20}$Ne${+}^{12}$C and ${}^{14}$N${+}^{12}$C, which do not exhibit rainbows, have distinctly more absorptive potentials and do not follow the above systematics. This suggests that the imaginary part of the optical potential reflects the shell structure of the target and/or projectile in important ways, and so will not be easy to calculate from an infinite-matter many-body approach.

A neural network is used to determine the impact parameter in ${}^{40}$Ca+${}^{40}$Ca reactions. The effect of the detection efficiency as well as the model dependence of the training procedure has been studied carefully. An overall improvement of the impact parameter determination of 25% is obtained using this technique. The analysis of Amphora ${}^{40}$Ca+${}^{40}$Ca data at 35 MeV per nucleon using a neural network shows two well-separated classes of events among the selected “complete” events.

We derive a relation between the temperature $T$ of the disassembling excited nucleus and the double ratio $R$ of fragment yields within the macrocanonical description by adopting Maxwell-Boltzmann statistics and the Wigner-Seitz approximation for the Coulomb interaction between fragments and imposing only the condition of thermal equilibrium. Under the same assumptions, this relation between $T$ and $R$, which differs from that of Albergo et al. by a Coulomb term, is also derived within the canonical description by considering realistic values for the multiplicities of fragments.

An extended Hauser-Feshbach method (EHFM) is developed for light heavy-ion fusion reactions in order to provide a detailed analysis of all the possible decay channels by including explicitly the fusion-fission phase space in the description of the cascade chain. The mass-asymmetric fission component is considered as a complex-fragment binary decay which can be treated in the same way as the light-particle evaporation from the compound nucleus in statistical-model calculations. The method of the phase-space integrations for the binary decay is an extension of the usual Hauser-Feshbach formalism to be applied to the mass-symmetric fission part. The EHFM calculations include ground-state binding energies and discrete levels in the low-excitation-energy regions which are essential for an accurate evaluation of the phase-space integrations of the complex-fragment emission (fission). In the present calculations, the EHFM is applied to the first-chance binary decay by assuming that the second-chance fission decay is negligible. In a similar manner to the description of the fusion-evaporation process, the usual cascade calculation of light-particle emission from the highly excited complex fragments is applied. This complete calculation is then defined as EHFM+CASCADE. Calculated quantities such as charge-, mass, and kinetic-energy distributions are compared with inclusive and/or exclusive data for the ${}^{32}\mathrm{S}{+}^{24}$Mg and ${}^{35}\mathrm{Cl}{+}^{12}$C reactions which have been selected as typical examples. Finally, the missing charge distributions extracted from exclusive measurements are also successfully compared with the EHFM+CASCADE predictions.

Quasielastic $K^{+}$-nucleus scattering data at $q=290\mathrm{}$, 390, and 480 MeV/c are analyzed in a finite nucleus continuum random phase approximation framework, using a density-dependent particle-hole interaction. The reaction mechanism is consistently treated according to Glauber theory, keeping up to two-step inelastic processes. A good description of the data is achieved, also providing a useful constraint on the strength of the effective particle-hole interaction in the scalar-isoscalar channel at intermediate momentum transfers. We find no evidence for the increase in the effective number of nucleons participating in the reaction which has been reported in the literature.

Cavitation and heating of the target nucleus in the first instances of ${}^3$He-induced collisions in the GeV/nucleon range are investigated in an intranuclear cascade model for the formation of this structure and a stochastic one-body dynamics calculation to study its evolution. The hard collisions having essentially ceased when the structure is fully developed, the latter model is particularly suited to study the possible breakup of the system. It is shown, however, that the target recovers a spherical shape rather rapidly, and has thus a good chance to decay by standard evaporation, justifying the use of a cascade + evaporation model to analyze the data. It is also shown that the system has to be much more modified to break up into pieces instead of recovering a compact shape: in these reactions, it is thus expected that nuclear matter is resilient to shape deformation and thermal excitation. Arguments are given to explain that expansion of the system, not important in these reactions, is required to overcome this resilience.

