Distributions In Heavy Ion Collisions Research Articles

Density and boundary effects on pion distributions in relativistic heavy-ion collisions

We compute the pion inclusive momentum distribution in a heavy-ion collision, assuming thermal equilibrium and accounting for boundary effects at the time of decoupling. We calculate the chemical potential corresponding to an average pion multiplicity in central collisions and explore the consequences of having the pion system produced close to the critical temperature for Bose-Einstein condensation.

Fragment multiplicity dependent charge distributions in heavy ion collisions

The dependence of intermediate-mass-fragment (IMF) element distributions on the multiplicity, N{sub IMF}, of detected fragments has been measured for {sup 84}Kr+{sup 197}Au collisions at E/A=35, 55, 70, 100, 200, and 400 MeV. The observed dependence can be parametrized as P(N{sub IMF}{vert_bar}Z){proportional_to}P(Z)exp({minus}c{center_dot}N{sub IMF}{center_dot}Z), where c is a beam-energy and excitation-energy dependent parameter. Previous work indicated this parameter is zero in the liquid-gas coexistence region and positive in the gaseous phase. In contrast, we observe both negative and positive values for c, revealing the meaning of this parameter to be less straightforward than previously assumed. The magnitude of c appears nonetheless to provide a nontrivial test of multifragmentation models. {copyright} {ital 1997} {ital The American Physical Society}

Kaon azimuthal distributions in heavy-ion collisions

Kaon azimuthal distributions in Au+Au collisions at 1.0 GeV/nucleon are analysed using the relativistic transport model that includes explicitly the kaon degree of freedom. We find that the kaon azimuthal distributions in the target (and projectile) rapidity region are sensitive to the input kaon potential in the transport model and thus provide useful information on kaon properties in dense matter. Near mid-rapidity, the potential effects on kaon azimuthal distributions are, however, marginal.

Role of intrinsic width in fragment momentum distributions in heavy ion collisions.

It is demonstrated that the intrinsic widths incorporating correlations in conjunction with dynamical contributions give better agreement with experiments for collisions in the energy range of 200A MeV to 2A GeV than using only intrinsic widths without correlations. The sensitivity of the intrinsic width decreases with increasing projectile mass. A simple recipe for calculating intrinsic width with correlations is presented.

Azimuthal distribution in heavy-ion collisions.

We consider recent experimental data on azimuthal distributions of particles seen in heavy-ion collisions at 35 MeV/nucleon and at 50 MeV/nucleon. For $^{12}\mathrm{C}$ on $^{12}\mathrm{C}$ at 50 MeV/nucleon laboratory energy, the distribution shows features characteristic of flow; for $^{12}\mathrm{C}$ on $^{197}\mathrm{Au}$ experimental data show features characteristic of rotation. For $^{40}\mathrm{Ar}$ on $^{51}\mathrm{V}$ at 35 MeV/nucleon, effects of both flow and rotation are seen. In magnitudes the effects are small. We find that Boltzmann-Uehling-Uhlenbeck calculations are able to reproduce these results.

Geometry, scaling, and universality in the mass distributions in heavy ion collisions.

Various features of the mass yield in heavy-ion collisions are studied. Simple pictures are first developed from an exactly soluble canonical ensemble model which has its basis in a statistical view of the collision. Several different high energy proton-nucleus data may be understood in terms of a geometric property and a recursive feature of the distribution of fragments. The geometric property is discussed in terms of the concept of self-similarity and scaling laws associated with generalized Renyi entropies. The recursive feature is discussed in terms of iterative one-dimensional maps. Nuclear cobwebbing, attractors of the dynamics, Lyapunov exponents, correlation lengths, and dimensions associated with scaling relations are investigated. Fourier transforms of the mass yield are used to obtain power spectra which are then used to investigate a possible power-law behavior 1/[ital f][sup [beta]] (behavior) with frequency [ital f].

