The Hyperfine Structure of Hydrogen and Deuterium

Abstract

The atomic-beam magnetic resonance method has been applied to measure the h.f.s. separation of the ground state of H and D by observing frequencies of the r-f field required to induce transitions among certain of the magnetic levels of the h.f.s. multiplets in magnetic fields of the order of 1 gauss. The resonance minima were of the theoretical width for transitions which are field independent in the first order. For deuterium we find ${\ensuremath{\nu}}_{\mathrm{D}}=327.384\ifmmode\pm\else\textpm\fi{}0.003$ Mc which agrees with our previously reported value within the precision claimed for that quantity. For hydrogen we find ${\ensuremath{\nu}}_{\mathrm{H}}=1420.410\ifmmode\pm\else\textpm\fi{}0.006$ Mc which is less than the value previously reported by 0.06 percent. The ratio of the measured h.f.s. separations, $\frac{{\ensuremath{\nu}}_{\mathrm{H}}}{{\ensuremath{\nu}}_{\mathrm{D}}}$, is 4.33867\ifmmode\pm\else\textpm\fi{}0.00004.The h.f.s. separations, ${\ensuremath{\nu}}_{\mathrm{H}}$ and ${\ensuremath{\nu}}_{\mathrm{D}}$, may be calculated from known values of the magnetic moment of the proton, ${\ensuremath{\mu}}_{p}$, and the magnetic moment of the deuteron, ${\ensuremath{\mu}}_{d}$. The measured ${\ensuremath{\nu}}_{\mathrm{H}}$ and ${\ensuremath{\nu}}_{\mathrm{D}}$ are larger than the calculated values by 0.24 percent and 0.26 percent, respectively. The ratio $\frac{{\ensuremath{\nu}}_{\mathrm{H}}}{{\ensuremath{\nu}}_{\mathrm{D}}}$ may be calculated from the known ratio $\frac{{\ensuremath{\mu}}_{p}}{{\ensuremath{\mu}}_{d}}$ using the ordinary reduced mass correction (discussed in the section entitled "Discussion of Results" of this paper). This ratio is independent of ${\ensuremath{\alpha}}^{2}$ and ${R}_{\ensuremath{\infty}}$. The calculated ratio is found to be higher than our value by 0.017 percent. This discrepancy is 18 times the probable error in our measurements.