# Europium - Sinha S.P.

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In making calculations, often 4/-radial eigenfunctions are approximated to hydrogenic ones and the Ft s are calculated accordingly. However, actual calculations show that the 4/-radial eigenfunctions are far from being hydrogenic. Calculations of hydrogenic eigenfunctions were made by Trefftz [484] but there was a mistake in her FefFz ratio. The following corrected ratios are due to Judd [568], from which the Racah parameters, E*'s may easily be evaluated in terms of F2 only from eq. 48.

Absorption Spectra of the Europium Ion and Its Complexes 105

FaIF2 =(41/297) = 0.13805 FeIF2 = {7 X 25/81 X 143) = 0.01511 (50)

It has been found that these ratios do not depend on the precise shape of the eigenfunction, as for example, the ratios for a 5/-radial eigenfunctions are

Fa/Fz = 0.142 FgIF2 = 0.0161 (51)

which are very much the same as in eq. 50, in spite of the dissimilarity between 4/ and 5/ radial eigenfunctions.

Judd [569] has also found that the parameter F% for the rare earth series can be expressed in terms of atomic number, Z, as

F% = 12.4 (Z — 34) (52)

Now, if the 4/-hydrogenic ratios are used for the Slater integrals, the elements of the energy matrices may be expressed in terms of two parameters only, F2 and £4/. By diagonalizing the matrices for several values of F2 and £4/5 the best fit parameters giving close agreement between theory and experiment, are obtained. However, one has to be very cautious in using such approximations to calculate fn energy levels because although the splittings of the ground state multiplet are mainly determined by the spin-orbit coupling constant (£4/), these are relatively insensitive to the choice of i^Vs; whereas for higher energy levels the contribution from £4/ becomes negligible in comparison to the iVs. The discrepencies between the calculated and experimental energy levels may also be due to configuration interactions and spin-spin or spin-other orbit interactions which are neglected in assuming hydrogenic wavefunctions. The electrostatic interactions between the fn configuration and other configurations of the same parity sometime becomes appreciable.

For a hydrogen-like atom or ion the spin-orbit coupling constant Cni is expressed as

7*4

Ui = - 11.644 cm-i (52 a)

w*3 I (Z+l) (2Z + 1)

where Z* is the effective nuclear charge and n* is the effective principal quantum number. Z* is equal to (Z—a), Z being the atomic number and a, the Screening constant. For the M®+ rare earth ions a has a value between 33 to 36.

Spin-orbit interactions mix states with the same J but different L 8 by second (or higher) order perturbations, such perturbations become important when the separation between the levels is small. The spin-orbit coupling constants (£4/) increase more rapidly through the rare earth series with increasing number of /-electrons than do the Fk s. This results in the breakdown of L S coupling even more near the middle of the rare earth series, because of the greater population of the upper

106 Spectroscopic Properties of Europium

energy levels. The magnitude of the LS breakdown increases rapidly untif1 the half-filled shell is reached, and then slowly decreases. This decrease in the case of the heavy rare earths may be due to the spreading of the energy levels which is strongly influenced by the increase in the £4f values.

Energy Levels of Europium

In both neutral and singly ionized rare earths the 4/, 5d and 65 electrons all have roughly the same energy and hence the overlap between configurations like 4/n, 4/B_15d, 4/”-16s, 4/B“26s, . .. etc. produces lowlying energy levels, and the separations become too complicated to deal with. However, for some divalent (where the ground state is not derived from a 4/n-15d state) and definitely for trivalent rare earths the situation is much simpler and the ground state has the fn configuration. In the case of the divalent rare earth ions at the beginning of the series 4fn and 4/n -15d are nearly coincident in energy, and 4/n-15d crosses over to higher energy than 4/n-16s near dysprosium. Except for cerium and praseodymium the free ion spectra of rare earths in the divalent and trivalent states are still unknown. The spectra of a few neutral (first spectrum) and singly ionized (second spectrum) rare earths have recently been investigated.

The spectrum of neutral europium (Eu°, Eu I). — Russell and King [485] analyzed the first spectrum of europium (spectroscopic notation Eu I) in 1939 and showed the ground level to be 8$7/2 for the configuration 4/76s2. These authors were able to identify a large number of terms arising from the addition of two electrons to the parent core. Using the experimental data of Russell and King, an extensive theoretical analysis of the spectrum was carried out by Smith and Wybourne \486\. They included both electrostatic and spin-orbit interactions in the energy matrices in order to get a best fit for the observed and calculated energy levels (Table 39). The configurations 4/7(8&)6s6p, 4p(sS)6s5d and 4f7(8S)5d5p were considered and the following set of “best fit” electrostatic and spin-orbit coupling parameters were evaluated. Other conifigu-

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