The interaction of a color center with many lattice modes is analyzed by the adiabatic approximation method with Franck-Condon approximation. The exact solution of the absorption-shape function can be obtained by using the central limit theorem which gives a correct result for the absorption shape and the half band width. The effective frequency model used by O'Rourke is then proved to be basically correct, but with different definition for the frequency and can be calculated easily from experimental H(T)-T^(1/2) plot. The variation of half band width with temperature of KC1 F-center is found to be fixed with experimental data. This suggests that the diffusion model is as good as configurational coordinate model to explain the color-center transition.