Zeeman Effect in the Rotational Spectrum of NO

Abstract

The Zeeman splitting of the 2-mm wave, $J=\frac{1}{2}\to \frac{3}{2}$ rotational transit on of ${\mathrm{N}}^{14}$ ${\mathrm{O}}^{16}$ in the ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ electronic state has been measured with fields of the order of 100 gauss. The observations were made with a wave-guide cell coiled between the poles of a Varian magnet. Magnetic field measurements were made with the electronic resonance of DPPH at frequencies of the order of 300 Mc/sec. A general theory of the Zeeman effect with hfs has been developed and applied specifically to ${\mathrm{N}}^{14}$ ${\mathrm{O}}^{16}$. The $g$ factors for the four states under investigation were found theoretically to be expressed as: $J=\frac{1}{2}$, $g_c=0.0007-\alpha$, $g_d=0.0007+\alpha$; $J=\frac{3}{2}$, $g_c=\overline{g}-\frac{2}{5}\alpha$, $g_d=\overline{g}+\frac{2}{5}\alpha$, where $c$ and $d$ are the lower and upper components of the $\Lambda$-type doublet, respectively. This relation was found to hold experimentally well with the values, $\overline{g}=-0.0230\mathrm{}$ and $\alpha =+0.0025\mathrm{}$. Theoretically, $\overline{g}$ comes from the mixing of ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}$ states and $\alpha$ comes from that of ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Sigma$ states. It was found by the theory, in which the centrifugal force and the spin orbit coupling were taken into account, that the electronic wave function of the two rotational states should be: $J=\frac{1}{2}$, $\left({}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}\right|-0.0021\left({}_{}{}^2{}_{}{}^{}\Sigma \right|$; $J=\frac{3}{2}$, $\left({}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}\right|-0.0247\left({}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}\right|-0.0021\left({}_{}{}^2{}_{}{}^{}\Sigma \right|$. These wave functions give $\overline{g}(\mathrm{theor}.\mathrm{})=-0.0229\mathrm{}$ and and $\alpha (\mathrm{theor}.\mathrm{})=+0.0020\mathrm{}$, which agree very well with the observed values. The observed $g$ factor in $J=\frac{3}{2}$ state, $\overline{g}=0.0230\mathrm{}$ Bohr magnetons, shows that in the supposedly "nonmagnetic" ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ state the NO molecule has a sizeable magnetic moment.