J multiplets

Table 6.1 Energies of the low-lying J-multiplets predicted within the CASSCF/RASSI approach for the free Ln3+ ions. ANO-RCC of single-zeta quality were employed. The active space of the CASSCF method included only n electrons spanning the 4f shell. 

Atomic multiplet Spin free states J multiplet Kramers Doublets... 

The inclusion of the crystal field destroys the rotational symmetry of the ion and lifts the degeneracy of J levels (except of course Kramer s degeneracy) the only good quantum numbers will be T s, the irreducible representations of the point-group symmetry operation. If the crystal field interaction is comparable to J-J splitting (and we see from Table 2 that this is the case of actinides) it will also cause an admixture of different J multiplets. 

We take as an example the case of plutonium monopnictides PuP, PuAs, PuSb, the susceptibility of which is well fitted by Eq, (17). Results are given in Table 8 while bare data are in agreement with the full J multiplet value ( 1 pP in the intermediate coupling), the corrected value is substantially smaller and points towards a Fg ground state (see Table 8) in agreement with more detailed discussions ... 

In the scope of the Judd-Ofelt theory three parameters .22, 24, and 2 are commonly used to describe the transitions between J multiplets. For this case, the contributions from individual crystal field split levels of a given multiplet are simply summed up. To account for individual transitions, effective transition operators can be used to derive a parametrization... 

The g-factor of the Zeeman Hamiltonian of a given J multiplet is given by ... 

Two semiempirical approaches are commonly applied in calculating the energies and intensities of f-f transitions in rare earth ions. The most common is the so-called Judd-Ofelt method. At this level of theory, the total oscillator strength for an f-f transition between SL/) and S L J ) multiplets is given by Eq. (27) [34,35] ... 

In calculations involving higher J multiplets, matrix elements of the crystal field Hamiltonian between states belonging to different J multiplets are needed. Although these can be calculated by the method of operator equivalents extended to elements non-diagonal in J, it is convenient to use a more general approach, utilizing Racah s tensor operator technique (26). In this method the crystal field interaction may be written as... 

Combining this with 6.8.46. gives the form most useful for determining the multiphonon (MP) rate of the J-multiplet ... 

The experimental lineshapes of the carboxyl and methyl carbon resonances of fully enriched L-Alanine have been studied in detail at different MAS frequencies and decoupling field strengths. Complex lineshapes at intermediate spinning speeds were explained by the joint effect of off rotational resonance and coherent CSA-dipolar cross-correlation. It was found that coherent CS A-dipolar cross-correlation introduces either a differential intensity and/or a differential broadening of the lines of the J-multiplet. The conditions that lead to such effects were explained and experimentally verified. Additional simulations showed that these effects can be expected over a wide range of static magnetic fields and are not restricted to L-Alanine. 

In the majority of lanthanide cases, with the ground J multiplet (often referred to as the Hund s rule state) so isolated, the CEF analysis is simplified. When /=constant, I= X) j,jz), and the action of each r Z/ term on any such state can be expressed as a dimensionless Stevens factor (Stevens 1967) 0/ = /, yj, for / = 2,4,6, respectively... 

Alternative approaches have been presented using a more general field theory with all the J multiplets of the ground state serving as a basis. This leads to deviations of the dependence of Ap (except for Eu + and Sm +). However, McGarvey has shown that equation (6) is adequate for estimating shifts to an accuracy of 10-20%. ... 

The crystal-field interaction splits the ground-state J multiplet of the lanthanide ions. The splitting is determined by the charge distribution at the site of the lanthanide ion and by... 

In conventional neutron spectroscopy of CF levels (Fulde and Loewenhaupt 1986) we are dealing with transitions within the ground-state J multiplet, so-called intramultiplet transitions. As is well known, J multiplets exist at energies above that of the ground-state 7-multiplet. The value of performing intermultiplet spectroscopy has been demonstrated by optical results on ionic systems. Well-defined atomic spectra finm inter-4f transitions have been measured up to 6 eV in all trivalent lanthanides, except promethium, and these are illustrated up to 2 eV in fig. 6. A complete review of both the experiments (up to 1990) and theory has recently been given by Osborn et al. (1991) and the reader is referred to this for more details. In this section we shall summarize the salient points needed to interpret the experiments. 

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