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Chinese Physics C

QUANTUM BROWNIAN MOTION AND NUCLEAR FISSION

Yuanshun Huo

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

Based on a simplified Hamiltonian model the transition from quantum to classical diffu- sion behaviours for a system has been shown.The approximation of a locally harmonic oscilla- tor and reduced density operator propagator in the harmonic oscillator are generalized to cal- culate the escape rate over the barrier for the system in a fission potential consisting of a gro- und state well and barrier.

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Based on a simplified Hamiltonian model the transition from quantum to classical diffu- sion behaviours for a system has been shown.The approximation of a locally harmonic oscilla- tor and reduced density operator propagator in the harmonic oscillator are generalized to cal- culate the escape rate over the barrier for the system in a fission potential consisting of a gro- und state well and barrier.
Based on a simplified Hamiltonian model the transition from quantum to classical diffusion behaviours for a system has been shown by studying the dependence of the quantum Brownian motion in a harmonic oscillator potential on the viscosity and temperature of the system. The approximation of a locally harmonic oscillator and reduced density operator propagator in the harmonic oscillator are generalised to calculate the escape rate over the barrier for the system in a fission potential consisting of a ground-state well and barrier. Compared with the results of the Fokker-Planck equation the model in this paper is completely quantum mechanical.
Analytical expressions for the spectral density of the tunnelling rate are found for a fission-like analytical barrier, having three parts: an internal part approximated by a harmonic oscillator, a top part considered constant and an external part considered as a Coulomb potential. We found that environment-assisted tunnelling processes are present for all three regions and that an environment-stimulated decay is significant only for the Coulomb part of the barrier. Numerical calculations are made for the cold fission of 236 U to 138 Xe+ 98 Sr.
Quantum diffusion equations with time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytical formulas for calculating friction and diffusion coefficients in nuclear processes are obtained. The asymptotics of the transport coefficients and of the correlation functions are investigated. The problem of correlation decay in quantum dissipative systems is studied. A comparative analysis of diffusion coefficients for the harmonic and inverted oscillators is performed. The role of quantum statistical effects during passage through a parabolic potential barrier is investigated. Sets of diffusion coefficient assuring the purity of states at any time instant are found in cases of non-Markovian dynamics. The influence of different sets of transport coefficients on the rate of decay from a metastable state is studied in the framework of the master equation for reduced density matrices describing open quantum systems. The approach developed is applied to investigation of fission processes and the processes of projectile-nuclei capture by target nuclei for bombarding energies in the vicinity of the Coulomb barrier. The influence of dissipation and fluctuation on these processes is taken into account in a self-consistent way. The evaporation residue cross sections for asymmetric fusion reactions are calculated from the derived capture probabilities averaged over all orientations of the deformed projectile and target nuclei.
The induced nuclear fission is considered a transport process over the fission barrier underlying dissipative forces. Using a quantum master equation for the reduced density matrix, the influence of microscopical diffusion coefficients on the total fission time and transient time is studied. The influence of transient effects on the probability of the first-chance fission is estimated. For different temperatures and friction coefficients, the quasistationary fission rate is compared with the analytical Kramers formula.
This paper is devoted to the study of quantum dissipation in nuclear cluster decay phenomena within the framework of the Lindblad approach to quantum open systems. Typical examples of nuclear decay phenomena, such as cluster radioacivity, spontaneous cold fission of actinide nuclei or quasi-fission of super-heavy nuclei can be described by considering the tunnelling of a metastable state across a piecewise quadratic potential. Two study cases are considered: (i) a harmonic well smoothly joined to an inverted parabola which simulates the barrier and (ii) the inverted parabola of case (i) is continued with a second harmonic well. The width and depth of the second harmonic oscillator well are varied over a wide range of values in order to encompass particular cases of tunnelling in the double-well potential. The evolution of the averages and covariances of the quantum sub-system is studied in both under- and over-damped regimes. For a Gaussian initial wavepacket we compute the tunnelling probability for different values of the friction coefficient and fixed values of the diffusion coefficients. The ansatz used for these coefficients corresponds to the case with temperature T = 0.