Regularities in the transformation of the oscillating decay rate in moving unstable quantum systems

Decay laws of unstable quantum systems, which move with constant linear momentum in the laboratory reference frame and exhibit oscillating decay rate, are analyzed over intermediate times. The transformations of the decay laws and intermediate times at rest, which are induced by the change of reference frame, are obtained from the basic principles of quantum theory and special relativity by approximating the modulus of the survival amplitude at rest via the superposition of purely exponential and exponentially damped oscillating modes. The mass distribution density is considered to be approximately symmetric with respect to the mass of resonance. Under determined conditions, the modal decay widths at rest, Γj, and the modal frequencies of oscillations at rest, Ωj, reduce regularly, Γj/γ and Ωj/γ, in the laboratory reference frame. Over a determined time window, the survival probability at rest, the intermediate times at rest and, if the oscillations are periodic, the period of the oscillations at rest transform regularly in the laboratory reference frame according to the same time scaling. The scaling reproduces the relativistic dilation of times if the mass of resonance is considered to be the effective mass at rest of the moving unstable quantum system with relativistic Lorentz factor γ