Selected Works of Hans A. Bethe: With Commentary by Hans A Bethe

By Hans A Bethe

Hans A Bethe bought the Nobel Prize for Physics in 1967 for his paintings at the construction of power in stars. A residing legend one of the physics neighborhood, he helped to form classical physics into quantum physics and elevated the certainty of the atomic strategies answerable for the homes of subject and of the forces governing the buildings of atomic nuclei.This selection of papers via Prof Bethe dates from 1928, while he acquired his PhD, to now. It covers numerous components and displays the numerous contributions in study and discovery made through the most vital and eminent physicists of all time. detailed commentaries were written via Prof Bethe to counterpoint the chosen papers.

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Ds =Do+Dt+Ds+D3+D, The free atom can he in an s, P. D. F, or G state ; which of these is the lowest term can of course not be decided without exact calculation. b) Orientation of the total orbital angular momentum in the crystal, reduction of that representation of the rotation group which corresponds to the term of the entire atom as representation of the octahedral group (Table 2): De = rt D r = r, D2 =r3+rs D3 =1s+r,+rs D, =1r+ra+14+1s Strong crystal field Intermediate crystal field I nteraction of Orientation of Interaction of O ientation the individual the oriented ofthe entire the electrons in electron in the electrons atom in the the free atom.

Three-fold term, representation I's). We present the corresponding cigenfunctions both in written - out torm and also in Ehlert's t notation . In this notation ( l t (afy)=ft+t a p r \r1, l-a+t4+} az°av a \ CO IRepl Eigenfui :ction, ordinary notation (27), = n, r, ra V T (2 coal 9 - = 1 'i Eigenfunction. t coo p (101) 15 (28)2 = Y P2' sin 0 = 2 ain 9 cos & sin (011) Ehlert, loc. cit. -29- 33 In like fashion we obtain the eigenfunctions for the results of the splitting up of an F term in the crystal , by assigning to the same term the eigenfunctions that transform into each other on interchange of the axes.

Sin q (012)-(210) (3 s), - 1/ 2 F. (030) a, 8 Here as is will known Psi = V21 Cos'3 - s) sing (4 PIS = 8 sins Similarly for a G-term: Eigenfunction, ordinary notation E' 11_- II_ G. ' 9 - 1) sin' 9 P4' 10 coo 9 sin' 9 P,4 =T3 1/35 sin' 3 All our eigenfunctions are the correct zeroth-order eigenfunctions for the electron in the crystal atom, for two terms never belong to the same representations. This would first occur in the splitting-up of an H term. § 13. Connection between the Splitting-Up of Terms and the Interpretation of Spherical Harmonics as Potentials of Multipoles Every spherical harmonic of Ith order gives the angular dependence of the potential of a multipole of the same order , as can most easily be seen from the Maxwell form of the spherical harmonics, (aRY) art + t a' 1 am" ay)Zr , 1 =a +3+r To every term of the electron for cubic symmetry there now corresponds a definite decomposition ("partition") of 1 into three summands a, 8, y, as was already remarked by Ehlert.

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