The true face of quantum decay processes: Unstable systems in rest and in motion

Abstract

Since the discovery of the radioactive decay law by Rutherford and Sody the belief that the decay law has the exponential form has become common. This conviction was upheld by Wesisskopf–Wigner theory of spontaneous emission [1]. Further studies of the quantum decay process showed that basic principles of the quantum theory led to rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: The early time (initial), exponential (or ”canonical”), and late time having inverse–power law form [2]. The question arises, if indeed this is the true picture of quantum decay processes. From the standard, text book considerations one finds that if the decay law of the unstable particle at rest has the exponential form P0(t) = exp [−0 t ~ ], then the decay law of the moving particle looks as follows: