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 α 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 generalizations of the atomic master equation. (atomic and molecular physics)