  The autoionization dynamics of superexcited superfluid He nanodroplets doped
with Na atoms is studied by extreme-ultraviolet (XUV) time-resolved electron
spectroscopy. Following excitation into the higher-lying droplet absorption
band, the droplet relaxes into the lowest metastable atomic $1s2s$ $^{1,\,3}$S
states from which Interatomic Coulombic Decay (ICD) takes places either between
two excited He atoms or between an excited He atom and a Na atom attached to
the droplet surface. Four main ICD channels are identified and their time
constants are determined by varying the delay between the XUV pulse and a UV
pulse that ionizes the initial excited state and thereby quenches ICD. The time
constants for the different channels all fall in the range $\sim$1~ps
indicating that the ICD dynamics are mainly determined by the droplet
environment. A periodic modulation of the transient ICD signals is tentatively
attributed to the oscillation of the bubble forming around the localized He
excitation. The ICD efficiency depends on the total number of excited states in
a droplet rather than the density of excited states pointing to a collective
enhancement of ICD.