Description of heavy ion collisions with medium dependent forces

One of the proclaimed goals of heavy ion collisions with 100 MeV up to 2000 MeV per nucleon is the determination of the equation of state of nuclear matter, which one needs for example for neutron stars, supernova explosions and the early universe. But the situation in heavy ion collisions is quite different from thermal equilibrium with a spherical momentum distribution and a fixed temperature. The effective nucleon-nucleon interaction as determined for example by the solution of the Bethe-Goldstone equation depends through the Pauli operator and through the single particle energies on the surrounding nuclear matter. This dependence is especially pronounced since the nucleon-nucleon interacting is highly momentum dependent: It is attractive at small relative momenta and repulsive at higher values. Thus the effective nucleon-nucleon interaction in heavy ion collisions depends on the distribution of the surrounding nuclear matter in orbital and momentum space. Here results are presented using for the description of heavy ion reactions at intermediate energies Quantum Molecular Dynamics (QMD) in a non-relativistic and in a completely covariant (RQMD) form. We show that the production of gamma-rays, pions and the inclusive spectra of nucleons and light nuclei are not sensitive to the equation of states. An observable sensitive to the equation of state is the perpendicular momentum distribution in heavy ion collisions. Also sensitive is the production of heavier particles like K + and K − mesons and antiprotons below the NN threshold. These collisions can have enough energy to compress and heat up nuclear matter and since they are below the NN threshold several nucleons must cooperate.

Origin of transverse momentum in relativistic heavy-ion collisions: Microscopic study.

We study the origin of the transverse momentum distribution in heavy-ion collisions within a relativistic transport approach. To achieve a better understanding of the reaction dynamics, we decompose the total ${\mathit{p}}_{\mathit{t}}$ distribution into a mean-field, N-N collision, and Fermi-momentum part. We find that the origin of the transverse momentum strongly depends on the rapidity region. Our investigation of the impact-parameter and mass dependence suggests that peripheral collisions may be useful to investigate the momentum dependence of the mean-field in the nucleus-nucleus case, whereas the mass dependence could give hints about the N-N-collision part. Only after these two issues are settled it may be possible to extract information about the density dependence in central collisions, which may, however, necessitate reactions at even higher energies than the 800 MeV/nucleon considered in this work.

Modification of the j/ ψ momentum distribution in heavy-ion collisions through dispersion by the nuclear medium

The forces felt by a J/ Ψ produced in a heavy-ion collision, arising from the dependence of its self-energy on the inhomogeneous surrounding medium, can, as discussed here, lead to a significant distortion of its transverse momentum distribution.

Ambiguities in the description of nucleon transfer in deep inelastic scattering

In this paper we have discussed certain ambiguities which arise in the description of the mass and charge distributions in heavy ion collisions. We have concentrated on two additional mechanisms, beyond the simple nucleon transfer with average relative momentum, required in the random walk formalism to obtain an agreement with the experimental data. We have shown that these two mechansims, Δ-process involving an additional "Fermi momentum" transfer and γ-process involving new non-transfer process for an energy dissipation, are formally interchangable as regards their effect on the total mass width. We have discussed the possible physical mechanisms responsible for these processes and their relationship to transport theories.

Transfer energy loss probability distributions in heavy ion collisions

Transfer energy loss probability distributions in low energy heavy ion reactions have been calculated in a realistic case for the first time. They are rather large in general and so they play a crucial role in the evolution of the dissipation mechanisms. It is proved that transfer processes, in peripheral collisions, can be treated as independent channels, generating energy loss spectra which can be described with a product of poissonian distributions.

Transverse momentum analysis in the relativistic BUU approach

We investigate the transverse momentum distributions in heavy-ion collisions obtained in the relativistic BUU approach for different mean-field interactions characterized by their effective mass m ∗ and the compression modulus K. The different contributions from the mean-field and the collision part are separated. In the midrapidity region we observe for m ∗ = 0.83 M an almost equally strong contribution from both parts, whereas for a more repulsive mean-field ( m ∗ = 0.7 M ) its contribution dominates over the collision part. In the spectator rapidity regions we observe a strong contribution fiom the transverse component of the initial fermi-momentum due to a rearrangement of the particles into different rapidity zones during the collision. This effect is compensated by the mean-field which turns attractive in these regions.

