Decaymetoden

Decaymetoden, or the decay method, is a group of analytical techniques used to determine decay constants and related parameters from time-series data that exhibit exponential decay or decline. It is widely used in physics, chemistry, biology, pharmacology, and materials science to quantify how a quantity diminishes due to a first-order process or a combination of such processes.

The typical model is N(t) = N0 exp(-λ t) + B, where N(t) is observed signal at time t, λ is the decay constant, N0 is initial quantity, and B is background. For multi-exponential decays, a sum of exponentials may be used. Parameter estimation often relies on nonlinear least squares or linear regression after transforming the data by taking logarithms, with appropriate background subtraction. The half-life t1/2 relates to λ by t1/2 = ln(2)/λ.

Data collection requires good time resolution and control of systematic effects such as background, instrument response, and dead time. The method includes steps: data preprocessing, model fitting, parameter uncertainty assessment (confidence intervals or Bayesian posterior), and model validation through goodness-of-fit metrics and residual analysis.

Applications include radiocarbon dating, drug elimination kinetics, luminescence decay in materials, radioactive decay in nuclear physics, and environmental isotope studies. Limitations include noise, background uncertainty, identifiability issues in multi-exponential fits, non-exponential decay behaviors, and potential biases from measurement artifacts. Variants of the decaymetoden employ Bayesian inference, deconvolution, or constrained optimization to address these challenges.