# Europium - Sinha S.P.

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1 In denoting the valence state of an element, Chemists very often use M°, M+, M2+ etc., or M°, M(I), M(H) etc. for neutral, mono and divalent ions. Spectroscopists, however, prefer to write M I, M II, M III in describing the above valence states. We have used the very first notation throughout the book with regard to chemical compounds. In this chapter spectroscopic notations are also included beside the chemical notation for the sake of clarity.

Absorption Spectra of the Europium Ion and Its Complexes 101

those of europium. Before doing so, however, it is perhaps necessary to discuss some theoretical aspects of rare earth spectroscopy.

In spectroscopy the number of states that may arise from a given electronic configuration, is equal to the number of orthogonal wave-functions that can be written for that configuration. For n electrons in a partly filled shell, the number of states occuring is equal to 2x\jn\(2x—n)!, where x is the degeneracy number. The number of states is independent of the distribution of the levels, which may vary due to different sorts of coupling and also with ligand field.

Any term arising from a given configuration usually consists of one or more energy levels and the number of states contained in a multiplet term is {2L + 1) (2S + 1) taking into account the most common form to coupling scheme Russell-Saunders coupling. The total orbital angular momentum, L, is defined as the resultant of the vectorial sum of the orbital angular momenta (I) of the electrons, and the total spin, S, is the spin (s) equivalent part. In some configurations there may arise terms having the same L and S values. An additional quantum number, t, must now be used to distinguish pairs of states, and a basis state could be lebeled as t8LJM. The quantity (2S + 1) is called the multiplicity. Electrostatic interactions (parameters Fu or Ek) separate the different terms of a configuration and the spin-orbit interactions (Lande parameter Cnf) give rise to the fine structure of the terms themselves.

The levels of a given multiplet are identified by their J values, where J is the vector sum of L and 8. The number 2J -|- 1 is often called the degeneracy number of the level. The possible J values and hence the

number of levels, when L > S are, L—S, L—S + 1.....L S and

when L< S they are S—L, 8—L -j- 1, ..., S -f- L.

The standard notation given to a term with L = 0, 1, 2, 3, 4, 5, ... etc. is 8, P, 2), F, O, //,... respectively. It is usual to write the multiplicity number (i.e. 28 + 1) as a superscript at the left and hence a term is represented as 2S+1L. A level is then denoted by 2S+1Lj.

A study of the energy levels of a configuration yields valuable information regarding the nature of the interactions between the electrons and the coupling involved. The calculation of energy levels for terms of the fn configuration becomes too cumbersome and lengthy (but may not be so for a modem computer) by the Slater-Condon-Shortley [480] method. As we shall see, later several states having the same L and S quantum numbers occur and the Slater method gives only the average energy.

A single electron or one hole in / shell give rise to a single term 2F (characteristic of Ce3+ and Yb3+). In the case of Pr3* with two 4/ electrons (or with two holes as in Tm3+) the following terms arise

*F, 3P, *H, lD, *G, U, lS.

As we go on adding electrons in the 4/ shell the number of terms increases

102

Spectroscopic Properties of Europium

and it becomes exceedingly difficult to label the terms by LS, as more than* one term with the same L and S values may occur within the same configuration. An unique labeling scheme using another quantum number v, the seniority number, was introduced by Racah [481] to classify such states. Racah [481] first applied the group theoretical method to the systematic classification, calculation of the coefficients of the fractional parentage and the energy matrices of the fn configuration.

We will not attempt here to produce any classification of the states derived from the 4fn configuration, but simply list a few terms that can originate from different fn configurations thereby indicating the complexity of the problem when one considers the LS classification. We will use dash and double dash to denote any term occuring more than once or twice. A thorough discussion of the application of group theory to the fn configuration is given by Judd [482].

f1 and /18: ZF

P and /12: *F, 8P, 8ff, W, xO, 1I, *S

f* and f11: *S, *F, *D, 4G, 4J, 2P, 2I1, ZD, *G, 2J, 2F, *G', *H', *K, 2L, *F f* and /10: *S, 5F, 5£>, 5<2, *1, 8F, 8P, 8tf, 8D, *6?, */, ZD\ *F', *G', *H', *K, aL, 8P/, *F\ 3G”, 8J', *K', 8ikf, . .. etc. f and/8: 6F, 6P, 6H, 4P, *P, 4Z), 4G, 47, 4D', 4P', 4Gf/, 4iT', 4K, 4£, 4P', 4P", 4G', *!', 47T, 4Jkf, 4£, .. . etc. f and /8: 7jP, 5P, *H, 5D, bG, 5J, 5D'f 5P, 5G', 5H', 5K, 5i, *£, 5P', 5/T,

5r, *F, 8P, 8H, 8JD, 3G, 8J, 8D', 3P', 3(2', 8H'. 3K, *L, 3P', 3P", 8G', 8£P, 8I', SX', 8M, ... etc. f: 8£, 6D, 6G, 6J, 6P, 6P, 6i7, 4D, 4G, *1, *D', 4P, 4<?', 4ff, 4K, *£, 4£,

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