Fast dissipative collisions

At a bombarding energy of 14.7 MeV/u the charge, mass and angular distributions have been measured as a function of energy loss for reaction products induced by ⁹⁸Mo and ⁹²Mo projectiles on targets of ⁹⁸Mo, ¹⁴⁷Sm, ¹⁵⁴Sm and ⁹²Mo, ¹⁵⁴Sm, ²³⁸U, respectively. An analysis of the product distributions shows the presence of a non-equilibrium sharing of the excitation energy, an exponential growth of the charge and mass variances, a complete $\text{N}\text{Z}$ equilibration and a large yield of non-binary complex fragments. Monte Carlo simulations are found to be an indispensable tool of the analysis.     

Cross section coherence energy and interaction time in heavy ion dissipative collisions

A recent formulation of the cross section autocorrelation function, specially developed to take into account the angular momentum effects, is compared to the experimental results concerning the²⁸Si +⁴⁸Ti and²⁸Si +⁶⁴Ni reactions. The possibility of determining the mean lifetime of the dinucleus excited states populated in dissipative collisions is also discussed.     

Structure effects in dissipative collisions

An ansatz representing a generalisation of the one-body recoil formula is proposed on the basis of the total kinetic energy loss versus σ_Z² correlation systematics observed in collisions between very heavy nuclei. It is shown that such correlations are surprisingly sensitive to the shell structure of the colliding nuclei. The mechanism of energy dissipation appears also to be strongly influenced by the structure effects.     

Ericson fluctuations in dissipative collisions

We generalize Ericson's theory of fluctuations to deep inelastic reactions. Following Ericson we assume that theS-matrixS _βα(E, l) can be written as a sum of pole terms in the complex energy plane, but the dependence ofS _βα (E, l) on the angular momentuml is assumed to be coherent. Semi-classical approximations for the summation of the angular momenta lead to a simple formula for the energy autocorrelation function. It contains the average widthΓ(l) describing the lifetimeτ(l) of the intermediate dinuclear system and the numberN _eff of unresolved primary channels. These quantities can be determined from a measurement of the autocorrelation function.     

Transport theory of dissipative heavy-ion collisions

The non-perturbative quantum-statistical theory of dissipative heavy-ion collisions introduced earlier, is generalized by including explicitly the relative motion of the colliding nuclei. We start from the Liouville equation in the Wigner representation which allows for useful and illustrative interpretations of the resulting quantities and equations. Using the randomness of the coupling matrix elements and the semi-classical approximation for the relative motion we derive a general time-dependent transport equation for the macroscopic Wigner functions (phase-space distribution functions). The limits of weak and strong coupling are discussed.     

Statistical fluctuations in dissipative heavy-ion collisions

We investigate statistical fluctuations in the relative motion of colliding heavy ions as well as in the nucleon transport. Approximate analytical expressions for the fluctuations in energy loss, scattering angle, and fragment charge number are derived from a Fokker-Planck equation and evaluated at the scission point using previously determined mean interaction times. In a detailed comparison with the data for¹³⁶Xe +²⁰⁹Bi and⁸⁶Kr +¹⁶⁶Er we can account for the observed multidifferential cross sections except at low energy loss where the calculated fluctuations in scattering angle are too small.     

Relaxation times in dissipative heavy-ion collisions

The classical model introduced earlier for analyzing experimental data on dissipative heavy-ion collisions, is generalized to include effects from the gradual dissipation of radial kinetic energy and from the development of fragment deformations during the collision. Relaxation times for the dissipation of radial kinetic energy (τ _R ) and relative angular momentum (τ _l ) as well as for the development of deformations (τ_α) are fitted to the reaction⁸⁶Kr (8.18 MeV/u) +¹⁶⁶Er and applied to three other reactions. A consistent set of relaxation times isτ _R = 0.3 · 10^?21 s,τ _l =1.5 · 10^?21 s andτ _α = 5 · 10^?21 s. Empirical mass transport coefficients are deduced from comparisons with experimental element distributions. Effects from fluctuations in the deflection function are discussed. Evidence is found for the existence of a relaxation time of the order 10^?21 s in the mass-drift coefficient.     

Time-dependent shell-model theory of dissipative heavy-ion collisions

A transport theory is formulated within a time-dependent shell-model approach. Time averaging of the equations for macroscopic quantities lead to irreversibility and justifies weak-coupling limit and Markov approximation for the (energy-conserving) one- and two-body collision terms. Two coupled equations for the occupation probabilities of dynamical single-particle states and for the collective variable are derived and explicit formulas for transition rates, dynamical forces, mass parameters and friction coefficients are given. The applicability of the formulation in terms of characteristic quantities of nuclear systems is considered in detail and some peculiarities due to memory effects in the initial equilibration process of heavy-ion collisions are discussed.     

