Geometric phases of electrons due to spin-rotation coupling in rotating C-60 molecules

The rapidly rotational motion of ${\mathrm{C}}_{60}$ molecules will provide us with an ingenious way to test Mashhoon's spin-rotation coupling. Since in the low-temperature phase (below 300 K) of ${\mathrm{C}}_{60}$ solid the noncentral intermolecular potential will cause the precession and nutation of rotating frequency of ${\mathrm{C}}_{60}$ molecules, which gives rise to a time-dependent coupling of valency electron spin to the ${\mathrm{C}}_{60}$ rotation, the electron wave functions in rotating ${\mathrm{C}}_{60}$ molecules will acquire geometric phases arising from this time-dependent spin-rotation coupling. The geometric phases of valency electrons in ${\mathrm{C}}_{60}$ molecules is calculated by using the Lewis-Riesenfeld invariant theory in the present paper. It is shown that geometric phases of electrons in ${\mathrm{C}}_{60}$ molecules may be measured through the photoelectron spectroscopy of ${\mathrm{C}}_{60}.$ A physically interesting fact that the information about rotation and precession of ${\mathrm{C}}_{60}$ molecules in the orientational ordered (or disordered) phase may be read off from the photoelectron spectroscopy of ${\mathrm{C}}_{60}$ is also demonstrated. Thus, the measurement of variation of ${\mathrm{C}}_{60}$ rotating frequency through the photoelectron spectroscopy will enable us to obtain the noncentral intermolecular potential, which is helpful in investigating the molecular mechanics of ${\mathrm{C}}_{60}$ solid.