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arXiv:0810.2860

The Schrodinger-Chetaev Equation in Bohmian Quantum Mechanics and Diffusion Mechanism for Alpha Decay, Cluster Radioactivity and Spontaneous Fission

V. D. Rusov, S. Cht. Mavrodiev, M. Deliyergiyev

Published Oct 16, 2008• 0 citations
arXivHTMLPDF

Abstract

In the framework of Bohmian quantum mechanics supplemented with the Chetaev theorem on stable trajectories in dynamics in the presence of dissipative forces we have shown the possibility of the classical (without tunneling) universal description of radioactive decay of heavy nuclei, in which under certain conditions so called noise-induced transition is generated or, in other words, the stochastic channel of alpha decay, cluster radioactivity and spontaneous fission conditioned by the Kramers diffusion mechanism. Based on the ENSDF database we have found the parametrized solutions of the Kramers equation of Langevin type by Alexandrov dynamic auto-regularization method (FORTRAN program REGN-Dubna). These solutions describe with high-accuracy the dependence of the half-life (decay probability) of heavy radioactive nuclei on total kinetic energy of daughter decay products. The verification of inverse problem solution in the framework of the universal Kramers description of the alpha decay, cluster radioactivity and spontaneous fission, which was based on the newest experimental data of alpha-decay of even-even super heavy nuclei (Z=114, 116, 118) have shown the good coincidence of the experimental and theoretical half-life depend upon of alpha-decay energy.

DOI
10.48550/arxiv.0810.2860

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In the framework of Bohmian quantum mechanics supplemented with the Chetaev theorem on stable trajectories in dynamics in the presence of dissipative forces we have shown the possibility of the classical (without tunneling) universal description of radioactive decay of heavy nuclei, in which under certain conditions so called noise-induced transition is generated or, in other words, the stochastic channel of alpha decay, cluster radioactivity and spontaneous fission conditioned by the Kramers diffusion mechanism. Based on the ENSDF database we have found the parametrized solutions of the Kramers equation of Langevin type by Alexandrov dynamic auto-regularization method (FORTRAN program REGN-Dubna). These solutions describe with high-accuracy the dependence of the half-life (decay probability) of heavy radioactive nuclei on total kinetic energy of daughter decay products. The verification of inverse problem solution in the framework of the universal Kramers description of the alpha decay, cluster radioactivity and spontaneous fission, which was based on the newest experimental data of alpha-decay of even-even super heavy nuclei (Z=114, 116, 118) have shown the good coincidence of the experimental and theoretical half-life depend upon of alpha-decay energy.
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.
According to theories of classical physics, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by transition coefficient. Correct calculation of this coefficient is particularly important because extremely sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient was generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In the previous papers, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results were applied to calculate the half-life values of the nuclei that emit alpha particle. In this article, the half-life calculation formulas obtained in previous studies were made simpler. It has been shown that it is applicable to all radioactive decays (alpha, beta, gamma etc.). The half-life values obtained from our calculations have been compared with the experimental values, and it has been found that the new half-life values are exactly consistent with the experimental values.
Using Chetaev's theorem on stable trajectories in dynamics in the presence of perturbation forces we obtain a generalized stability condition for Hamiltonian systems that has the form of the Schrodinger equation. We show that the energy of the perturbation forces generating generalized Chetaev's stability condition is of electromagnetic nature and exactly coincides with Bohm's "quantum" potential. We stress that not taking into account the reality of Bohm's electromagnetic Psi-field turns out to be the fundamental reason of violation of the famous Bell inequality, in the recent most precise direct experiments, as well as in theoretical calculations based on the simple Wigner model. We discuss the possibility of direct experiments, alternative to Bell's ideology and related, e.g. with observation of nuclear stochastic resonance during the alpha-decay process, which cannot occur in the framework of the probabilistic interpretation of quantum mechanics, but has to occur in the alternative Bohm interpretation.
Basing on the Chetaev's theorem on stable trajectories in dynamics in the presence of dissipative forces we obtain a generalized stability condition for Hamiltonian systems that has the form of the Schrodinger equation. We show that the energy of the dissipative forces generating generalized Chetaev's stability condition exactly coincides with Bohm's "quantum" potential. Using the principle of least action of perturbation we prove that the Bohmian quantum mechanics complemented with the Chetaev's generalized theorem does not have hidden variables.
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.
According to classical physics theories, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by a transition coefficient. Correct calculation of this coefficient is very important because very sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient is generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In this paper, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results are applied to calculate the half-life values of the nuclei that emit alpha particles. The half-life values obtained from our calculations and the classical method (WKB) have been compared, and it has been found that the new half-life values are exactly consistent with the experimental values.