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Physics of Particles and Nuclei Letters

A possibility of controlled variation of radioactive decay rate of atomic nuclei

В.Л. Михеев, V. A. Morozov, Natalia V. Morozova

Published Jul 1, 2008• 5 citations
Publisher

Abstract

An attempt of changing the radioactive decay rate of atomic nuclei due to interference of wave functions of the initial nucleus and nuclei identical to radioactive decay products has been made. The first experiments have been performed with 212 Po undergoing α decay with a half-life of 0.3 μs. For 212 Po implanted into natural metallic lead, the increase in the decay rate by ∼0.2%, as compared to the decay rate of 212 Po in nickel, has been registered.

DOI
10.1134/s1547477108040067

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An attempt of changing the radioactive decay rate of atomic nuclei due to interference of wave functions of the initial nucleus and nuclei identical to radioactive decay products has been made. The first experiments have been performed with 212 Po undergoing α decay with a half-life of 0.3 μs. For 212 Po implanted into natural metallic lead, the increase in the decay rate by ∼0.2%, as compared to the decay rate of 212 Po in nickel, has been registered.
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.
Instead of counting the number of nuclei ( ),tN it is easier to count the rate at which decays occur in the radioactive sample, and this is called the activity, defined as ( )0 tdN N e Ndt λλ λ−= = t (47.5) and follows the same exponential decay law (47.3). The SI unit for activity is the Becquerel (Bq), equal to one decay per second, and the common unit is the Curie (Ci), defined as It is also convenient to introduce the half-life as the time interval in which the activity is reduced to one-half .Bq107.3Ci1 10×= 2/1t 2ln2ln2/1 τλ ==t (47.6) The probability of radioactive decay through the direct transition of the nucleus from an initial state to a final state Ψi Ψ f , in time t, is given by (47.7) P t a tif f( ) | ( )|= 2 where the wave function amplitudes a are obtained from Eq.(37.11), which can be approximated by tf ( ) == /)()()()( tifiif ifetVtadt tda i εε −= (47.8) Since the probability of finding our decaying system in the initial state Ψi must decrease with time according to the radioactive decay law (47.3), which gives 2 2| ( ) | | | ti it e λ−Ψ = Ψ (47.9) we have to choose / 2( ) tia t e λ−= (47.10) rather than as considered in Eq.(37.13). Substituting this result into Eq.(47.8), and assuming a constant perturbation which is switched on at time t = 0, yields ai = 1, i εελ −+−= (47.11) Integrating, we get an oscillatory behaviour of the wave function amplitude, given by ( ) ( ) /2 V e a t i ε ε λ − +⎡ ⎤−⎣ ⎦= − + = == = (47.12) Figure 47.1. Energy spectrum of a decaying state of width Γ At the end of the nuclear transition we should consider the amplitude corresponding to ,∞→t which reads )( λεε = = i V a if fi f +−=∞ (47.13) and this yields the transition probability (47.7) in the form )( || )( Γ+−=∞ if fi if V P εε = (47.14) Hence, the probability to observe the nucleus with energy fε in the vicinity of iε follows a Lorentzian distribution, illustrated in Figure 47.1. By analogy with the atomic transitions, Γ = = 〈 〉= =λ / t gives the natural linewidth of the emitted radiation, which is the same as the width of the decaying nuclear state. Nuclear states which are populated in ordinary decays typically have lifetimes greater than corresponding to sec,10 12− ( ) τ/1066.0eV 15−×=Γ (47.15) which is of the order of Since this width is small compared with the energy spacing of nuclear levels, which is of the order of the nuclear decaying states may be regarded to be discrete quasi-stationary states.
The evolution of views on the possibility of external influence on the process of radioactive decay is briefly presented. Such an effect can lead to the appearance of periods in the time series of the radioactive decay rate fluctuations, which have been the subject of intensive study in the last decade. Two mechanisms for identifying periods are considered: the study of deviations from the theoretical curve of the radioactive decay law and the study of the properties of fluctuations. It is shown that the latter method leads to a universal spectrum of periods observed not only in the time series of the radioactive decay rate fluctuations, but also in the time series of fluctuations of processes of various nature. The main object of our study are periods in the radioactive decay rate fluctuations. The presence of such periods suggests the possibility of external influence on the process of radioactive decay. Therefore, we briefly consider the evolution of views on the possibility of such an effect. To do this, we distinguish several stages. The division into stages is only partially historical, but, mainly, each stage characterizes a certain ideas that is implemented in it.
Abstract Several experimental groups reported the evidence of periodic modulations of nuclear decay constants which amplitudes are of the order 10−3{{10}^{{ - 3}}}10−3 and periods of one year, 24 h or about one month. We argue that such deviations from radioactive decay law can be described in nonlinear quantum mechanics framework, in which decay process obeys to nonlinear Shrödinger equation with Doebner–Goldin terms. Possible corrections to Hamiltonian of quantum system interaction with gravitation field considered, it’s shown that they correspond to some emergent gravity theories, in particular, bilocal field model. It’s shown that proposed model describes decay parameter variations which agree with experimental results for Po-214 α\alpha α -decay life-time oscillations.
The halflife of αradioactive elements has already been measured out through experiments. But, classical theory's failure to explain the phenomenon of αDecay is found in this article according to the analysis of the mechanism of αDecay. And in this article, this problem is completely settled through introducing of the theory of quantum tunneling effect yet. Furthermore, the halflife of αDecay of238U is illustrated and figured out with this theory, and is approximately in accordance with the figure of experiments.