By D.R. BATES (Eds.)
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This is equal to I(nl) plus the interaction energy between nl and the Na + core. One obtains E(nl) = I(nl) + 2F0(lsnl) - ψψγ) Gi(lsnl) + 2F0(2snl) - ^ J j - ^ Gtfsnl) + 6F0(2pnl) - \ Σ (112) CiuGx(2pnl). λ 11. 1 Allowed Values of SL With two electrons ηχΙνη212 outside of closed shells the values of 5 and L for the whole system are obtained on coupling the angular momenta of the electrons ηλΙνη212. For two inequivalent electrons (η^ φ nj,2) the exclusion principle imposes no restrictions on ms ml ,ms ml and we can have S = 0 or 1, and L — (/x + l2), (/x + l2 — 1 ) , .
May be generalized 7-9 and after some lengthy algebra an explicit expression for the coupling coefficients may be obtained. The explicit expression is cumbersome and will not be quoted. 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.
2 it will be shown that D(A\X) will be normalized to unity when (42) is satisfied for all i,j. 3 Parity A function f(Tvv2t... ) is said to be of even parity if /(τντ2,... ) and of odd parity if /(τντ2,.. ) = - / ( - τν - r 2 , . . ) . 1 that the wave function must be either of even or of odd parity. However, the Hamiltonian for an external perturbation of an atom may be of even or of odd parity (for example, an external constant electric field will be a perturbation of odd parity). We may therefore expect to find atomic states of even and of odd parity.