N2+quadrupole transitions with small Zeeman shift

Abstract

The vibrational transition frequencies of a ${{\mathrm{N}}_{2}}^{+}$ molecular ion are advantageous for precise measurement because the Stark shift is much smaller than that of heteronuclear diatomic molecules. The ${}^{14}{{\mathrm{N}}_{2}}^{+}$ S(0) transition has been observed by a group in Basel. For most transitions, the Zeeman shift limits the attainable accuracy. This paper reports the quadrupole transitions (observed with simpler apparatus than that required for the Raman transition) for which the Zeeman shift is less than 100 Hz at a magnetic field of 1 G. $\mathrm{Q}\left(N\right)$ transitions ($N$: even) of the molecular ion with $I=0$ are advantageous for measurement within an uncertainty of ${10}^{\ensuremath{-}16}$. The transition frequencies of molecular ions with $I\ensuremath{\ne}0$ are difficult to measure within an uncertainty of ${10}^{\ensuremath{-}12}$ because $J$-mixing makes the linear Zeeman coefficient in the Q transitions large and narrow hyperfine splitting makes the quadratic Zeeman coefficient large.