Timescale of non-exponential decay for the nuclearβ-decay process in a decoherence model

Abstract

The quantum-mechanical time evolution of an isolated \ensuremath{\beta}-unstable nuclear state in the context of certain models predicts that the square of the amplitude of the initial undecayed state becomes an approximately exponential function of time on a timescale on the order of ${10}^{\ensuremath{-}22}--{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$. It was argued that a measurement process required to distinguish between the parent and the daughter nuclear states in such a short time would destroy the characteristics of the long-lived \ensuremath{\beta}-unstable nuclear state, thus fundamentally restricting the observability of \ensuremath{\beta} decay on a short timescale. Since the interaction of the nuclear state with the environment is almost inevitable, we have obtained the timescale of initial non-exponential decay for the nuclear \ensuremath{\beta} decay from an estimation of quantum decoherence time considering the atom of the decaying nucleus as a quantum detector. It has been found from such considerations that a decoherence timescale of \ensuremath{\beta} decay is on the order of ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ and the decay should remain reversible and non-exponential on this timescale. The possibilities of observing the effect of non-exponential decay in nuclear systems have been discussed.