Numerical study of two-phonon sidebands in the optical absorption of free polarons in the strong-coupling limit

Using the theory and the analytical results of Kartheuser, Evrard, and Devreese (KED), we have calculated numerically the two-phonon sideband in the optical absorption coefficient of free polarons. Therefore, integrals of the type (dk→k→2)(dk→′k→′2) k→′2jcos2jθ′k→2icos2iθδ((k→+k→ ′)2-ε2)e-xk→2-yk→′2 as obtained by KED, are treated analytically and reduced to a finite sum of single integrals for integer i and j>~0, for all real x, y>0 and for any real ε. Our numerical results, combined with the zero-phonon line and the one-phonon sideband obtained by KED, confirm the mechanism for the absorption of light by free polarons proposed by KED.