L. Genzel – författare

159 elements only between states which differ in one of the single-electron wave functions, in short, HeR induces only one-electron transitions. The matrix elements 1mn and Pmn reduce to matrix elements between the single-electron wave functions. We are interested primarily in crystalline solids for which the band model is a good approximation. The Bloch single-electron wave function in this model has the form: N''I ili-'';; U. r.;;) ( (1.14) ""nk r, =e nh\r , where n is the band index and U (r) has the periodicity of the lattice. The form of the Bloch function follows from the translational symmetry of the crystal, and the matrix elements between Bloch states are subject to the condition of wave-vector conservation: k''=k, for

159 elements only between states which differ in one of the single-electron wave functions, in short, HeR induces only one-electron transitions. The matrix elements 1mn and Pmn reduce to matrix elements between the single-electron wave functions. We are interested primarily in crystalline solids for which the band model is a good approximation. The Bloch single-electron wave function in this model has the form: N'I ili-';; U. r.;;) ( (1.14) ""nk r, =e nh\r , where n is the band index and U (r) has the periodicity of the lattice. The form of the Bloch function follows from the translational symmetry of the crystal, and the matrix elements between Bloch states are subject to the condition of wave-vector conservation: k'=k, for

The dynamical properties of solids have recently attracted renewed interest in connection with the increasing understanding of phase transitions and re­ lated phenomena. In particular, soft modes or, more generally, phonon ''anom­ alies'' seem to play an important role in structural and electronic phase tran­ sitions, such as ferroelectric or superconducting transitions. The understanding of the mechanisms responsible for the occurrence of unusually low frequencies in phonon spectra requires a detailed analysis of the microscopic forces governing the lattice vibrations. Of particular importance is the influence of the electron­ lattice interaction in the adiabatic approximation which in many cases is the origin of peculiarities in the phonon self-energy. In this work the vibrational spectra of pure non-metals and of those con­ taining point defects are investigated. '' In these materials the interrelation be­ tween the pseudo-harmonic forces (determining the phonon dispersion re­ lations) and the non-linear anharmonic and electron-phonon forces (as they act in infrared and Raman spectra) is most obvious and can be quantitatively analysed in terms of appropriate models. The main task is to arrive at a physically correct treatment of electronic degrees of freedom, as for example in an electronic ''shell'' model, which leads to the description of phonon spectra in terms of long-range polarizabilities and short-range deformabilities. The pur­ pose of our review is to stimulate further investigations which, we hope, will result in explicit relations between the parameters of the semi-microscopic models and the matrix elements from the electronic band structure.