Excitation-energy sharing in uranium induced dissipative collisions

Strongly damped collisions were studied in uranium induced reactions on¹¹⁰Pd and¹²⁴Sn target nuclei near the barrier. The excitation-energy splitting was deduced from binary reaction yields and those in which the heavy fragment undergoes sequential fission. For systems with 87≦Z≦95 for the heavy fragment, the excitation energy is concentrated in the lighter nucleus, at best shared equally. The results indicate a non-equilibrated energy dissipation, and support nucleon exchange based on average single-particle strength functions as the underlying dissipation mechanism at the barrier.     

Quantum dynamical semigroups and dissipative collisions of heavy-ions

The theory of quantum dynamical semigroups is briefly reviewed including the scattering theory and WKB approximation. This formalism is illustrated by a simple model of dissipative heavy-ion collision.     

Energy and angular momentum sharing in dissipative collisions

Primary and secondary masses of heavy reaction products have been deduced from kinematics and E-ToF measurements, respectively, for the direct and reverse collisions of ⁹³Nb and ¹¹⁶Sn at 25 AMeV. Light charged particles have also been measured in coincidence with the heavy fragments. Direct experimental evidence of the correlation of energy-sharing with net mass transfer has been found using information from both the heavy fragments and the light charged particles. The ratio of hydrogen and helium multiplicities points to a further correlation of angular momentum sharing with net mass transfer. Received: 18 September 2000 / Accepted: 2 December 2000     

Second-order dissipative fluid dynamics for ultrarelativistic nuclear collisions

The Müller-Israel-Stewart second-order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultrarelativistic heavy-ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.     

On the influence of shell structure in dissipative collisions

A kinematically complete study of the symmetric systems ¹⁴⁴Sm+¹⁴⁴Sm and ¹⁵⁴Sn+¹⁵⁴Sm has been performed at energies 30% in excess of the interaction barrier. They have been chosen because of their different internal structure: ¹⁴⁴Sm has a closed N = 82 neutron shell and a spherical ground-state configuration; ¹⁵⁴Sm with ten neutrons outside this shell is strongly deformed. The observed gross features of both reactions like energy, angular and total mass or element distributions are very similar; the ratio of the mass variances as function of the total kinetic energy loss indicates the number of exchanged nucleons to be comparable in all stages of the reactions. At small energy losses, however, the element distributions of the ¹⁴⁴Sm + ¹⁴⁴Sm reaction are considerably broader, pointing at an enhanced proton transfer at the cost of the number of exchanged neutrons in this system. This observation is attributed to the influence of the closed shell which seems to block the transfer of neutrons at low excitation energies. These results can be explained quantitatively by the different gradients of the shell-corrected potential energy surfaces of the two systems.     

Fourier analysis of nonself-averaging quasiperiodic oscillations in the excitation functions of dissipative heavy-ion collisions: quantum chaos in dissipative heavy-ion collisions?

We employ stochastic modelling of statistical reactions with memory to study quasiperiodic oscillations in the excitation functions of dissipative heavy-ion collisions. The Fourier analysis of excitation function oscillations is presented. It suggests that S-matrix spin and parity decoherence, damping of the coherent nuclear rotation and quantum chaos are sufficient conditions to explain the nonself-averaging of quasiperiodic oscillations in the excitation functions of dissipative heavy-ion collisions.     

Equilibrium in heavy ion collisions

We discuss the question of equilibration in heavy ion collisions and how it can be addressed in experiment     

Femtoscopy in heavy ion collisions

Non-trivial space-time geometrical effects are at the core of bulk-sector heavy ion physics, and two-particle correlations at low relative velocity are the most direct probe of this geometry at the femtometer scale. I present a brief overview of the wealth of femtoscopic measurements from the past two decades of heavy ion experiments. Essentially every conceivable “knob” at our disposal has been turned; the response of two-particle correlations to these variations has revealed much about the space-momentum substructure of the hot source created in the collisions. I discuss the present status of the femtoscopic program and questions which remain, and point to new efforts which aim to resolve them. PACS 25.75.Ld; 25.75.Gz; 24.10.Nz     

Processes with heavy ion collisions

Some Coulomb effects in heavy ion collisions are considered. Among them the process of muon and lepton pair creation, Coulomb and unitary corrections, statistics of multiple pair production. Effects of multiple photon exchange in process of lepton pair production by linearly polarized photon on nuclei are considered. This process is used for measuring the polarization of initial photon. Relativistic muon energy loss due to the light lepton pair production in the Coulomb field are calculated. Also we consider the effects of multiple photon exchange in elastic lepton scattering on unscreened atomic field and discuss the possible experimental testing.