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

Abstract

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 $\gamma$.

arXiv commentarXiv admin note: text overlap with arXiv:1902.05210

References in corpus (18)

• Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like ${}^{140}$Pr and ${}^{142}$Pm Ions
• High-resolution measurement of the time-modulated orbital electron capture and of the ${\beta }^{+}$ decay of hydrogen-like ${}^{142}$Pm${}^{60+}$ ions
• No classical limit of quantum decay for broad states
• General properties of the evolution of unstable states at long times
• Hidden evidence of non-exponential nuclear decay
• Deviation from the exponential decay law in relativistic quantum field theory: the example of strongly decaying particles
• Decay Law of Relativistic Particles: Quantum Theory Meets Special Relativity
• Search for Oscillation of the Electron-Capture Decay Probability of ${}^{142}$Pm
• New Test of Modulated Electron Capture Decay of Hydrogen-Like ${}^{142}$Pm Ions: Precision Measurement of Purely Exponential Decay
• Oscillations in the decay law: A possible quantum mechanical explanation of the anomaly in the experiment at the GSI facility
• Decay law and time dilatation
• Quantum decay law: Critical times and the Equivalence of approaches
• Moving system with speeded-up evolution
• The true face of quantum decay processes: Unstable systems in rest and in motion
• Time evolution of an unstable quantum system
• Moving unstable particles and special relativity
• Time dilation in the oscillating decay laws of moving two-mass unstable quantum states
• Transformation of intermediate times in the decays of moving unstable quantum systems via the exponential modes

Cited by in corpus (3)

• Formal Aspects of Quantum Decay
• Analysis of quantum decay law: Is quantum tunneling really exponential?
• Quantum Corrections to the Decay Law in Flight