The Propagation of Photons in the Dilute Ionized Gas

The dilute ionized gas is very popular in the Universe. Usually only the Compton interactions, the "Sunyaev-Zel'dovich" effect, were considered while photons propagated in this medium. In this paper the "soft-photon process" is considered. Due to the soft photons emitted during the propagation of a photon in the dilute ionized gas, the main photon (propagating in the original direction) will be redshifted. The formula to calculate this redshift is derived.