A new method of approach to the problem of absorption of light by trapped electrons in crystals is presented. The method is based upon the use of the Slater sum for an oscillator (density matrix). The absorption cross section is calculated under the assumption of an electron-lattice coupling which is linear in the normal coordinates of the lattice; this yields the shape of the absorption curve, but the maximum does not shift with temperature as required by experiment. This shift is then accounted for in a somewhat fundamental manner by considering the small change in the lattice frequencies which accompanies the photon induced electronic transition. The result is that the absorption maximum shifts with temperature, but the shape of the absorption curve is not effected by the change in the lattice frequencies.