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000132177 1001_ $$0P:(DE-Juel1)159161$$aBhat, Kaustubh$$b0$$eCorresponding author$$ufzj
000132177 245__ $$aCrystal Field Effects on Multiplets Observed in Open d- and f- shells$$f2012-02-03
000132177 260__ $$c2013
000132177 300__ $$a
000132177 3367_ $$0PUB:(DE-HGF)19$$2PUB:(DE-HGF)$$aMaster Thesis$$bmaster$$mmaster$$s132177
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000132177 502__ $$aRWTH Aachen, Masterarbeit, 2012$$bMS$$cRWTH Aachen$$d2012
000132177 520__ $$aThe subject of the thesis is to study a crystal field and spin-orbit coupling effects on multiplets observed in open d- and f-shells. The Coulomb interaction is considered by building the electrostatic matrix, where the required Gaunt coefficient are calculated recursively. Continuous fractions are used to produce Gaunt coefficients in the form of square roots of rational numbers to verify them. L-S coupling between orbital and spin angular momenta is assumed. Due to the spherical symmetry of the Coulomb potential, orbital and spin angular momenta are conserved separately. The corresponding quantum numbers are used to classify the eigenstates of the electrostatic matrix. These are compared with the eigenstates of simplified approximations to the electrostatic matrix. Then a cubic or tetragonal crystal field is introduced to electrostatic Hamiltonian and the interplay of Hund's rule and crystal-field splitting is studied. Finally spin-orbit coupling is added.
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000132177 65320 $$2Author$$aGaunt coefficients
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000132177 65320 $$2Author$$acrystal-field splitting
000132177 65320 $$2Author$$amodel Hamiltonian
000132177 65320 $$2Author$$aCoulomb tensor
000132177 65320 $$2Author$$amultiplets
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