Nonclassical face of quantum decay processes

Abstract

Abstract. A detailed analysis of the quantum decay processes shows the survival probability P(t) can not take that exponential form at any time interval including times smaller than the lifetime τ . We show that for times t ∼ τ and for the times later than τ the form of P(t) looks as a composition of an oscillating and exponential functions. The amplitude of these oscillations is very small for t ≪ τ and grows with increasing time and depends on the model considered. We also study the survival probability of moving relativistic unstable particles with definite momentum p = 0: It turns out that late time deviations of the survival probability of these particles from the exponential-like form of the decay law should occur much earlier than it follows from the classical standard approach resolving itself into replacing time t by t/γ (where γ is the relativistic Lorentz factor) in the formula for the survival probability P(t). IntroductionSince the discovery of radioactivity and the formulation of the radioactive decay law by Rutheford and Sody [1] there is a conviction that the decay law has the exponential form, N (t) = N 0 exp [−λt], where λ > 0 is a constant, N (t) is the number of atoms of the radioactive element at the instant t ≥ 0 and N 0 = N (0). Wesisskopf-Wigner theory of spontaneous emission [2] has extended this belief on the quantum decay processes: They found that to a good approximation the quantum mechanical non-decay probability of the exited atomic levels is a decreasing function of time having exponential form. Further theoretical studies of the quantum decay process [3,4] showed that such processes seem to have three stages: the early time (initial), exponential (or "canonical"), and late time having inverse-power law form [5]. Results of these theoretical studies were the reason that there is rather widespread belief that a universal feature of the quantum decay process is the presence of these three time regimes. In this situation, each experimental evidence of oscillating decay curve at times of the order of life times is considered as an anomaly: The so-called GSI-anomaly [6,7] is an example. The question arises, if indeed in the case of one component quantum unstable systems such oscillations of the decay process at the "exponential" regime are an anomaly. The another question is: Whether and how such a possible oscillations depend on the motion of the unstable quantum system. So we need also to know how to describe the decay process of unstable quantum systems in motion.Studying text books one finds that if the decay law of the unstable particle in rest has the following form P(t) = exp [− Γ 0 t ] ≡ P c (t), then in the case of the moving particle with