The thermal and statistical properties of hadronic matter under some extreme conditions are investigated using an exactly solvable canonical ensemble model. A unified model describing both the fragmentation of nuclei and the thermal properties of hadronic matter is developed. Simple expressions are obtained for quantities such as the hadronic equation of state, specific heat, compressibility, entropy, and excitation energy as a function of temperature and density. These expressions encompass the fermionic aspect of nucleons, such as degeneracy pressure and Fermi energy at low temperatures and the ideal gas laws at high temperatures and low density. Expressions are developed which connect these two extremes with behavior that resembles an ideal Bose gas with its associated Bose condensation. In the thermodynamic limit, an infinite cluster exists below a certain critical condition in a manner similar to the sudden appearance of the infinite cluster in percolation theory. The importance of multiplicity fluctuations is discussed and some recent data from the EOS collaboration on critical point behavior of nuclei can be accounted for using simple expressions obtained from the model.

Experimental results and a detailed analysis are presented of the transverse energy and charged particle azimuthal distributions measured by the E877 Collaboration for different centralities of Au+Au collisions at a beam momentum of 10.8$A$ GeV/$c$. The anisotropy of these distributions is studied with respect to the reaction plane reconstructed on an event-by-event basis using the transverse energy distribution measured by calorimeters. Results are corrected for the reaction plane resolution. For semicentral events we observe directed flow signals of up to 10%. We observe a stronger anisotropy for slow charged particles. For both the charged particle and transverse energy distributions we observe a small but nonzero elliptic anisotropy with the major axis pointing into the reaction plane. Combining the information on transverse energy and charged particle flow we obtain information on the flow of nucleons and pions. The data are compared to event generators and the need to introduce a mean field or nucleon-nucleon potential is discussed.

Particle and photon production is analyzed in the presence of transverse flow using two approximations to describe the properties of the hadronic medium, one containing only $\pi ,\rho ,\omega$, and $\eta$ mesons (simplified equation of state) and the other containing hadrons and resonances from the particle data table. Both are considered with and without initial quark gluon plasma formation. In each case the initial temperature is fixed by requiring ${\mathrm{dN}}_{\mathrm{ch}}/dy\sim$ 550 in the final state. It is shown that most observables are very sensitive to the equation of state. This is particularly evident when comparing the results of the simplified equation of state in the scenarios with and without phase transition. The hadronic gas scenario leads to a substantially higher rate for the $p_T$ distribution of all particles. In the complete equation of state with several hundreds of hadronic resonances, the difference between the scenarios with and without phase transition is rather modest. Both photon and particle spectra, in a wide $p_T$ range, show very similar behavior. It is therefore concluded that from the $p_T$ spectra it will be hard to disentangle quark gluon plasma formation in the initial state. It is to be stressed, however, that there are conceptual difficulties in applying a pure hadronic gas equation of state at SPS energies. The phase transition scenario with a quark gluon plasma present in the initial state seems to be the more natural one.

A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters $d,\hspace{0.5em}t$, and He are predicted for central Au(11.6$A$ GeV)Au and Si(14.6$A$ GeV)Si reactions in the framework of the relativistic quantum molecular dynamics transport approach. Transverse expansion leads to a strong shoulder-arm shape and different inverse slope parameters in the transverse spectra of nuclear clusters deviating markedly from thermal distributions. A clear “bounce-off” event shape is seen: The averaged transverse flow velocities in the reaction plane are for clusters larger than for protons. The cluster yields, particularly at low $p_t$ at midrapidities, and the in-plane (anti)flow of clusters and pions change if suitably strong baryon potential interactions are included. This allows one to study the transient pressure at high density via the event shape analysis of nucleons, nucleon clusters, and other hadrons.

We have studied the fluctuation effects in proton-proton collisions through the analysis of their observables. To investigate the role of fluctuations in the initial conditions, we have used the interacting gluon model, modified by the inclusion of the impact parameter, and have applied the one-dimensional Landau’s Hydrodynamical Model to the fireballs thus generated. The rapidity and pseudorapidity distributions were calculated using two distinct procedures, one taking the fluctuations into account and the other the usual method considering only one fireball with the average initial conditions. The results show indeed the importance of fluctuations.

The temperature dependence of the $\phi$ meson mass and its decay width $(\phi \to K\mathrm{K¯})$ have been studied from an effective nonlinear chiral Lagrangian in SU(3). The effective mass has been obtained from the pole position of the full propagator. The width has also been calculated. It has been found that the mass decreases with temperature very slowly whereas the decay width increases quite sharply. Possible consequences on the QGP signals are discussed.

