Eine Erweiterung Des Schalenmodells Zur Beschreibung Alkali-Ähnlicher Strukturen
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11. Die Elektronenspektren der Alkalien phänomenologisch und ihre Deutung innerhalb des Schalenmodells der Atome . . . . . . . . . . . . . . . . 11 lIl. Theoretischer Ansatz zur Beschreibung von Alkalien a) Die Einpartikelnäherung des quantenmechanischen Vielkörp- problems (stabiler Rumpf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 b) Die notwendige Gleichung bei stabilem Rumpf . . . . . . . . . . . . . . . . 15 c) Diskussion der Integralgleichung für Alkaliatome mit stabilem Rumpf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 d) Zusammenhang mit der Methode von HARTREE und FOCK . . -. . . 17 IV. Explizite Berechnung des Alkaliproblems in der Einteilchennäherung für Li und Li-ähnliche Ionen a) Lösung bei vereinfachtem Rumpf mit Hilfe eines Ersatzpotentials 19 b) Der EinfluB der Rumpfwellenfunktion auf die Eigenzustände der Alkalien in Einpartikelnäherung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 V. Die Polarisation des Rumpfes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 VI. Die H-Ähnlichkeit der Alkalispektren a) Das Problem der Definition der Hauptquantenzahl 28 b) Die H-Ähnlichkeit in störungstheoretischer Näherung . . . . . . . . . . 30 c) Näherungsrechnung für a bei Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 VII. Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 VIII. Einheiten und N otationen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5 Anhänge I. Die explizite Form des Antisymmetrisierungsoperators . . . . . . . . . . . . 39 11. U mrechnung der Einpartikelgleichung (14). . . . . . . . . . . . . . . . . . . . . . . 41 lIl. Eigenschaften der Lösungen von (14) . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 IV. Die Lösung der Schrödingergleichung des Ersatzpotentials . . . . . . . . 45 V. Die explizite Berechnung der Energie des Li-Atoms und Li-ähnlicher Ionen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 VI. Die Energie des Li-Atoms bei verbesserter Rumpfwellenfunktion . . . 53 VII. Explizite Berechnung der Rumpfpolarisation . . . . . . . . . . . . . . . . . . . " 57 VIII. Abschätzung der Variation der Rumpfpolarisation mit der Hau- quantenzahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 IX. Der Grenzfall z = 00 innerhalb der Definition der Hauptquantenzahl nach dem H-Atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 X. Umformung der Einpartikelnäherung des Alkaliproblems in eine Integralgleichung von einer Variablen . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 XI. Ergänzung zu Kap. VI. b . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . 67 Literaturverzeichnis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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