Collisional redistribution of radiation. III. The equation of motion for the correlation function and the scattered spectrum

We present a calculation of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation. We limit ourselves to field strengths such that ₂1, where is the Rabi frequency for the atomic transition, and ₂ is the duration of a strong collision. Our calculation is not limited to the impact regime, ₂^-1, or to the region where thermal correlations may be neglected, i. e. ,. (Here is the difference between either the incoming or outgoing photon's frequency and the atom's natural frequency. ) To do this we derive an equation of motion for the correlation function, valid outside the quantum-regression regime, whose solution for practical cases is straightforward. We present solutions for the weak-field (linear-response) regime in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles created.