Lifetime of a quasiparticle in an electron liquid. II

Inelastic lifetime of an electron quasiparticle in an electron liquid due to electron-electron interaction evaluated in previous work is calculated in an alternative way. Both the contributions of the "direct" and "exchange" processes are included. The results turn out to be exactly the same as those obtained previously, and hence confirm the latter. Derivation in the two-dimensional case is presented in great details due to its intricacies.