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By D.R. BATES (Eds.)

ISBN-10: 1483227413

ISBN-13: 9781483227412

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Condon and Shortley3 give tables which are sufficient for most atomic structure applications. With the usual phase conventions the coupling coefficients are real. ) jm where (ÌlÌ2Ìm\hÌ2mlm2) = (hÌ2ml^2ÌÌÌÌ2Ìm)' From (67) one obtains Σ jm (/l/2/ W |/l/2 W l W 2)(/l/2/w|h/ 2 wiw2) = Ò^'ò^' (68) 36 M. J. 7 Symmetry Properties of Coupled Eigenfunotions for j1 = j2 Consider the coupling of two spin angular momenta. 5. for the individual spin functions we have, from (65 a and b), SMs il ΜΗΑΛΓδ^,σ,) ò^aMWoè 10 (ΙΙ^2)[δ(ί\σι)δα\σ2) + WKWÏIa,)] IT ίίϊΚΜϋ*,) 00 (1/V"2j[- <5(Ìh)

60) It was this convention which led to the phase choice for the spherical harmonics defined by (20). 3 Angular Momentum Coupling Let 3V32 b e t w o commuting angular momenta; these could, for example, be the individual orbital angular momenta for two electrons, or they could be the orbital and spin angular momenta for a single electron. The total angular momentum operator is defined by J = Ji + 32t Jx = Ju + J2z. (61) Using the commutation relations for the components of Jx and / 2 , and the fact that JVJ2 commute it is readily shown that the components of J satisfy the commutation relations for an angular momentum operator.

43 1. COMPLEX ATOMS When (79) is satisfied only the (l/r12) term in H gives a nonzero contribution to the exchange integral. The energy is therefore I {Is) + I{nl) + 1 Isnl Isnl I i I Isnl '12 1 nils (80) '12 the + sign going with S = 0 and the — sign with 5 = 1 . The exchange integral (lsnl\llr12\nlls) has no classical analogue. It may be shown7 that this integral is positive. 4 The He Energy Level Diagram The observed energy levels of He (Fig. 8) may be divided into two distinct groups originally termed para-helium and ortho-helium.

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Aggregates of Particles by D.R. BATES (Eds.)

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