Variations of Hydrogen Rotational Magnetic Moments with Rotational Quantum Number and with Isotopic Mass

Abstract

Molecular beam observations have been made of the radio-frequency resonance spectra corresponding to reorientations of the rotational magnetic moment in hydrogen and deuterium molecules. For deuterium in the state $I=J=1\mathrm{}$, these observations were made in magnetic fields of approximately 1800, 3500, and 5100 gauss. The direct result of these experiments is that the rotational magnetic moment of the deuterium molecule in the zeroth vibrational and first rotational states is ${}_0{}^{}{}_{}{}^{}{}_{}{}^{\mathrm{D}}{}_{}{}^{}〈{\mu }_R〉_1^{}{}_{}{}^{}=0.442884\mathrm{}\pm 0.000052$ nuclear magneton, and the dependence of diamagnetic susceptibility on molecular orientation is $({\xi }_{\pm 1}-{\xi }_0)=-(3.50\mathrm{}\pm 0.40)\times {10}^{-31\mathrm{}}$ erg ${\mathrm{gauss}}^{-2\mathrm{}}$ ${\mathrm{molecule}}^{-1\mathrm{}}$. Combining these values with the recent theory of Ramsey on zero-point vibration and centrifugal stretching in molecules leads to an improved evaluation of the molecular susceptibility and quadrupole moment of the electron distribution. The experiments also provide a check on the values of the spin-rotational and spin-spin interaction parameters previously obtained from observations of the resonance spectrum corresponding to reorientations of the total nuclear spin.