Metstable Hydrogen Molecules. III. Hyperfine Structure of Orthohydrogen

Abstract

The fine structure (fs) and hyperfine structure (hfs) of the $N=1$ rotational level of a single vibrational state of the $(1{\ensuremath{\sigma}}_{g},1{\ensuremath{\pi}}_{u})c^{3}\ensuremath{\Pi}_{u}$ state of orthohydrogen has been measured by the molecular-beam magnetic-resonance method. Six independent frequency intervals have been measured to a precision of better than one part per million. The theory of fs and hfs, as developed by Fontana, Chiu, Jette, and Cahill has been used to fit the energy levels with four accurate, independent constants: the spin-orbit fs constant, $A=\ensuremath{-}3717.12$ MHz; the spin-spin fs constant, ${B}_{0}\ensuremath{-}\sqrt{6{B}_{2}}=9562.50$ MHz; the combined orbital and Fermi contact hfs constants, $\frac{1}{2}a+{a}_{F}=463.77$ MHz; the dipolar hfs term, $c\ensuremath{-}3d=104.18$ MHz; and the fifth, very much less accurately determined, orbital hfs constant, $a=26.6$ MHz. The Fermi contact constant ${a}_{F}=450.5$ MHz agrees remarkably closely with the value 440.1 found in ${\mathrm{H}}_{2}^{+}$ by Jefferts. This indicates that the contact hfs of this state arises largely from a single core electron which is virtually the same as in ${\mathrm{H}}_{2}^{+}$. The agreement between experimental energy levels and the theoretical fit is very good. The deviations are at worst 20 kHz, only a few parts per million in the measured intervals. If the previously measured fs of the $N=2$ state is used, the spin-spin constants become ${B}_{0}=\ensuremath{-}1420$ MHz, ${B}_{2}=\ensuremath{-}4480$ MHz. The spin-orbit constants for the $N=1$ and $N=2$ levels disagree by 3%. The constants $\frac{1}{2}a+{a}_{F}$ and $c\ensuremath{-}3d$ disagree by several percent with a priori calculations by Jette. The level of discrepancies among different experimental and theoretical results is an order of magnitude larger than can be obtained within the framework of the pure case-$b$ coupling scheme. Evidence is found for nonadiabatic transitions of a new type for molecular-beam experiments. The discovery of new transitions proves that there is more than one metastable vibrational level of the $c^{3}\ensuremath{\Pi}_{u}$ state of ${\mathrm{H}}_{2}$. It is likely, although not certain, that the present data are from the lowest ($v=0$) level.