Simple determination of Touschek and beam-gas scattering lifetimes from a measured beam lifetime

Derived are simple and accurate formulas breaking down a measured beam lifetime into its partial lifetimes of Touschek and beam-gas scattering. They are useful as practical means, because the existing formulas for the two partial lifetimes often fail to give numerically accurate numbers due to the lack of accurate information of necessary parameters. However, the new formulas need only the measured data of beam lifetime and are as accurate as the lifetime measurement. Also derived is the polarization dependence of the beam lifetime, which can be used to estimate the degree of polarization.