Transformation properties of the effective transition operator

the work on phonons in vanadium a strong effect was discovered which was related to hydrogen precipitations in vanadium. In separate electron microscopy studies the structure of the vanadium hydride phase was determined directly and the relative positions of the hydrogen atoms were determined. In a neutron diffraction study complementing the phonon work with x-rays the existence of anharmonic vibrations in single crystals of silicon was shown directly by determining, for the first time, a nuclear forbidden reflection. This reflection is due solely to anharmonic vibration of the nucleus of the atom and it was shown that its intensity increases with increasing temperature roughly as the 4th power of temperature. (auth)