Imaging superatomic molecular orbitals in a ${\bf C_{60}}$ molecule through four 800-nm photons

Superatomic molecular orbitals (SAMO) in C60 are ideal building blocks for functional nanostructures. However, imaging them spatially in the gas phase has been unsuccessful. It is found experimentally that if C60 is excited by an 800-nm laser, the photoelectron casts an anisotropic velocity image, but the image becomes isotropic if excited at a 400-nm wavelength. This diffuse image difference has been attributed to electron thermal ionization, but more recent experiments (800 nm) reveal a clear non-diffuse image superimposed on the diffuse image, whose origin remains a mystery. Here we show that the non-diffuse anisotropic image is the precursor of the $f$ SAMO. We predict that four 800-nm photons can directly access the $1f$ SAMO, and with one more photon, can image the orbital, with the photoelectron angular distribution having two maxima at 0$^\circ$ and 180$^\circ$ and two humps separated by 56.5$^\circ$. Since two 400-nm photons only resonantly excite the spherical $1s$ SAMO and four 800-nm photon excite the anisotropic $1f$ SAMO, our finding gives a natural explanation of the non-diffuse image difference, complementing the thermal scenario.