A four-channel unitary model for the description of heavy-ion collisions at relativistic energies

We expand a previously formulated model for nuclear abrasion in ion-ion collisions where now nucleons in both projectile and target can be excited. Describing the state of excitation by an effective channel we rigorously impose unitarity and compare the results with those of a heuristic treatment of unitarity by Hüfner, Schäfer and Schürmann. We find corrections to the latter theory which grow up to a factor of two with the number of abraded nucleons.     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

A set of hyperspherical harmonics especially suited for three-body collisions in a plane

We obtain a set of four-dimensional hyperspherical harmonics in closed form. These harmonics are not only quantized with respect to the rotation group (O ₂), but are an irreducible basis for the permutation groupS ₃. An additional symmetry is found which allows us to write hyperspherical harmonics classified with respect to a 12 element groupS ₃×i×O ₂. We give a set of three mutually commuting operators whose eigenvalues uniquely characterize each spherical harmonic with respect to degree, symmetry, and angular momentum in the plane.     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

A model for high-energy heavy-ion collisions

A model is developed for high-energy heavy-ion collisions that treats the variation across the overlap region of the target and projectile in the amount of energy and momentum that is deposited. The expression for calculating any observable takes the form of a sum over a series of terms, each one of which consists of a geometric, a kinematic, and a statistical factor. The geometrical factors for a number of target projectile systems are tabulated.     

A three-body model for the study of resonance phenomena

A three-body model suitable for the investigation of compound, quasi-compound and potential resonances is presented. The exact solution of the model based on Faddeev's method is discussed. Numerical calculations are performed for negative total energy.     

A quantal toy model for heavy-ion collisions

A one-dimensional toy model of two moving finite boxes is analysed with respect to quantal phenomena associated with heavy-ion dynamics at low and intermediate energies. Special attention is payed to the relation between energy and momentum of the nucleons inside and outside the time-dependent mean field. A Wigner transformation of the one-body density matrix in space and time allows for a unique comparison with classical phase-space dynamics. It is found that high momentum components of the nuclear groundstate wave function approximately become on-shell during the heavy-ion reaction. This leads to the emission of energetic nucleons which do not appear classically. It is furthermore shown, that the low lying eigenstates of the dinuclear system for fixed time are only partly occupied throughout the reaction at intermediate energies. This opens up final phase space for nucleons after producing e.g. a pion or energetic photon. Though the present model does not allow for a reliable calculation of double differential nucleon spectra, pion or photon cross sections, it transparently shows the peculiar features of quantum dynamics in heavy-ion collisions.     

A three-body optical model for two clusters and a meson

Conclusion In a very simplified -²⁰Ne scattering calculation with the fish bone optical model, we have found a big difference between results obtained with two different off-shell versions of the model, when the three-body Pauli potential is neglected. It seems to be safe to say that the three-body force may not be neglected in the M-model. Further calculations will be needed to see whether it may be neglected in the ¯M-model.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

A model for short range correlation in the three-body system

A method by means of which the two-body short-range correlations in the nucleon-nucleon interaction are taken accurately into account in three-body bound-state calculations is described. The method is independent of the nucleon-nucleon interaction. We employ our method to calculate meson-exchange corrections to the magnetic moments of ³H and ³He and the Coulomb energy of ³He.     

Periodic orbits and binary collisions in the classical three-body Coulomb problem

In the helium case of the classical three-body Coulomb problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. Focusing our attention on binary collisions with these tools, a sequence of periodic orbits are predicted and are actually found numerically. A family of periodic orbits found has regularity in their actions. For this family of periodic orbits, it is shown that thanks to its regularity, a partial summation of the Gutzwiller trace formula with a daring approximation gives a Rydberg series of energy levels.     

A model for multiplicity distributions in high energy collisions

A phenomenological model is presented which regards the system after collision as a single entity that emits hadrons directly. The evolution of this entity gives a new two parameter distribution which fits the high energypp, \(\bar pp\) ,e ⁺ e ^?, π⁺ p andK ⁺ p data reasonably well. The entity emits hadrons along the rapidity axis and exhibits intermittency behaviour under certain conditions.     

