Multichannel Decay: Alternative Derivation of the i-th Channel Decay Probability
Francesco Giacosa
In the study of decays, it is quite common that an unstable quantum state/particle has multiple distinct decay channels.In this case, besides the survival probability p(t), also the probability wi(t) that a decay occurs between (0, t) in the i-th channel is a relevant object.The general form of the function wi(t) was recently presented in PLB 831, 137200 (2022).Here, we provide a novel and detailed "joint" derivation of both p(t) and wi(t).As it is well known, p(t) is not an exponential function; similarly, wi(t) is not one either.In particular, the ratio wi/wj (for i = j) is not a simple constant as it would be in the exponential limit.The functions wi(t) and their mutual ratios may therefore represent a novel tool to study the non-exponential nature of the decay law.
arXiv:2207.13977•Acta Physica Polonica A•Sep 1, 2022•1 citation