Precision tests of decay law of radioactive nuclei have not so far found any deviation from the exponential decay law at early time, as predicted by quantum mechanics. In this paper, we show that the quantum decoherence time (i.e. the timescale of nonexponential decay) of the quasifission or fission process should be of the order of attosecond considering the atom of the fissioning nucleus as a quantum detector. Hence, the observed decay timescale of the quasifission or fission process of even highly excited (EX greater than 50 MeV) transuranium and uraniumlike complexes should be rather long (of the order of attosecond) in spite of their very fast exponential decay timescale (of the order of zeptosecond) as measured by the nuclear techniques. Recent controversy regarding the observation of very long (of the order of attosecond ) and very short (of the order of zeptosecond ) quasifission or fission timescales for similar systems at similar excitation energies as obtained by direct techniques (crystal blocking, X ray fission fragment) and nuclear techniques could be interpreted as evidence for nonexponential decays in nuclear systems
Precision tests of decay law of radioactive nuclei have not so far found any deviation from the exponential decay law at early time, as predicted by quantum mechanics. In this paper, we show that the quantum decoherence time (i.e. the timescale of nonexponential decay) of the quasifission or fission process should be of the order of attosecond considering the atom of the fissioning nucleus as a quantum detector. Hence, the observed decay timescale of the quasifission or fission process of even highly excited (EX greater than 50 MeV) transuranium and uraniumlike complexes should be rather long (of the order of attosecond) in spite of their very fast exponential decay timescale (of the order of zeptosecond) as measured by the nuclear techniques. Recent controversy regarding the observation of very long (of the order of attosecond ) and very short (of the order of zeptosecond ) quasifission or fission timescales for similar systems at similar excitation energies as obtained by direct techniques (crystal blocking, X ray fission fragment) and nuclear techniques could be interpreted as evidence for nonexponential decays in nuclear systems
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.
The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.
The self-consistent methods in time analysis of nuclear collisions and decays are based on the properties of time as a quantum observable, canonically conjugate to energy, and the appropriate definition of mean durations of quantum collisions, the variances in their distributions, the decay functions, and the surviving functions of the meta-stable states, including radioactive and compound nuclei. Even a simplified application of these methods for the elementary study of the α-decay in the exponential-law-decay approximation resulted in the simple phenomenological method of the determination of the α-particle one-step virtual and real sojourn time inside the parent α-radioactive nucleus between the α-particle successive incoherent multiple internal reflections during the α-decay. And also the direct temporal study of the quasi-monochromatic proton scattering by 12 C and 14 N nuclei at the range of isolated resonances distorted by the nonresonant background, accompanied by the bremsstrahlung, brings to the simple revealing of the possible existence of the delay–advance phenomenon in the proton emission during scattering (in the center-of-mass system). The utilization of the self-consistent methods of time analysis to the study of high-energy nuclear reactions (near and above 0.1 GeV per nucleon in the final compound–fragment formations) resulted in the discovery of the phenomenon of time resonances (or explosions) for such formations. Some perspectives of the further study of the evident temporal phenomena in nuclear processes are also indicated.
The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.
By using an exact analytical approach to the time evolution of decay we investigate the tunneling decay of ultracold single atoms to discuss the conditions for deviations of the exponential decay law. We find that R, given by the ratio of the energy of the decaying fragment Er to its corresponding width ${\mathrm{\ensuremath{\Gamma}}}_{r}$, is the relevant quantity in this study. When R is less than 0.3, the decay of the atom goes to a good approximation for the first few lifetimes as $exp(\ensuremath{-}{\mathrm{\ensuremath{\Gamma}}}_{r}t/2\ensuremath{\hbar}){t}^{\ensuremath{-}3/2}$. We also find that for values of $R\ensuremath{\sim}1$, the nonexponential behavior occurs in a postexponential regime that goes as ${t}^{\ensuremath{-}3}$ after around a dozen lifetimes. The above conditions depend on suitably designed potential parameters and suggest that for values $R\ensuremath{\lesssim}1$, the experimental verification of nonexponential decay might be possible.
The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called “survival” probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann’s projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint. The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove’s pioneering work and his well-known “λ2T” limit. In the attempt to further clarify the mechanism of the appearance of a purely probabilistic behavior without resort to any approximation, a solvable dynamical model is presented and extensively studied. The model describes an ultrarelativistic particle interacting with N two-level systems (called “spins”) and is shown to exhibit an exponential behavior at all times in the weak-coupling, macroscopic limit. Furthermore, it is shown that the model can even reproduce the short-time Gaussian behavior followed by the exponential law when an appropriate initial state is chosen. The analysis is exact and no approximation is involved. An interpretation for the change of the temporal behavior in quantum systems is drawn from the results obtained. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.