Survival probability of a single resonance

Abstract

An exact single-level resonance formula for the survival probability S(t) in the full time interval, that depends only:on the resonance energy epsilon (r) and the decay width Gamma (r), and fulfils time-reversal invariance

is used to discuss the nonexponential contributions to decay. At short times the formula behaves as S(t) approximate to 1 - ct(1/2) with c a constant, whereas at long times it behaves as S(t) approximate to dt(-3), d being a constant. With the time expressed in lifetime units, the onset of non-exponential decay is given at short times by tau (S) approximate to 4/[pi (R-2 + R + 1/4)] and at long times by tau (L) approximate to 5.41 ln(R) + 12.25, where R = epsilon (r)/ Gamma (r). The predictions of the formula are compared with numerical examples and some experimental results searching for non-exponential contributions to decay.