Azimuthal distributions in heavy ion collisions and the nuclear equation of state

For near central collisions of Nb on Nb at a laboratory energy of 650 MeV per projectile nucleon we calculate inclusive cross sections as a function of the azimuthal angle where this angle is measured from the reaction plane. The azimuthal dependence is strongly influenced by the nuclear equation of state and is a useful quantity to measure.

Relativistic Vlasov-Uehling-Uhlenbeck model for heavy-ion collisions.

The previously derived relativistic Vlasov equation from the Walecka model is generalized to include both a collision term and the self-interaction of the scalar meson. From studying the transverse momentum distribution in heavy-ion collisions, we conclude that the nuclear equation of state at high density is softer than that determined previously using the normal Vlasov-Uehling-Uhlenbeck model and is consistent with that from the analysis with a momentum-dependent potential. We have also found that in relativistic model the magnitude of the transverse momentum from heavy-ion collision is more sensitive to the value of the nucleon effective mass at saturation density than the value of the compressibility at this density.

A model study of two interacting fermion gases

To gain a better understanding of the mass distribution in heavy-ion collisions we solve numerically the time-dependent many-body Schrödinger equation for a fermion system. The model describes the motion of A 1 + A 2 interacting fermions in one dimension. Initially the particles are separated into two subsystems. Then they are brought into contact and particle transfer between the systems causes the relative mass number to dissipate and fluctuate. Special attention is focussed on the variance of the mass distribution. The strong influence of the Pauli exclusion principle is demonstrated and conclusions are drawn concerning the extended time-dependent Hartree-Fock theories which include collision terms.

Anticorrelated angular-momentum distributions in heavy-ion collisions

The angular-momentum distributions of the fragments in deeply inelastic heavy-ion collisions are shown to be anti-correlated. We derive the correlation coefficient in a transport model. The correlation angle increases towards mass symmetry and reaches —45° for symmetric fragmentation.

Exact calculation of the mass distribution in the collision process of32S on medium-weight nuclei

This work deals with the exact integration of a Fokker-Planck equation for the mass distribution in heavy ion collisions. The results are compared to those obtained in a previous calculation in which the distribution is approximated by its two lowest moments.

Quantum fluctuations within the fragmentation theory

The measured spread of the fragment mass distributions in heavy ion collisions may be due to two quite different physical mechanisms: the quantum-mechanical uncertainty associated with collective motion in the mass asymmetry degree of freedom, and the spread caused by thermal excitation of the nuclear system. The fluctuations in physical observables induced in these ways will be referred to as quantum fluctuations and statistical fluctuations. In this lecture quantum fluctuations are studied within the fragmentation theory. Mass distributions for spontaneous fission and low energy heavy ion collisions are investigated.

Inner and outer shell contributions to the charge state distribution in heavy ion collisions

The charge distributions of N + q ions after small impact parameter collisions in the medium energy range ≈ 50 keV/amu, were studied. For symmetric and nearly symmetric systems they display a simple convex structure as a function of the impact parameter. This structure is interpreted as a result of an inner shell promotion effect superimposed on a purely statistical, impact parameter independent distribution. Good agreement with the shape predicted by the rotational coupling model allows the separation of the inner and outer shell contributions to the charge distribution.

On mass and charge distributions in heavy ion collisions

A statistical model based on the independent particle picture is used to calculate mass and charge distributions in deep inelastic heavy ion collisions. Different assumptions on volume and charge equilibration are treated and compared with measured variances of charge distributions. One combination of assumptions is clearly favoured by experiment and gives a reasonable description of the variance versus energy loss curves up to energy losses of about 200 MeV in Kr+Ho and Xe+Bi reactions.