M. Dworzecka

Microscopic nuclear dissipation

Abstract We have formulated a microscopic, nonperturbative, time reversible model which exhibits a dissipative decay of collective motion for times short compared to the systems Poincare time. The model assumes an RPA approximate description of the initial collective state within a restricted subspace, then traces its time evolution when an additional subspace is coupled to the restricted subspace by certain simplified matrix elements. It invokes no statistical assumptions. The damping of the collective motion occurs via real tansitions from the collective state to other more complicated nuclear states of the same energy. It corresponds therefore to the so called “one-body” long mean free path limit of nuclear dissipation when the collective state describes a surface vibration. When the simplest RPA approximation is used, this process associates the dissipation with the escape width for direct particle emission to the continuum. When the more detailed second RPA is used, it associates the dissipation with the spreading width for transitions to the 2p-2h components of the nuclear compound states as well. The energy loss rate for sharp n-phonon initial states is proportional to the total collective energy, unlike the dissipation of a classical damped oscillator, where it is proportional to the kinetic energy only. However, for coherent, multi-phonon wave packets, which explicitly describe the time-dependent oscillations of the mean field, dissipation proportional only to the kinetic energy is obtained. Canonical coordinates for the collective degree of freedom are explicitly introduced and a nonlinear frictional hamiltonian to describe such systems is specified by the requirement that it yield the same time dependence for the collective motion as the microscopic model. Thus, for the first time a descriptive nonlinear hamiltonian is derived explicitly from the underlying microscopic model of a nuclear system.

TDHF eigenstates: Gauge invariant periodic solutions☆

Abstract Gauge invariant periodic TDHF solutions are shown to form the same discrete subset of a continuum as would be selected by the Bohr-Sommerfeld quantization condition of the field. Such solutions promise an approximate description for bound eigenstates within the time-dependent framework. Analysis of specific model cases supports the view that this spectrum of gauge invariant periodic TDHF eigensolutions can indeed provide that description.

Nuclear dissipation as damping of collective motion in the time-dependent RPA: (I). The microscopic model

Abstract A microscopic model for describing nuclear dissipation as the damping of collective motion in the time-dependent RPA is considered. The collective state is defined as a solution of the RPA equations of motion in a restricted subspace, S1, of discrete 1p-1h states. The damping of the collective motion is described by the time evolution of the wave packet which solves the time-dependent Schrodinger equation in an extended subspace, S, when initialized with the collective state. In the present paper we consider additional state of the 1p-1h structure only. The RPA solution for the wave packet describing the damping enables one to calculate — as a function of time — both the probability amplitude for finding the system in the collective state and the collective energy, and to extract their time decay under appropriate conditions. The rate of decrease of the collective energy is interpreted as the energy dissipation rate.

Nuclear Dissipation as Damping of Collective Motion in Rpa. 1. The Microscopic Model

Abstract A microscopic model for describing nuclear dissipation as the damping of collective motion in the time-dependent RPA is considered. The collective state is defined as a solution of the RPA equations of motion in a restricted subspace, S1, of discrete 1p-1h states. The damping of the collective motion is described by the time evolution of the wave packet which solves the time-dependent Schrodinger equation in an extended subspace, S, when initialized with the collective state. In the present paper we consider additional state of the 1p-1h structure only. The RPA solution for the wave packet describing the damping enables one to calculate — as a function of time — both the probability amplitude for finding the system in the collective state and the collective energy, and to extract their time decay under appropriate conditions. The rate of decrease of the collective energy is interpreted as the energy dissipation rate.

