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

ISBN-10: 0387076999

ISBN-13: 9780387076997

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It will now be shown how bases, such as the orbital states implied by Fig. 38a) (Eq. 38b). xn i I i 2 { i2 in, i I i 2 ... i = i = (Xl)~i2(x2) S, ilil ... ~, i2i 2 ".. 39. There the factor D ~ (p) is an Sn representation using Fig. 7-a, and Ny constant to be evaluated shortly. ~,,,> = N~, 1s~ II 2 ... in~ of definite "order. " By order we mean that single particle states have been numbered (Recall the numbering 1-3 in Sec. 2B) and these numbers are ordered: i1~ i 2 ~ ... ~ in . 39 then give all other orderings.

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. The routines for treating multiple shells are only slightly different from those that treat pure configurations, so most of the procedural details are are contained in the discussion of the latter which is given next below.

A a c b Ebf d = -c e d f e , a a c b Ebe d = c e d f f (32) the tableau formula in Fig. 10 gives the to t r a n s f o r m b e t w e e n these vertical tableau 24 U6 states and the U3~U 2 or L-S states of Eqs. 29 or 30. 33 for which the coefficients can quickly be checked by simple matrix arithimetic. (33) i2 @ 2 ¢$ i' 2 Ig5 17:1 The spin-orbit operator of Eq. 34 follows from the relation in Eq. 31. ~( Ebc + E d e + Ecb + Eed This operator is invariant to rigid rotations of both spin and orbit, so it is convenient to deal with the LSJ states made from Eq.

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

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