Radio-Frequency Spectra of Hydrogen Deuteride in Strong Magnetic Fields

Molecular beam observations have been made of the radiofrequency spectra corresponding to reorientations of the deuteron, proton, and rotational magnetic moments in the HD molecule. For HD in the zeroth vibrational and first rotational state, these observations were made in magnetic fields of approximately 1700, 3400, and 4800 gauss. The results are found to be consistent with the theory of heteronuclear diatomic molecules. The direct result of these experiments is the determination of the Hamiltonian interaction constants: $\frac{(1-{\sigma }_{J1\mathrm{}})b}{{\nu }_d}$ equals 0.773527±0.000016, $c_p$ is 85 600±18 cps, $c_d$ equals 13 122±11 cps, $d_1$ is 17 761±12 cps, $d_2$ equals 22 454±6 cps, and $\frac{f}{H^2}$ is (-26.90±0.40)×${10}^{-6\mathrm{}}$ cps ${\mathrm{gauss}}^{-2\mathrm{}}$. From these values of the interaction constants are derived the following physical quantities: the HD rotational magnetic moment ${}_{}{}^{\mathrm{HD}}{}_{}{}^{}{}_0{}^{}{}_{}{}^{}〈\frac{{\mu }_J}{J}〉_1^{}{}_{}{}^{}$ equals 0.663211±0.000014 nuclear magneton, the quadrupole moment $Q$ of the deuteron is (2.738±0.014)×${10}^{-27\mathrm{}}$ ${\mathrm{cm}}^2$, the rotational magnetic field ${H_p}^{\prime }$ at the proton is 19.879±0.006 gauss and ${H_d}^{\prime }$ at the deuteron is 20.020±0.028 gauss, the internuclear spacing in the zeroth vibrational and first rotational state is such that ${}_{}{}^{\mathrm{HD}}{}_{}{}^{}{}_0{}^{}{}_{}{}^{}{〈R^{-3\mathrm{}}〉}_1_{}^{-\frac{1}{3}}{}_{}{}^{}$ equals (0.74604±0.00010)×${10}^{-8\mathrm{}}$ cm, and the dependence of the diamagnetic susceptibility on molecular orientation (${\xi }_{\pm 1}-{\xi }_0$) is -(3.56±0.20)×${10}^{-31\mathrm{}}$ erg ${\mathrm{gauss}}^{-2\mathrm{}}$ ${\mathrm{molecule}}^{-1\mathrm{}}$. Combining these values with Ramsey's theory on zero-point vibration and centrifugal stretching in molecules gives the high-frequency contribution to the molecular susceptibility, ${}_{}{}^{\mathrm{HD}}{}_{}{}^{}{}_0{}^{}{}_{}{}^{}〈{\xi }^{\mathrm{hf}}〉_1^{}{}_{}{}^{}=(1.675\mathrm{}\pm 0.005)\times {10}^{-31\mathrm{}}$ erg ${\mathrm{gauss}}^{-2\mathrm{}}$ ${\mathrm{molecule}}^{-1\mathrm{}}$; the quadrupole moment of the electron distribution relative to the internuclear axis, ${}_{}{}^{\mathrm{HD}}{}_{}{}^{}{}_0{}^{}{}_{}{}^{}〈Q_e〉_1^{}{}_{}{}^{}=(0.324\mathrm{}\pm 0.010)\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$; and the high-frequency contribution to the magnetic shielding constant for HD, ${}_{}{}^{\mathrm{HD}}{}_{}{}^{}{}_0{}^{}{}_{}{}^{}〈{\sigma }^{\mathrm{hf}}〉_1^{}{}_{}{}^{}=(-0.594\mathrm{}\pm 0.030)\times {10}^{-5\mathrm{}}.$