Lecture26-1

Lecture26-1 - CHEM 356, Lecture 26, Fall 2009 1 Atomic...

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Unformatted text preview: CHEM 356, Lecture 26, Fall 2009 1 Atomic Structure and Atomic Spectroscopy. We shall assume that the wavefunctions for a multi-electron atom are determined in zeroth order by a centralfield Hamiltonian, : we shall study the effect of adding systematically interelectron repulsion, followed by spinorbit coupling. RussellSaunders Coupling Scheme: The most common coupling scheme for angular momenta is the RussellSaunders scheme, which corresponds to building up the atomic Hamiltonian in three stages, = , = + ee , = + ee + so . Notation: lower case letters are used to designate the angular momenta of the individual electrons in a multi-electron atom: , s , j , etc. Procedure: makes extensive use of the fact that mutually commuting operators can have si- multaneous eigenfunctions. We shall require at each step that the operators used to label our energy eigenfunctions all commute with . 1. Centralfield Hamiltonian : All , s commute with and with one another: we say that 2 , , 2 , and are SHARP operators, which means that we can obtain simultaneous eigenfunctions of the full set of operators { 2 , , 2 , , } . The form for the Hamiltonian provides a description of the atom at the level of electronic CONFIGURATIONS. 2. Inclusion of Interelectronic repulsions: = + ee The individual vector operators no longer commute with (because they do not commute with ee ); however, two new angular momentum operators L = and S = s do. The corresponding set of sharp operators is then { 2 , 2 , , } . This form for the Hamiltonian provides a description of the atom at the level of electronic TERMS. CHEM 356, Lecture 26, Fall 2009 2 3. Inclusion of SpinOrbit Coupling: = + ee + so . L and S do not commute with so = S L , and hence they do not commute with . The vector operator J , with J = L + S , which represents the total electronic angular momentum of the multi-electron atom does commute with , however. The corresponding set of sharp operators is now 2 , and ....
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This note was uploaded on 02/28/2011 for the course CHEM 356 taught by Professor Prof.iaskjd during the Fall '09 term at Waterloo.

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Lecture26-1 - CHEM 356, Lecture 26, Fall 2009 1 Atomic...

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