Decay Law of Moving Unstable Particle

Quantum relativistic decay law of moving unstable particle is analytically calculated in the model case of the Breit–Wigner mass distribution. It turns out that Einstein time dilation of the moving particle decay holds approximately at times when the decay is exponential. The related correction is calculated analytically. Being very small at these times it is practically unobservable. It is shown that Einstein dilation fails for large times t when decay is not exponential. An unstable system of the kind of K ₀-meson (which is the superposition of K _s and K _I) is also considered. In this case, the violation of Einstein dilation is shown to be appreciable at all times under some condition