Quasi-fission mass distributions as a random walk process: The 63Cu+197Au system

doi:10.1016/0375-9474(76)90652-7

Nuclear Physics A

Volume 267, 16 August 1976, Pages 181-189

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Abstract

The quasi-fission mass distributions have been measured at 365 and 443 MeV lab bombarding energy. Assuming a Markov process, a Fokker-Planck equation has been derived, the coefficient of which have been calculated using an analogy with the classical theory of Brownian motion. These coefficients have been shown to be energy dependent and they have been expressed in terms of a correlation function calculated in an equilibrium situation. This model has been successfully applied to the Cu+Au system at two different bombarding energies.

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Cited by (16)

A bibliography on applications of random walks in theoretical chemistry and physics
1982, Advances in Molecular Relaxation and Interaction Processes
Dissipative collisions of heavy ions at energies close to the Coulomb barrier
1981, Nuclear Physics, Section A
²⁰⁸Pb induced deep inelastic reactions on several target nuclei between ⁹⁴Zr and ¹⁷⁰Er have been studied at incident energies close to the Coulomb barrier. From the analysis optimum conditions for the transfer of many nucleons in deep inelastic collisions are deduced. The system ²⁰⁸Pb + ¹¹⁰Pd exhibits the largest mass transfer observed so far. This is attributed to the softness of the transitional nucleus ¹¹⁰Pd. At incident energies close to the barrier the exchange of neutrons is enhanced. The mass, charge and energy flow is analyzed within a model derived from Langevin's theory of Brownian motion. An equilibration phase (~10⁻²¹ s) preceding a diffusion phase was observed. This equilibration phase is controlled by nuclear structure effects. In the later diffusion phase strongly deformed configurations are produced.
Mass transport in nuclear collisions
1978, Nuclear Physics, Section A
The exchange of nucleons during a nuclear collision gives rise to a transport of mass between the two collision partners. The coefficients entering in the transport equation for the nuclear mass asymmetry are related to the microscopic currents of nucleons between the two interacting nuclei; quantum-statistical effects are taken into account. By a method similar to that introduced for the calculation of the nuclear proximity potential simple analytical expressions are obtained for the coefficients governing the drift and diffusion of the nuclear mass asymmetry; the result contains no arbitrary parameters. Illustrative application is made to the collision of idealized nuclei.
Mechanisms of very heavy-ion collisions: The 209Bi + 136Xe reaction at E<inf>Lab</inf> = 1130 MeV
1978, Physics Reports
The mechanisms of kinetic-energy dissipation and nucleon exchange operating in damped heavy-ion collisions, and the corresponding time scales are investigated. As an example of a very heavy system, the reaction ²⁰⁹Bi + ¹³⁶Xe at E_Lab = 1130 MeV is choosen for a comparison with various reaction models. The experimental data include atomic number, energy and angular distributions of the projectile-like fragments and the correlations between these experimental observables. The integrated fragment Z distribution is found to be broad, but centered at the charge of the projectile. The kinetic energy distribution extends from quasi-elastic down to Coulomb energies of highly deformed fragments. The angular distribution of the reaction products is focussed into a narrow angular range a few degrees forward of the quarter-point angle. Examining the correlations of experimental observables with fragment charge and energy loss in detail, it is concluded that the kinetic-energy loss is a fundamental parameter indicating the stage of evolution of the reaction, i.e., the interaction time. The energy loss is inferred to decrease linearly with angular momentum, and this relation is used to construct an average experimental deflection function. The latter is compared to the predictions of classical dynamical models employing various potentials and frictional forces. These calculations do not provide a consistent description of the experimental results.
Employing a simple phenomenological reaction model, l-dependent interaction times are deduced which are used to evaluate proton-number diffusion coefficients. A rather model-independent comparison of the time dependence of the mechanisms of nucleon exchange and kinetic energy dissipation is achieved by using the microscopic time scale provided by the nucleon-exchange mechanism. Energy dissipation is found to be of the one-body type, nucleon exchange contributing about 30% to the total energy loss. A consistent description of the observed reaction phenomena has been achieved in terms of a statistical mechanism of damped reactions evolving in time as nucleons are exchanged and energy is dissipated. It connects in a continuous fashion the domains of quasi-elastic scattering and strongly damped collisions.
Transport theory of deeply inelastic heavy-ion collisions based on a random-matrix model. i. Derivation of the transport equation
1977, Annals of Physics
A random-matrix model is used to describe the transformation of kinetic energy of relative motion into intrinsic excitation energy typical of a deeply inelastic heavy-ion collision. The random-matrix model is based upon statistical assumptions regarding the form factors coupling relative motion with intrinsic excitation of either fragment. Average cross sections are calculated by means of an ensemble average over the random matrix model. Summations over intermediate and final intrinsic spin values are performed. As a result, average cross sections are given by the asymptotic behavior of a probability density which in turn obeys a transport equation. In the transport equation there is no further reference to intrinsic spins. The physical and mathematical properties of this equation are exhibited.
Quasi-fission and other strongly damped collisions between 63Cu ions and 197Au nuclei
1977, Nuclear Physics, Section A
The interaction of ⁶³Cu ions with ¹⁹⁷Au nuclei have been studied experimentally at incident energies of 365 and 443 MeV (1.1 and 1.4 times the Coulomb barrier). Mass and kinetic energy distributions of reaction products have been measured at several angles. Near the grazing angle, a continuous transition was found from elastic events to partially damped (PD) events, and to fully damped events (quasi-fission, QF). Away from the grazing angle a clean separation between elastic and QF events was observed. Events that may be due to fission following fusion (CF) were also obtained. Results are discussed in terms of decomposition into PD, QF, and CF components. The QF kinetic energy is independent of the incident energy (implying full damping of the initial relative motion). It is lower than the Coulomb barrier and close to the kinetic energies from the fission of similar systems. The angular distribution is peaked somewhat forward of the grazing angle for low mass transfers. For large mass transfers the yield increases slowly with decreasing angle. At 443 MeV a large contribution from negative angles is present. σ_QF accounts for more than 65 % of the reaction cross section σ_R at 443 MeV and for more than 50 % at 365 MeV. The upper limit on CF is about 10 % of σ_R, and σ_PDis of the order of 25 % of σ_R.

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Nuclear Physics A

Abstract

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Cited by (16)

A bibliography on applications of random walks in theoretical chemistry and physics

Dissipative collisions of heavy ions at energies close to the Coulomb barrier

Mass transport in nuclear collisions

Mechanisms of very heavy-ion collisions: The <sup>209</sup>Bi + <sup>136</sup>Xe reaction at E<inf>Lab</inf> = 1130 MeV

Transport theory of deeply inelastic heavy-ion collisions based on a random-matrix model. i. Derivation of the transport equation

Quasi-fission and other strongly damped collisions between <sup>63</sup>Cu ions and <sup>197</sup>Au nuclei