A theoretical analysis of the one-dimensional cooling of atoms by velo
city-selective coherent population trapping (VSCPT) is presented. The
analysis is performed in the framework of both full quantum and quasi-
classical (for the translational motion of atoms) approaches. The temp
oral evolution of atomic momentum distribution and the efficiency of t
he cooling method are considered. The analytical solution for an atomi
c density matrix is obtained in the limit of large interaction time an
d small kinetic momentum of the atom. It is the rate of the coherence
relaxation between two low-lying states in the three-level A-configura
tion; (2) due to this relaxation, the evolution of the atomic momentum
distribution is divided into two stages: first, high narrow peaks cor
responding to cold atoms are formed, second, they are slowly diffused.