Effects of Mixing Collisions on Photon Echoes in Gases

Abstract

Effects of electric dipole reorienting collisions on photon echoes are investigated. In an extension of the author's earlier work, a general expression is derived, including terms from binary collisions, for the photonecho dipole moment amplitude. The explicit results are worked out for simple cases such as ${j}_{1}=\frac{1}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=0$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=1$, and ${j}_{1}=\frac{3}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$ transitions. While it is shown that echoes resulting from the above simple transitions will not be depolarized by atomic collisions, photon echoes induced by any other transitions are necessarily depolarized by collisions. In addition, it is possible to show that the general expression for the echo dipole moment can be written as a sum of multipole moments. Only the odd moments contribute to the echoes. The importance of this picture is that collision-induced relaxation of each moment is described by a single time constant---as in the model commonly used for Hanle-effect experiments. As a result, for an echo arising from a ${j}_{1}\ensuremath{\leftrightarrow}{j}_{2}$ transition (${j}_{1}\ensuremath{\ge}{j}_{2}$), there must be $\frac{1}{2}{j}_{1}({j}_{1}+1)$ time constants to describe the collision damping of the echo intensity, ${j}_{1}$ being an integer. The corresponding formula for the half-integer case is $\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})$.