(2d)], it can be seen from (A2) that the Bragg reflection condition for the vector KTs(k~) reads 0~-0(ks) = 0~(ks) + 27rn.(A3) ~ parameterWe have introduced 77 in (20)"Let kB be a vector in the Bragg reflection position, i.e.0"~o(ks)= 0~(ks)+ 27rn.Let k be a vector in the neighbourhood of the vector ks. Then using (A4), (A5b) and (2e) we obtainso that the 77 parameter is a function of the known vectors ks and k. Correction of a misprint in equation (1.53)There is a misprint in equation (I.53); the term _ l___~,(igpqz~ Kpqz \ 2B /should be replaced by oz . Kpqz \ 2B ] P parameter appearing in equation (lib)When comparing (llb) and (I.53) we obtain AbstractThe Coulomb potential in a crystal is discussed. It is shown that its Fourier series expansion has a singular-

The optical absorption spectra of trivalent holmium in single crystals of HoPO, and (I-, Ho)PO, have been measured in the range from 15000 to 29000 em-l including the Zeeman effect of the ground level 51: and the two excited levels 3K; and 5Gk at 85 and 4.2 OK. The splitting factors of the degenerate components of the ground level and the level 3Ki indicate a small mixing of the states Y~J M with different M . With this fact some special features of the transitions between these two levels can be explained qualitatively. Es wurden die Absorptionsspektren des dreiwertigen Holmiums in Einkristallen vonHoPO, und (Y, Ho)PO, zwischen 15000 und 29000 cm-l und der Zeeman-Effekt des Gririidterms 51k und der beiden angeregten Terme 3K; und 5Gk bei 85 und 4,2 OK gemessen. Die Aufspaltungsfaktoren des Grundterms und des Terms 3Ki deuten auf eine geringe Durchmischung der Zustinde yY J M mit unterschiedlichem $1 hin. Damit lassen sich einige Besonderheiten der Ubergange zwischen diesen beiden Termen qualitativ erklaren.

Sets of crystal field parameters are derived to describe the splittings of the 5F', the 3Ki, the 5Gi, and the 5GJ,, levels of H o~+ in YPO, separately. The differences of the At(?) parameter for different levels by a factor of about 20 are explained qualitatively by different shielding factors for electrons in different LS-states.Den Aufspaltungen der Terme 5 F , 3Ki, 5Gi und 5G;,3 von Ho3' in YPO, werden einzeln Kristallfeldparameter angepaI3t. Unterschiede des Parameters A i ( r 2 ) urn einen Faktor 20 zwischen den verschiedenen Termen werden qualitativ durch unterschiedliche Abschirmfaktoren fur Elektronen in verschiedenen LS-Zustanden erklart.

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