Multiplet level

It is assumed that upper and lower levels are separated by a gap of AE. If the lower level is occupied by N electrons the transition probability is P = N/AE, with a maximum of P = 1, which describes fully resonating levels. The probability of resonance within the highest multiplet level is always equal to one. The transferred energy from all affected levels to the topmost level is then calculated as... 

Two specific features determine the similarity and difference of energy levels in di- and trivalent ions of rare-earth elements. First, isoelectronic configurations of TR " and of the next elements in the periodic system determines a qualitatively similar pattern of terms and multiplet levels, namely for TR the order of the 4/ -configuration levels and of excited 4f 5d-configuration levels... 

The total magnetic moment can be added up if the populations of the various sublevels are known. Assuming that the spacing of the multiplet levels is large compared to the splitting of the levels of a given J, the mean magnetization can be expressed as... 

Fig. 5. Experimental [Ref. (. < )] and theoretical [Ref. (7S)] 4fn - -4/B 1 photoexcitation energies for the rare-earth metals. For the theoretical estimates "complete screening of the if vacancy was assumed (see text). The lower curves are for photoexcitation into the lowest multiplet level of the 4/n 1 system. When the initial state involves an over half-filled (n > 7) 4/ shell of spin S, the final states may have spins S + 1/2 and S — 1/2. The lower curves for Tb through Tm are for spin S + 1/2 the upper curves are for excitation to spin S — 1/2...

For the ions Pu3+ and Am3+, the phenomenon noted for Sm3+ and Eu3+ is found since the multiplet levels are comparable to kT, anomalous temperature dependence of the susceptibilities occurs. 

Recently, Alexander et al [29] carried out an ab initio study of the four states (X A, A A", a A" and a A ) that correlate to OH-H in the product region and the electronic and spin-orbit couplings between them. These PESs were used to study the nonadiabatic effects on the branching between the product OH ( 77) multiplet levels, using a statistical model of atom-diatom insertion reactions combined with coupled-states capture theory. 

Fig. 16 Importance of the inclusion of dynamic correlation when going from CASSCF to NEVPT2 multiplet levels for the correct prediction of the spin-ground state and d-d absorption spectra of Ni(dtc)2...

The distribution of intensity between the different multiplet levels is given directly if Dirac functions are used to evaluate the transition probabilities, since the electron spin is incorporated in the equations. The total intensity of all the transitions within a multiplet, calculated from Dirac functions, is inappreciably different from that obtained with Schrddinger... 

Indications of such restricted orientation become apparent in the increasing magnitude of the Weiss constant. The Weiss constant actually depends on several factors of which three are important. These factors are (o) the possible existence of multiplet levels having energy differences comparable with normal temperature thermal energies, (5)... 

Fig. 24, Multiplet (a) Diagram showing multiplet levels and radia-...

Fig. 1. Schematic energy level diagram of the in-terconfigurational fluctuation (ICF) model describing valence fluctuations between two 4f configurations (4r, 4r ), characterized by their /multiplet level structure. The basic parameters of the ICF model and denote the interconfigurational excitation energy and interconfigurational mixing width, respectively.

The ground state of Sm " in the Sm monochalcogenides is 4f ( F = 0,1,.. . , 6), with a 0.6 eV wide spin-orbit-split multiplet. Electronic Raman scattering from the different /-multiplet levels of cleaved (100) faces of semiconducting SmSe (Guntherodt et al. 1981a) is shown in fig. 2. The odd-/ levels show up for perpendicular incident ( ,) and scattered (Ej polarization vectors, where-... 

Fig. 3. Electronic Raman scattering from the /-multiplet levels of Smj Yj.Se at 80 K for sl.O for = 0.05, the La-substituted Sm jjLao ojSe is shown. The scattering configuration is the same as in fig. 2. The hatched area indicates the electronic scattering from the J-0-> 1 excitation. Phonon scattering is seen below 200 cm ...

Transitions between crystal-field-split f-electron multiplet levels of various trivalent lanthanide ions (R) have also been observed by Raman scattering in the insulating phase of high-Tc cuprates (Heyen et al. 1991, Ruf et al. 1992, Dufour et al. 1995, Sanjuijo et al. 1995, Jandl et al. 1995, Cardona 1999), particularly those containing Nd " ... 

On the other hand, if /iv is small compared to kT) all multiplet levels are equally populated and... 

Here. S. L and J are the quantum numbers of the resultant spin, orbital and total angular momentum, respectively. In the general case where the multiplet separation is comparable to k T, the magnetic moment is determined by a Boltzmann distribution [178] over the different multiplet levels. These considerations hold only, if the (2J + l)-fold degeneracy of each multiplet level is not split or if its splitting is small as compared to kT... 

These data result in the value of = 2.114 kHz/Oe, which exceeds the measured one by 6%. Possibly, this is due to the influence of the excited multiplet level separated from the ground multiplet by a fairly small interval of 2100cm . ... 

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