  The relaxation dynamics of superexcited superfluid He nanodroplets is
thoroughly investigated by means of extreme-ultraviolet (XUV) femtosecond
electron and ion spectroscopy complemented by time-dependent density functional
theory (TDDFT). Three main paths leading to the emission of electrons and ions
are identified: Droplet autoionization, pump-probe photoionization, and
autoionization induced by re-excitation of droplets relaxing into levels below
the droplet ionization threshold. The most abundant product of both droplet
autoionization and photoionization is He$_2^+$, whereas the delayed appearance
of He$^+$ is indicative of the ejection of excited He atoms from the droplets.
The state-resolved time-dependent photoelectron spectra reveal that
intermediate excited states of the droplets are populated in the course of the
relaxation, terminating in the lowest-lying metastable singlet and triplet He
atomic states. The slightly faster relaxation of the triplet state compared to
the singlet state is in agreement with the simulation showing faster formation
of a bubble around a He atom in the triplet state.
