Landau levels of molecules: Angular-momentum coupling between cyclotron motion and core rotation

In a high magnetic field of 3--7 T, nitric oxide (NO) molecules are excited by the double-resonance method through the intermediate $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\ensuremath{\Sigma}}^{+}{F}_{1}({v}^{\ensuremath{'}\ensuremath{'}}=0,{N}^{\ensuremath{'}\ensuremath{'}}=0)$ level to the Landau levels in the energy region above the zero-field ionization limit to the NO${}^{+}\phantom{\rule{0.222222em}{0ex}}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{+}=0,{N}^{+}=0)$ ion. By detecting NO${}^{+}$ ions, the photoionization cross section through the Landau levels is determined as a function of the second laser's frequency. The cross section contains broad structures and fine structures. Fourier analysis of the cross section and classical trajectory calculations of the Rydberg electron demonstrate that the broad structure is formed by the Landau level generated by the cyclotron motion of the electron around the ${N}^{+}=0$ core in a plane perpendicular to the field, while the fine structure is formed by the Landau level generated by the three-dimensional cyclotron motion around the excited ${N}^{+}=2$ core. By simulating the energy structure of the Landau level, the electron's orbital angular momentum is confirmed to be decoupled from the core rotation in the Landau levels. From the selection rules of the excitation, it is demonstrated that the Landau levels with the ${N}^{+}=0$ core are excited using the $s$ character in the $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\ensuremath{\Sigma}}^{+}$ state, while those with the ${N}^{+}=2$ core are excited using the $d$ character. The dominant partial wave, thus determined, explains well the starting direction of the classical trajectory.