Page - 103 - in Entwicklung und Anwendung explizit korrelierter Wellenfunktionsmodelle

C.Erla¨uterungenzuKapitel 3 mitdenGro¨ßen: V xy ij = 〈xy|f12Qˆ12g12|ij〉 (C.14) V˜ xy ij = 〈xy|f12Qˆ12g˜12|ij〉 (C.15) = 〈xy|f12g12|ij〉− ∑ mn 〈xy|f12|m˜n˜〉〈mn|g12|i˜j˜〉 − ∑ mq′′ 〈xy|f12|m˜q ′′〉〈mq′′|g12|i˜j˜〉 − ∑ mq′′ 〈xy|f12|q ′′m˜〉〈q′′m|g12|i˜j˜〉 (C.16) Bxy,uv = (T¯xy,uv− P¯xy,uv+Q¯xy,uv) + 1 2 ∑ p′ ( Xxy,p′vFup′−Xxy,up′Fvp′+Fp′xXp′y,uv−Fp′yXxp′,uv ) (C.17) T¯xy,uv = 1 2 (Txy,uv+Txy,vu) (C.18) Txy,uv = 〈xy|f12Qˆ12[Tˆ12, f12]|uv〉 (C.19) Pxy,uv = 〈xy|f12Qˆ12Kˆ12 f12|uv〉 (C.20) Kˆ12 = Kˆ1+ Kˆ2 (C.21) Qxy,uv = ∑ p ( 〈xy|f12Qˆ12 f12|r ′v〉Kr′u+〈xy|f12Qˆ12 f12|ur ′〉Kr′v ) (C.22) Xxy,uv = 〈xy|f12Qˆ12 f12|uv〉 (C.23) (C.24) DasUpdatederR12-Amplitudenerfolgt nach: c uv (neu) ij = c uv (alt) ij + ∑ xy [B−1]uv,xyΩ xy ij . (C.25) Brueckner-Orbitalupdate DasBrueckner-Update erfolgt nachRef. [112]: U = exp(Λ)=1+Λ+ 1 2 Λ 2+ · · · , (C.26) Λai = t a i , (C.27) Λia = −t a i , (C.28) Λij = Λab= 0. (C.29) AusgangspunktderTransformation sinddamitdieurspru¨nglichenOrbitale: U(n) = exp(Λ(n)) · · ·exp(Λ(2))exp(Λ(1)) . (C.30) 103