Hybridization and coherence in subshell differential intercluster plasmonic decay in $Na_{20}@C_{240}$

We study the ground state structure and aspects of photoionization dynamics of the $Na_{20}@C_{240}$ endofullerene. The structure shows effects from the electronic coupling between the nested cluster and the fullerene cage. They include the (i) alterations of the overall potential, and thus, the force field, (ii) electron transfer from the cluster to the fullerene forming ionic units, and (iii) hybridization from the admixture of free $Na_{20}$ occupied levels with experimentally known super-atom molecular orbital (SAMO) type empty levels of $C_{240}$ accessible in the jellium-DFT model. These modifications influence the photoionization dynamics of the endofullerene. For the high energy ionization of $Na_{20}$-type levels, a significant overall enhancement of the cross section is noted from additional ionizing force that $C_{240}$ offers. More remarkably, the photoexcited plasmons, both the giant plasmon and the higher energy plasmon, in decay in parts through $Na_{20}$ ionization continuum via the resonant intercluster Coulombic decay (ICD) process. These lead to dramatic enhancements in the ionization of individual $Na_{20}$-type levels resulting enhancements in the cluster's total ionization yield. Based on hybridization, this enhancement incorporates a coherent mixing of the ICD and SAMO-induced Auger-decay amplitude, in which the ICD contribution is dominant.