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Few-particle energies e ( ) can be expressed as a sum over the single-particle energies of electrons e (em) and holes e (hn), attractive C em hn and repulsive C hm hn Coulomb interaction and exchange and correlation energies K ( ). For X + that yields: e (X +) =e (e0) +e (h0) +e (h1) + C e0 h0 + C e0 h1 + C h0 h1 +K (X +). The transition energies Edet and Eexc for the recombination X + → hj and excitation process h0 →X + are defined as the difference between e (X +) and the energy of the final e (hj) and initial e (h0) states. By subtracting both energies, Δ h0 hj e (hj) -e (h0) = Eexc (h0 →X +) - Edet (X + → hj), all contributions from few-particle effects are eliminated.
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