Approximate Wave Functions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi></mml:math>-Center by the Point-Ion Lattice Method

Abstract

Qualitative arguments are presented, suggesting that the point-ion lattice model, first used by Gourary and Adrian for the $F$-center, should be generalized to all those states of electron-excess color centers in the alkali halide crystals which give rise to transitions, obeying the Ivey relations.The point-ion lattice model is then postulated for Seitz's model of the $M$-center, and two sets of transition energies are obtained for a whole series of alkali halides. The ${A}_{1}{B}_{1}$ transition agrees with the $M$-band within some 15%. Its dipole matrix element has the [110] direction. The ${A}_{1}{B}_{2}$ transition lies at a shorter wave-length. In LiF and NaF it is close to the $F$-band. Its dipole matrix element has the [100] direction. Oscillator strengths are also given. There is some possibility, however, that the ${B}_{2}$ state may not be bound.The contact term in the hyperfine structure is estimated for LiF and LiI, using an alternate form of wave function.Experiments are suggested to verify the Ivey relations and the other predictions of the point-ion lattice model in suitably chosen sets of alkali halide crystals, which have almost identical interionic distances.