Zerfallsmuster

Zerfallsmuster describes the characteristic distribution of decay events from an unstable system, such as a radioactive nucleus or unstable molecule, including when decays occur and through which channels. It encompasses the time dependence of activity and the relative probabilities of competing decay modes, as well as the sequence of products in decay chains.

In the simplest case, a single decay channel with decay constant λ governs the kinetics. The number of undecayed nuclei N(t) obeys N(t) = N0 e^{-λ t}, and the activity A(t) = λ N(t) = λ N0 e^{-λ t}. The half-life is T1/2 = ln 2 / λ.

When multiple decay channels exist, the total decay constant is λ = sum λi, and the fraction decaying by channel i is fi = λi / λ. The total activity remains A(t) = λ N0 e^{-λ t}, while the activity in a given channel is Ai(t) = λi N0 e^{-λ t}. In decay chains, daughter nuclides may themselves decay, described by the Bateman equations, yielding a mixture of exponentials and characteristic ingrowth curves.

Experimentally, Zerfallsmuster is obtained by measuring emitted radiation (alpha, beta, gamma) and by timing decays. Fitting decay curves yields half-lives, branching ratios, and information about decay schemes.

Applications include radiometric dating, production and use of medical isotopes, reactor physics, and environmental radiochemistry. The concept also informs models of nucleosynthesis and astrophysical decay processes.