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International Journal of Modern Physics E

SOME PHENOMENA THEORETICALLY PREDICTED AND EXPLAINED BY THE TIME ANALYSIS OF THE EXPERIMENTAL DATA ON NUCLEAR PROCESSES

V. S. Olkhovsky, V. V. DAVYDOVSKY, М.E. Dolinska, N.L. Doroshko

Published Aug 1, 2009• 0 citations
Publisher

Abstract

The self-consistent methods in time analysis of nuclear collisions and decays are based on the properties of time as a quantum observable, canonically conjugate to energy, and the appropriate definition of mean durations of quantum collisions, the variances in their distributions, the decay functions, and the surviving functions of the meta-stable states, including radioactive and compound nuclei. Even a simplified application of these methods for the elementary study of the α-decay in the exponential-law-decay approximation resulted in the simple phenomenological method of the determination of the α-particle one-step virtual and real sojourn time inside the parent α-radioactive nucleus between the α-particle successive incoherent multiple internal reflections during the α-decay. And also the direct temporal study of the quasi-monochromatic proton scattering by 12 C and 14 N nuclei at the range of isolated resonances distorted by the nonresonant background, accompanied by the bremsstrahlung, brings to the simple revealing of the possible existence of the delay–advance phenomenon in the proton emission during scattering (in the center-of-mass system). The utilization of the self-consistent methods of time analysis to the study of high-energy nuclear reactions (near and above 0.1 GeV per nucleon in the final compound–fragment formations) resulted in the discovery of the phenomenon of time resonances (or explosions) for such formations. Some perspectives of the further study of the evident temporal phenomena in nuclear processes are also indicated.

DOI
10.1142/s0218301309013713

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The self-consistent methods in time analysis of nuclear collisions and decays are based on the properties of time as a quantum observable, canonically conjugate to energy, and the appropriate definition of mean durations of quantum collisions, the variances in their distributions, the decay functions, and the surviving functions of the meta-stable states, including radioactive and compound nuclei. Even a simplified application of these methods for the elementary study of the α-decay in the exponential-law-decay approximation resulted in the simple phenomenological method of the determination of the α-particle one-step virtual and real sojourn time inside the parent α-radioactive nucleus between the α-particle successive incoherent multiple internal reflections during the α-decay. And also the direct temporal study of the quasi-monochromatic proton scattering by 12 C and 14 N nuclei at the range of isolated resonances distorted by the nonresonant background, accompanied by the bremsstrahlung, brings to the simple revealing of the possible existence of the delay–advance phenomenon in the proton emission during scattering (in the center-of-mass system). The utilization of the self-consistent methods of time analysis to the study of high-energy nuclear reactions (near and above 0.1 GeV per nucleon in the final compound–fragment formations) resulted in the discovery of the phenomenon of time resonances (or explosions) for such formations. Some perspectives of the further study of the evident temporal phenomena in nuclear processes are also indicated.
Precision tests of decay law of radioactive nuclei have not so far found any deviation from the exponential decay law at early time, as predicted by quantum mechanics. In this paper, we show that the quantum decoherence time (i.e. the timescale of nonexponential decay) of the quasifission or fission process should be of the order of attosecond considering the atom of the fissioning nucleus as a quantum detector. Hence, the observed decay timescale of the quasifission or fission process of even highly excited (EX greater than 50 MeV) transuranium and uraniumlike complexes should be rather long (of the order of attosecond) in spite of their very fast exponential decay timescale (of the order of zeptosecond) as measured by the nuclear techniques. Recent controversy regarding the observation of very long (of the order of attosecond ) and very short (of the order of zeptosecond ) quasifission or fission timescales for similar systems at similar excitation energies as obtained by direct techniques (crystal blocking, X ray fission fragment) and nuclear techniques could be interpreted as evidence for nonexponential decays in nuclear systems
Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself‐adjoint) operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four‐momentum and four‐position operators, for relativistic spin‐zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi‐self‐adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays) are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes) are reviewed.
A critical examination of the theory of resonance radiation has been carried through, employing the mathematical technique of Laplace and Stieltjes transforms. Particular attention has been devoted to the question of the temporal behavior of the excited state. With no restrictions on the interaction between atom and radiation field other than that it be real, and that processes of sufficiently high frequency contribute only negligible effects, one can prove that the probability amplitude of the excited state cannot decay according to the general law ${\ensuremath{\Sigma}}_{\ensuremath{\mu},\ensuremath{\nu}}{C}_{\ensuremath{\mu}\ensuremath{\nu}}{t}^{{\ensuremath{\lambda}}_{\ensuremath{\mu}}}{e}^{\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\nu}}t},$ where the ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$ and ${\ensuremath{\beta}}_{\ensuremath{\nu}}$ are complex constants lying in the right half-plane and the ${C}_{\ensuremath{\mu}\ensuremath{\nu}}$ are arbitrary complex coefficients. The deviation from the law just cited can be termed a straggling phenomenon since exact analysis shows that the probability amplitude, for sufficiently long times, is greater than that defined according to the radioactive decay law.Rigorous analysis of the source of this apparently anomalous behavior reveals the following explanation. Although the probability amplitude of the excited state is, strictly speaking, a functional of the interaction between the transition current in the atom and the photon states of the electromagnetic field, the essential features are determined principally by those states lying near the resonance frequency. Three elementary observations are immediately apparent. First, a particularly tractable analytical approximation for the interaction can be made such that the value of the actual interaction is reproduced at the resonance frequency and such that the behavior for high and low frequency photon states is at least qualitatively correct. Exact solutions in closed form can be obtained for this interaction. Second, in terms of the preceding representation it is possible to show that, associated with the transition between two atomic states, one is presented with a concomitant picture of a damped oscillation of charge describable in purely classical terms. Third, this classical motion can be interpreted as forming a source function for a continuous stochastic process in terms of which one finally derives the representation of the probability amplitude of the excited state. The straggling phenomenon previously cited is therefore that associated with all diffusion processes. The consideration of the exact interaction leads to more involved diffusion phenomena but does not in any case permit a radioactive decay law.
The framework to describe natural phenomena at their basics being quantum mechanics, there exist a large number of common global phenomena occurring in different branches of natural sciences. One such global phenomenon is spontaneous quantum decay. However, its long time behavior is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possible to infer on this large time behavior, directly from data. Specifically, we find evidence for nonexponential behavior of alpha decay of 8Be^{8}\mathrm{Be}8Be at large times from experiments.
The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.
Abstract Features of the Robertson–Schrödinger coordinate–momentum and energy–time uncertainty relations and connection between them have been considered. A method has been proposed to determine the duration of giant energy fluctuations of particles in a correlated coherent state. This method makes it possible to justify both a huge (many orders of magnitude) increase in the probability of the tunnel effect with the subsequent low-energy nuclear reaction and the automatic selection of low-energy reaction channels involving charged particles and the exclusion of the production of radioactive daughter isotopes. It has been shown that the same mechanism of formation of correlated coherent states explains a very significant suppression of gamma radiation observed in such reactions stimulated by the virtual energy as compared to similar reactions proceeding at a high “real” energy of particles.