Rotational Perturbations in CN. Zero-Field Theory, Optical Zeeman Effect, and Microwave Transition Probabilities

The theory of rotational perturbations in doublet states of diatomic molecules is developed and is applied to the long-standing problem of perturbations in the $B{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}-X{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, $v^{\prime }=0\mathrm{}$ violet bands of CN. Analysis of the available optical data yields experimental values for two rotational perturbation parameters: $\left(\Pi \right|A{L}_y\left|\Sigma \right)=-0.39\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\left(\Pi \right|B{L}_y\left|\Sigma \right)=0.011\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, which account satisfactorily for all the observed spectral line shifts. These two parameters then are used to predict the Zeeman effect of the rotational perturbations. The calculated Zeeman effects are checked against new observations of the 0, 0 band of the violet CN system at magnetic field strengths up to 28 kG, and good agreement is found between theory and experiment. Finally, the zero-field analysis is used to examine the feasibility of proposed microwave resonance investigations of the perturbed excited states of CN.