NominalΔm=±1,2,3,4,5Magnetic Nuclear Transition Probabilities in Ruby

Abstract

The nominal $\ensuremath{\Delta}m=\ifmmode\pm\else\textpm\fi{}1,2,3,4, \mathrm{and} 5$ magnetic transition probabilities between ${\mathrm{Al}}^{27}$ nuclear energy levels in ruby are calculated, and the energy-level populations are determined with the presence of an external perturbation connecting two energy levels. A simple model where the relaxation of the ${\mathrm{Al}}^{27}$ spins is via a direct magnetic interaction with the ${\mathrm{Cr}}^{3+}$ paramagnetic impurity is used to compare the calculated $\ensuremath{\Delta}m=\ifmmode\pm\else\textpm\fi{}2$ magnetic transition probability to the observed effects in a 4% ${\mathrm{Cr}}^{3+}$-doped ruby sample. The calculated magnitude and angular dependence fit the experimental data and indicate that the effect is large enough to cause leakage effects when attempting a pure quadrupole saturation experiment in ruby.