[en] A simple semi-empirical model is presented which explains observed positron momentum distribution p(k) in alkali metals as well as large apparent positron effective mass m** defined by p(k) varies as exp(-k²/2m**ksub(B)T). It is shown that p(k) can be taken as a Boltzmann-type distribution only when the lifetime broadening GAMMA(k, E) of a positron quasi-particle increases with the energy as approximately Esup(1/2). Such an energy dependence of GAMMA(k, E) is actually expected for phonon effects in both solid and liquid metals. The deviation of m** from the true effective mass m* is directly related to the magnitude of GAMMA(k, E) and m**/m* is calculated as a function of GAMMA(k, E). (author)