Classical wall formula and quantal one-body dissipation

Abstract Within the quantal, self-consistent RPA description of the dissipation of nuclear collective energy, a specific set of assumptions is shown to reduce the RPA system to a vibrating potential model which, with the stipulation of certain additional assumptions, yields precisely the dissipation rate given by the Swiatecki wall formula. This correspondence is utilized to explore the explicit and the implicit assumptions of the wall model. Various implications emerge, the most important of which is the fact that, for finite nucleonic binding energy, the true one-body dissipation rate of giant resonance states is reduced by about an order of magnitude from the wall formula value. The wall formula overestimate is due mostly to the fiction it assumes ab initio that all particles are totally reflected at the wall, whereas realistically only bound particles can be totally reflected. In addition, the self-consistency of the quantal description implies that no dissipation occurs to the bound one-particle one-hole subspace from which the RPA phonon is constructed, imposing an absolute prohibition of one-body dissipation for phonon energies less than the nucleonic binding energy. Finally, the quantal dissipation rate exhibits an explicit, but relatively weak, dependence upon the collective phonon energy, ħω. The result is that the wall formula yields a gross overestimate of the quantal one-body dissipation rate over the whole range of realistic nuclear situations.

Two-dimensional random walk on the ground state energy surface: The N-Z distributions from nuclear heavy-ion collisions

Abstract The nucleon transfer process in deep inelastic collision is formulated as a two-dimensional random walk process on the N - Z plane. The probability of each step is assumed to be proportional to the available final state density which is determined by the ground state energy surface of the colliding dinuclear system. Here a model problem is considered, where the long and narrow valley in the energy surface is replaced by a slot with a flat bottom. Even in this crude model, good agreement is obtained between the calculated widths of the N - Z distribution and the experimental values, indicating that the ground state energy surface plays an important role in the mass and charge transfer phenomena in deep inelastic processes.

Qualitative properties of the discrete random walk evolution of projectile-like (N, Z) values on the dinuclear liquid-drop surface

Abstract A discrete random walk calculation of the evolution of the ( N , Z ) distribution of projectile-like fragments from a nuclear heavy ion collision is presented. It incorporates energy conservation explicitly for each nucleon transfer, utilizing the liquid drop energies of osculating dinuclei to estimate the ( N , Z ) dependence of the ground state energy of the system. The results show that energy conservation and the liquid-drop energy surface suffice to prescribe the characteristic shapes in ( N , Z ) of the distributions when the transfer probabilities are defined by the total nuclear level densities; the rate at which the distribution spreads, on the other hand, is dominated by the fraction of the kinetic energy which is assumed to be dissipated by mechanisms other than nucleon transfer. Possible alternative prescriptions for the transfer probabilities are considered and shown to be qualitatively in disagreement with the observations at higher total kinetic energy loss (TKEL). Also it is shown that the overall width. σ 2 A , is less sensitive to such variations of the transfer probabilities than σ 2 Z , and how this feature is a natural consequence of the dinuclear energy surface. Finally, a residual discrepancy between calculation and observation at low TKEL values is identified as the most prominent remnant weakness of the description.

Collective degrees of freedom and one-body dissipation in heavy ion collisions☆

Abstract We employ a three-parameter family of volume conserving nuclear shapes to couple relative motion and collective degrees of freedom in heavy ion collisions. Damping is achieved through the one-body dissipation mechanism. Results are compared with experimental data.

Macroscopic implications of diverse reaction mechanisms in ion-ion collisions

Abstract Discrete random walk calculations of the ( N , Z ) evolution of a liquid-drop dinucleus are reported for various assumptions about the transfer dynamics. Transition probabilities are assumed which correspond to the transferred nucleons being able to reach (a) any energy-conserving state of the final dinucleus, (b) any energy-conserving final state more complicated by not more than 1p and 1h than the initial state, and (c) any 1p1h excitation of the initial state. Physically these assumptions correspond to restricting the transfer, not at all, somewhat, and totally to be a pure one-body process. In every case, the Pauli exclusion principle is honored in the allowed final states. One finds that the assumption (c) generally leads to predictions easily distinguishable from those of (a) and (b), which do not differ substantially.

Reaction theory for a nonlinear dynamics: The S-matrix time-dependent Hartree-Fock theory☆

Abstract A single determinantal TDHF reaction theory structurally analogous with the S -matrix Schrodinger theory is constructed. It involves time averaging in an essentail way, displays the interpretatively crucial properties of asymptoticity and channel specificity, and excludes the effects of multi-channel spurious cross channel correlations.