The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.

arXiv:1703.05238Europhysics Letters (EPL)Aug 1, 201467 citations

Seeking non-exponential decay

P. Thornton Greenland

NatureSep 22, 198866 citations

An explicit model of exponential decay

David P. Vasholz

PhysicaJun 1, 19743 citations

Survival Amplitude, Instantaneous Energy and Decay Rate of an Unstable System: Analytical Results

K. Raczyńska, K. Urbanowski

We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude $a(t)$ of the state considered is found. Our attention is focused on the late time properties of $a(t)$ and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$ . This effect can be described using a time-dependent decay rate $γ(t)$ and then the Khalfin result means that this $γ(t)$ is not a constant but at late times it tends to zero as $t$ goes to the infinity. It appears that the energy $E(t)$ of the unstable state behaves similarly: It tends to the minimal energy $E_{min}$ of the system as $t \to \infty$ . Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of $E(t)$ and $γ(t)$ . We discuss also possible implications of such a late time asymptotic properties of $E(t)$ and $γ(t)$ and cases where these properties may manifest themselves.We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude $a(t)$ of the state considered is found. Our attention is focused on the late time properties of $a(t)$ and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described using a time-dependent decay rate $γ(t)$ and then the Khalfin result means that this $γ(t)$ is not a constant but at late times it tends to zero as $t$ goes to the infinity. It appears that the energy $E(t)$ of the unstable state behaves similarly: It tends to the minimal energy $E_{min}$ of the system as $t \to \infty$. Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of $E(t)$ and $γ(t)$. We discuss also possible implications of such a late time asymptotic properties of $E(t)$ and $γ(t)$ and cases where these properties may manifest themselves.

arXiv:1802.01441Acta Physica Polonica BJan 1, 201810 citations

The Decay Process: An Exactly Soluble Example and its Implications

Gastón García‐Calderón, G. Loyola, M. Moshińsky

Springer eBooksJan 1, 199210 citations

We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude

a(t)

of the state considered is found. Our attention is focused on the late time properties of

a(t)

and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as

t

goes to the infinity more slowly than any exponential function of

t

. This effect can be described using a time-dependent decay rate

γ(t)

and then the Khalfin result means that this

γ(t)

is not a constant but at late times it tends to zero as

t

goes to the infinity. It appears that the energy

E(t)

of the unstable state behaves similarly: It tends to the minimal energy

E_{min}

of the system as

t \to \infty

. Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of

E(t)

and

γ(t)

. We discuss also possible implications of such a late time asymptotic properties of

E(t)

and

γ(t)

and cases where these properties may manifest themselves.