Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section E / 27 / a / i / Solution

Assume all contributing decay rates satisfy ${\nu }_l>0$ and the summed expression is a nonnegative density. ThenThus ${\sum }_l{A}_l=1$ normalizes the first-passage distribution. A zero decay rate would require separate treatment of a nonabsorbing component; eventual absorption is implicit here. Individual spectral coefficients need not all be positive, but the full density must be.