An Electrical Quadrupole Moment of the Deuteron The Radiofrequency Spectra of HD and ${\mathrm{D}}_2$ Molecules in a Magnetic Field

The molecular-beam magnetic-resonance method has been applied to study the radiofrequency spectra of the molecules ${\mathrm{D}}_2$ and HD, in the state $J=1\mathrm{}$. All the measurements were made in applied magnetic fields large enough to decouple the angular momentum vectors concerned. The spectrum of ${\mathrm{D}}_2$ for the transitions $m_I=\pm 1$ consists of six lines as in ${\mathrm{H}}_2$. The HD spectrum consists of two sets, one of nine lines in the region of the Larmor frequency of the proton, and another of twelve lines in the region of the Larmor frequency of the deuteron. The analyses of these spectra into sets of energy levels and a consistent theory are presented. As a consequence of the analysis one has to assume the existence in the deuteron of an electrical quadrupole moment, $Q$. The other quantities which are evaluated from these measurements are the spin-orbit interaction constants for the molecules concerned and the magnetic moments of the proton and deuteron, through the magnetic dipole-dipole interactions. The values of the constants are $Q=2.73\mathrm{}\times {10}^{-27\mathrm{}}$ ${\mathrm{cm}}^2$, $H^{\prime }\left({\mathrm{D}}_2\right)=14.0\mathrm{}$ gauss, $H_{}^{\prime }{}_D{}^{}\left(\mathrm{HD}\right)=20.1\mathrm{}$ gauss, and $H_{}^{\prime }{}_P{}^{}\left(\mathrm{HD}\right)=20.48\mathrm{}$ gauss. These spin-orbit interaction constants represent the magnetic field produced by the molecular rotation at the position of a nucleus. The values of the magnetic moments of the proton and deuteron agree with the direct measurements previously reported.