Fully resolved Zeeman pattern in the Stern-Gerlach deflection spectrum of ${\mathrm{O}}_2$ ${(}^3$${\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{-}}$, K=1)

The Stern-Gerlach magnetic deflection spectrum of a molecular beam of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ cooled by supersonic expansion to its lowest rotational level (K=1) reveals nine spatially separated peaks within a span of 2 cm. These peaks readily are assigned from a calculation of the Zeeman energies of the K=1 spin-rotation sublevels characterized by $M_J$, and the assumption of a uniform field gradient within the deflecting magnet gap. However, the variable widths of the observed peaks and the decreasing deflection of certain $M_J$ peaks with increasing field above 14 kG require the explicit consideration of field-gradient inhomogeneities. The theory for this is developed and the spectral profiles again computed with field-gradient inhomogeneity and rotational temperature ($T_{\mathrm{rot}}$) as variables. Agreement of the theoretical shifts, bandwidths, and relative intensities with increasing field gradient when compared with the experimental spectra is very good, and $T_{\mathrm{rot}}$ is found to be 3.5 K. The deflection spectrum of a beam of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ differs from that of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$, reflecting the population of the K=0 rotational level in the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ isotopomer. The oxygen dimer and trimer appear to be paramagnetic, but this result is tentative.