The production of low-mass dileptons and soft photons from thermalized quark-gluon plasma (QGP) and hadronic matter in relativistic heavy ion collisions is evaluated. A boost invariant longitudinal and cylindrically symmetric transverse expansion of the systems created in central collision of lead nuclei at CERN SPS, BNL RHIC, and CERN LHC, and undergoing a first-order phase transition to hadronic matter is considered. A large production of low-mass $(M<\mathrm{}$ 0.3 GeV) dileptons, and soft photons ${(p}_T<$0.4 GeV) is seen to emanate from the bremsstrahlung of quarks and pions. We find an increase by a factor of 2 to 4 in the low-mass dilepton and soft-photon yield as we move from SPS to RHIC energies, and an increase by an order of magnitude as we move from SPS to LHC energies. Most of the soft radiations are found to originate from pion driven processes at SPS and RHIC energies, while at the LHC energies the quark and the pion driven processes contribute by a similar amount. The study of the transverse mass distribution is seen to provide interesting details of the evolution. We also find a unique universal behavior for the ratio of $M^2$ weighted transverse mass distribution for $M=$ 0.1 GeV to that for $M=$ 0.2 and 0.3 GeV, as a function of $M_T,$ for SPS, RHIC, and LHC energies, in the absence of transverse expansion of the system. A deviation from this universal behavior is seen as a clear indication of the flow.

We study the self-energy amplitudes for the $\rho$-$\omega$ meson system produced by an effective field theory model at the quark level characterized by a finite range quark-quark interaction and an isospin breaking bare quark mass difference $m_u-m_d.$ Dynamical effects associated with confinement and dressing of quarks and the finite size of the produced $\mathrm{q¯}q$ meson modes are treated. Parameters of this approach, previously constrained by soft pion physics, are here supplemented in a minimal way to reproduce $m_{\omega }$ and $g_{\rho \pi \pi }.$ Calculations are carried out up to the one-pion-loop level and the predictions for ${\rho }^0$-$\omega$ mixing, mass splitting, the $\rho$ width and the symmetry breaking $\omega \pi \pi$ coupling constant and form factor are presented. The contribution of the direct $\omega \to \pi \pi$ process relative to the $\omega \to \rho \to \pi \pi$ process is discussed within this model.

We study chiral symmetry breaking, making use of a generalized Nambu–Jona-Lasinio (NJL) model that includes a description of confinement. The Schwinger-Dyson and Bethe-Salpeter equations are solved for our model of the self-energy of a quark. We show that our analysis is consistent with the Goldstone theorem. That is, the pion has zero mass, if the current quark masses are zero. We use a confining interaction with a (Dirac) matrix structure that leads to simple equations for the self-energy and for a vertex function that serves to sum a ladder of confining interactions. We consider spacelike values of $q^2$, and carry out our analysis in a Euclidean momentum space. For timelike $q^2$, we use calculational procedures that we have developed in our earlier work in order to exhibit properties of the confining vertex. For the spacelike values of $q^2$ considered here, we see that the effects due to the introduction of our model of confinement are small. (However, such effects are very important for timelike $q^2$. Their consideration is essential, if we wish to study mesons, such as the rho and omega, in our model.)

We investigate the properties of different modifications to the linear $\sigma$ model (including a dilaton field associated with broken scale invariance) at finite baryon density $\rho$ and nonzero temperature $T$. The explicit breaking of chiral symmetry and the way the vector meson mass is generated are significant for the appearance of a phase of nearly vanishing nucleon mass besides the solution describing normal nuclear matter. The elimination of the abnormal solution prohibits the onset of a chiral phase transition but allows one to lower the compressibility to a reasonable range. The repulsive contributions from the vector mesons are responsible for the wide range of stability of the normal phase in the $(\mu$, $T)$ plane. The abnormal solution becomes not only energetically preferable to the normal state at high temperature or density, but also mechanically stable due to the inclusion of dilatons.

A rigorous multipole analysis of the recent $\gamma p\to {\pi }^{0}p$ cross-section measurement is presented. The data were taken using the photon spectrometer TAPS at the tagged photon beam of the Mainz microtron. The $s$ and $p$ wave multipoles were extracted using minimal model assumptions. The predicted unitary cusp for the $s$-wave multipole $E_{0+}$ due to the two step $\gamma p\to {\pi }^{+}n\to {\pi }^{0}p$ reaction was observed. The results are consistent with one-loop chiral perturbation theory calculations for which three low-energy constants have been determined by a fit to the data. The uncertainties in the analysis and the need for polarization observables are discussed.