Fig. 3: Schematic of the investigated processes and states generated after 1s ionization of solvated Al³⁺.

The first step forms Al⁴⁺(1s⁻¹) ions and initiates a decay cascade, where ~90% of the ionized species undergo local KLL Auger–Meitner decays to predominantly (~63%) form Al⁵⁺(2p⁻²) states. Alternatively, a single Al 2p level vacancy can be created by initial ionization at lower photon energy (2p⁻¹). These 2p vacancies are filled by non-local ETMD processes, in the case of Al⁴⁺(2p⁻¹) in one ETMD\({}_{2{{{{\rm{p}}}}}^{-1}\to {{{\rm{GS}}}}}\) step, and for Al⁵⁺(2p⁻²) in two steps, ETMD\({}_{2{{{{\rm{p}}}}}^{-2}\to 2{{{{\rm{p}}}}}^{-1}}\) followed by ETMD\({}_{2{{{{\rm{p}}}}}^{-1}\to {{{\rm{GS}}}}}\), after which the Al ion is back to its ground state Al³⁺ (GS). Each ETMD process ionizes up to two water molecules and emits one slow ETMD electron. Note that, for clarity, the figure only shows ETMD processes involving two water molecules, ETMD(3); for further details, see the main body of text.