By Hans A Bethe

Hans Bethe obtained the Nobel Prize for Physics in 1967 for his paintings at the creation of strength in stars. He helped to form classical physics into quantum physics and bring up the knowledge of the atomic approaches liable for the homes of topic and of the forces governing the constructions of atomic nuclei. This number of papers by way of Hans Bethe dates from 1928, while he bought his PhD, to the current.

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11 - 'PRi eft M CIS, PI (Cos $) . (9) Accordingly we need integrals of the form If„1us - fVeip j (r)Pi'" (coss9) Pir(cost9)M„myo : µ yc dr (10) By means of such integrals we can evidently also determine all the term values when severai terms bblong to the same representation of the crystal group (1 10, 11) and to calculate the eigenvalues one has to set up a special perturbation calculation in which the matrix elements IIn practice transitional conditions between intermediate and strong fields ( or between intermediate and weak) are probably of most frequent occurrence.

The matrix element ets in § 11, also § 22). The only important summand in Eq. (10c ) is in this case the term with s = 4 (because of the falling off of the terms with increasing S). For this term we have: 9 P4 4 - sine t9 sin*9cos4d5m 10 ' 1 14 a + 4 ays -3 d: Furthermore, in view of the tetragonal symmetry, -50- 54 a• v 84 v a: y' K- - - e - 4l ' 18 (8 a s For cubic or nearly cubic ' _ g B v) r+ f sin° r9 P,- Pe sin 3 d r? -} terms <,f higher order (16) symmetry we have also e v •' v TF 'a -37 R^ r _ e , it .

Xe - - Xs Xs - - Xs TABLE 12 Irreducible Components of the (2j + 1)-Dimensional Double-Valued Representation of the Spherical Rotation Group when Reduced as Two-Dimensional Representation of the Octahedral Group j Irreducible components re re r, +r, r,+r'+21' re+r,+2r; r, + r, + 2r, + components for 21 (re + r, + 2re) + i = with interchange of with 1 components for j = j All angular momenta up to j = ^/s are arbitrarily oriented in the cubic crystal : for larger angular momenta , the directional degeneracy is partly destroyed.