Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.