  Decay laws of moving unstable quantum systems with oscillating decay rates
are analyzed over intermediate times. The transformations of the decay laws at
rest and of the intermediate times at rest, which are induced by the change of
reference frame, are obtained by decomposing the modulus of the survival
amplitude at rest into 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, $\Gamma_j$, and the modal frequencies of
oscillations at rest, $\Omega_j$, reduce regularly, $\Gamma_j/\gamma$ and
$\Omega_j/\gamma$, in the laboratory reference frame. Consequently, 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,
over a determined time window. The time 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 $\gamma$.
