A unitary calculus for electronic orbitals - download pdf or read online

By W. G. Harter, C. W. Patterson

ISBN-10: 0387076999

ISBN-13: 9780387076997

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Example text

A pattern calculus for a bigger group U 6 covers this, as described next. D. Spin,and Orbit ~ _ 1 Together: U 6 A single electron confined to the p-shell has six possible states which we label as follows: i~=11~>= IA=I ~~s=½\ m=l =~/ , I ~ : ! 1 ~ , I ~ =12f>,ld>=12~>,l~=13%>, and 1~:13~. Along with this comes a set of 36 1-body operators which could be the U 6 elementary operators Eaa Eab... 31. (31a) (31b) iliill , , , , , , , , , ° . , (31c) I , . , , . - - I . . , ° . ° . ° 11 v00 2 " ° ' ' ' ° ....

KIi> ... . . Suppose, as before, that the tableaus or components i, j, k .... corresponded to the first non-zero components of II>, II~ , IIII~ .... respectively. °. will require only the i, j, k .... j> in the basis of the equal-M tableaus I ~ , 12> . . In>. (18) ... v _- ... 19b. 47 ~i~> ~II~";

The for dealing with particles structure than the non-rela- This theory has led to the tableau formu- las of (I) and is certainly capable of producing more general analyses of states involving nucleons, istic models. hadrons, or relativ- 38 i. UNITARY ANALYSIS FOR NEARLY-FREE ATOMS The unitary analysis of atomic Russell-Saunders (LS) coupling states was introduced in (I) and will be treated in more detail now. " We now treat the simplest exam- ples that do exhibit these problems, and give routines for obtaining the energy and transition matrices using the least number of mathematical operations.

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A unitary calculus for electronic orbitals by W. G. Harter, C. W. Patterson

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