A semi-statistical model of high-energy collisions

The emission of particles directly created in high-energy collisions is considered to be only partly governed by statistical laws as in Fermi's model. The motion of the created particles is to some degree related to the former motion of the incoming colliding particles. In first approximation this intermediate state is built up of two extremes: two Lorentz systems are introduced from which the particles are emitted isotropically and according to statistical laws. In the centre-of-momentum system (CMS) of the collision these two systems move in the directions of the incoming particles after collision. This approximation corresponds to the two-fireball model which we regard as a representative of a mathematical method of dealing with correlations. In further approximation phase space distributions are replaced by the thermodynamic Fermi or Bose distributions for relativistic particles. Both experimental data such as the nearly constant mean transverse momentum¯p _t and phase space calculations with constant interaction volume show that the temperaturekT reaches an upper limit asymptotically at high energies; the asymptotic region begins at about 30 GeV. The comparison with experimental particle spectra from accelerators in the 10–30GeV region shows good agreement if one uses a smooth dependence ofkT on the collision energyE ₀ and, for each independent set of measurements, an individual choice of \(\bar \gamma _f \) , the mean Lorentz factor of the “fireballs” in the CMS, and of ¯n, the mean number of created particles. The p_t-distribution of pions and the dependence of¯p _t on the particle mass can also be successfully described. At very high energies the model gives production ratios of the various kinds of particles which lie within the range of the experimental determinations. The dependence of \(\bar \gamma _f \) onE ₀ is concluded to be of the form \(\bar \gamma _f \propto E_0^{1/2} /\bar n(E_0 ) \approx 0.5E_0^{1/4} \) , i.e. CMS anisotropy is related to multiplicity.     

A model for multiparticle production in high energy hadronic collisions

A model for multiparticle production process in high-energy hadronic collisions is proposed. In the centre of mass (CM) system of colliding particles the target and the projectile are assumed to pass through each other sharing energies allowed by kinematical constraints. Thus in app collision the energy associated with each is √S/2 (S being the square of the CM energy) which is taken to be the real variable that governs the number of particles produced. In the case of hadronnucleus collisions the projectile and the target ofv nucleons lying in a (Lorentz contracted) tube pass through each other sharing energies ⋍ √S _A2, whereS _A ⋍vS. Before the final state particles emerge from these systems, the constituents of the target, i.e.,v nucleons share equally (= √S _A2v) the total energy associated with the target and become the centres from which final state particles stem out. Several results have been discussed.     

III. A stochastic two-stage reaction model for heavy-ion collisions

We propose a two-stage, stochastic model of heavy-ion reactions. Nucleons becoming participants by mean-field effects or by nucleon-nucleon interactions are transferred to definite final states, creating a PLF, a TLF, clusters, or escaping to continuum. Nucleon transfer probabilities are governed by state densities. In this way different hot particle sources are created which afterwards decay by particle emission. Received: 12 March 2001 / Accepted: 20 June 2001     

A two-stage model for fast particle emission in heavy-ion collisions

Using Bertsch's TDHF-motivated trajectory model we combine two physically distinct approaches to describe fast particle emission. In the early stage we calculate particle emission in the spirit of the Fermi-jet mechanism. In the later stage, after neck formation, particles are assumed to be emitted from a rapidly expanding hot zone of appreciably large initial dimension, which is strongly anisotropic in momentum space. We calculate absolute double-differential cross sections for preequilibrium neutron emission and obtain a remarkable agreement with experimental data without introducing free parameters.     

Variable-range projection model for turbulence-driven collisions

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.     

A new model in high energy collisions

In this work a hydrodynamical model is presented in order to explain physical phenomena appearing in nucleus-nucleus collisions. The model is based on a shock wave propagation in the fluid nuclear matter. The Burger- de Vries equation of shock waves is treated in the framework of mathematical topology. Experimental data for five pairs of nuclei is used in order to demonstrate the viability of the model.