A FRACTIONAL INTEGRAL REPRESENTATION FOR INTERBAND DIELECTRIC FUNCTION OF CRITICAL POINT ELECTRONS IN VARIOUS DIMENSIONAL CRYSTALS

The dielectric function for direct interband transitions of critical point electrons in an n-dimensional crystal has been derived as the n/2-th iterated integra1s of the dielectric function of a harmonic oscillator. A generalized expression for the derivatives of interband dielectric function has also been presented by fractional integration. The results present an explicit physical picture and provide a new approach to the investigations of optical properties of low dimensional and anisotropic crystals.