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105) It is obvious that Cm, is independent of the order of the numbers IW. may be shown that Clw is zero unless : \l - V\ ^ λ ^ (/ + /'), It (106) (I + λ + I') = an even integer. Some values of Cm> are given in Table V. TABLE V T H E COEFFICIENT CJW CM 2 sp 2/3 sd 2/5 PP 2/3 4/15 pd 4/15 6/35 dd 2/5 4/35 4/35 The final expression for the interaction energy between nl*l+2 and n'V is (21 + 1) 2F0(nln'l') - — J£ Cm>Gk(nln'l') (107) 54 M. J. 5 Interaction Between Two Closed Shells The interaction energy 2(2/ + 1)(2/' + 1) Ì2F0(nlnT) - λ £ Cm>Gx(nln'l')\ (108) between nlil+2 and η7' 4Γ + 2 is obtained on multiplying (107) by 2(2/' + 1).

For a given nl it is found that the ortho-helium levels are lower than the para-helium levels. 1p 1r Is3p Is3d 0 10,000 _ T Is3s 3 S 3 P Is3p 3 D Hydrogen js3d n=2 20,000 Is2p E - 30,000 h g 40,000 0) f— < Is2p Is2s n=2 Is2s 190,000 200,000 FIG. 8. S, P and D states in the He energy level diagram. This entire picture is in complete agreement with what the theory would lead one to except. We may identify para-helium with the singlet spin states and ortho-helium with the triplet states. The fact that the ground state belongs to the para-helium group is convincing evidence in favour 44 M.

From (60), ^T(2 2) = 2% and ^ ( 1 1) = ]/2 K. Therefore φ(21)=~{φ(01) + φ(10)}. By continued operation with / _ all states 0(2w) may be obtained. (00) + y(lT)] 1 (1/1/2) [φ(ΙΟ) + (01) and ç>(10), that is, ψ(11) = αφ(01) + οφ(10). Since 0(11) should be orthogonal to 0(21) and should be normalized, we obtain a + b = 0 and \a\2 + |6| 2 = 1. Therefore φ(11) = (β»ΐ]/2)[φ(01)-φ(10)1 the phase ô being arbitrary.

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