Splitting of J levels

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. 

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... 

Kramers theorem requires that all half-integer spin systems be at least doubly degenerate in the absence of a magnetic held. Next, note that the splitting of these levels by a magnetic held depends on its orientation relative to the axes of the ZFS tensor of the metal ion. The VTVH MCD saturation magnetization curve behavior reflects the difference in the population of these levels and their spin expectation values in a specific molecular direchon. This direction must be perpendicular to the polarizations of the transition (Mih where i / j are the two perpendicular polarizations... 

Gmber JB, Zandi B, Merkle L (1998) Crystal-field splitting of energy levels of rare earth ions Dy (4/) and Yb (4/ ) inM(ll) sites in fluorapatite crystal Sr5(P04)3p. J Appl Phys 83 1009-1016 Gmber JB, Zandi B, Ferry M, Merkle L (1999) Spectra and energy levels of bivalent samarium in strontium fluorapabte. J Appl Phys 86 4377-4382... 

Higher order effects introduce additional distortion terms and also distortion terms that can give rise to splittings of certain -levels. The effects of centrifugal distortion on the observation of forbidden h.K = 3 transitions have already been mentioned. Induced dipole moments also allow the observation of pure rotational spectra of spherical tops which, because they have no permanent dipole moment, would otherwise have no rotational spectra. For CH4, the distortion moment is on the order of 5 X 10 D. Both J J +l and J J transitions have been observed. The leading terms in the frequency equation for the 7 y -I-1 transitions are like those for a linear molecule, Eq. (51) however, the molecular distortion in such molecules is more complicated, and additional terms are required to adequately characterize the rotational spectrum. Such observations have provided the rotation and distortion constants. Some examples of nonpolar molecular studies via microwave spectroscopy are spherical tops with Td symmetry like CH4, SiHd, and GeITt and those with Dsh symmetry like BF3 and SO3. For SO3, a planar molecule, the centrilugally induced rotational spectrum provides = 1.4175 A. 

Photoelectron peaks are labelled according to the quantum numbers of the level from which the electron originates. An electron coming from an orbital with main quantum number n, orbital momentum / (0, 1, 2, 3,. .. indicated as s, p, d, f,. ..) and spin momentum s (+1/2 or -1/2) is indicated as For every orbital momentum / > 0 there are two values of the total momentum j = l+Ml and j = l-Ml, each state filled with 2j + 1 electrons. Flence, most XPS peaks come in doublets and the intensity ratio of the components is (/ + 1)//. When the doublet splitting is too small to be observed, tire subscript / + s is omitted. 

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