Isotope Shift in theRLines of Chromium in Ruby and MgO

At 4.2°K the $R$ lines of chromium in ruby and in MgO exhibit an isotope shift of 0.13 and 0.17 ${\mathrm{cm}}^{-1\mathrm{}}$ per unit mass, respectively. This is a much larger value than is found for free atoms of intermediate mass. We consider the possibility that this isotope shift is caused by the interaction of the ion with the vibrating lattice. The ion-phonon interaction causes a frequency shift in these $R$ lines, and this shift depends on the amplitude of vibration of the chromium ion. The lighter chromium isotopes, however, have a larger amplitude of vibration than the heavier isotopes, and consequently the frequency shift varies from isotope to isotope. This leads to an isotope shift. For the $R$ lines of ruby and MgO: ${\mathrm{Cr}}^{3+}$ the isotope shift due to the interaction with the zero-point vibrations is calculated, and is in very good agreement with the experimental values, both in magnitude and direction.