Magnetic Resonance with Large Angular Momentum

Multiple quantum transitions present in molecular-beam magnetic resonance of molecules of high rotational angular momentum are treated in terms of a purely classical model. The probability of a change ($\frac{\Delta m_J}{J}$) in rotational magnetic quantum number per unit angular momentum is shown to be given by $P\left(\frac{\Delta m_J}{J}\right)=\frac{1}{\left[4\mathrm{}sin\right(\frac{1}{2}\epsilon \left)\right]}$ if $\left|\frac{\Delta m_J}{J}\right|<\mathrm{}2\mathrm{}sin\left(\frac{1}{2}\epsilon \right)$ and $P\left(\frac{\Delta m_J}{J}\right)=0\mathrm{}$ if $\left|\frac{\Delta m_J}{J}\right|>\mathrm{}2\mathrm{}sin\left(\frac{1}{2}\epsilon \right)$, where $P\left(\frac{\Delta m_J}{J}\right)d\left(\frac{\Delta m_J}{J}\right)$ is the fraction of molecules for which this change lies between $\frac{\Delta m_J}{J}$ and $\frac{\Delta m_J}{J}+d\left(\frac{\Delta m_J}{J}\right)$, and $\epsilon$ is the angle which the angular momentum makes with the magnetic field after the transition for a molecule whose angular momentum is initially along the field. By way of comparison, the transition probability of a spin-½ particle under the same conditions is ${sin}^2\left(\frac{1}{2}\epsilon \right)$. This probability is weighted according to the probability of detecting a transition with a change in magnetic moment of ${\mu }_J\Delta m_J$ and averaged over the thermal distributions of $J$ and $V$ to give a theoretical line shape. The theory is applied to rotational magnetic moments of molecules. The calculated line shape is shown to agree reasonably well with an experimental curve of the rotational magnetic-moment resonance of the molecule OCS.