cPES & ligand field

Dear Quanty developers,

I kindly ask for indications on setting up core-level photoemission calculations. In the example file about 2p core-level photoemission from NiO including ligand field effects, the energy balance for the final states is reported as :

-- The 2p^5 L^10 d^n+1 configuration has an energy 0
-- The 2p^5 L^9  d^n+2 configuration has an energy Delta + Udd - Upd
-- The 2p^5 L^8  d^n+3 configuration has an energy 2*Delta + 3*Udd - 2*Upd

These configurations correspond to the expressions
-- 5 ep + 10 eL + (n+1) ed + (n+1)(n)   Udd/2 + 5 (n+1) Upd == 0
-- 5 ep +  9 eL + (n+2) ed + (n+2)(n+1) Udd/2 + 5 (n+2) Upd == Delta+Udd-Upd
-- 5 ep +  8 eL + (n+3) ed + (n+3)(n+2) Udd/2 + 5 (n+3) Upd == 2*Delta+3*Udd-2*Upd

My question: is this treatment correct for cPES or, since the $2p$ electron is photoemitted rather than promoted in the $d$ states as for XAS, I have to reduce the final state occupation of the $d$ states by one electron (e.g. $2p^5 L^{10} d^n$, $2p^5 L^9 d^{n+1}$, etc…)?

Thanks a lot in advance.