Splitting, of energy levels

The hyperfine structure (splitting) of energy levels is mainly caused by electric and magnetic multipole interactions between the atomic nucleus and electronic shells. From the known data on hyperfine structure we can determine the electric and magnetic multipole momenta of the nuclei, their spins and other parameters. 

The splitting of energy levels is due to electron repulsions which is denoted by f-,. 

This is the case of most molecules. There are, however, certain molecules in which the inversion barrier is so low that the vibrational wave functions cannot be considered as localized. Frequencies of the transitions between symmetrically equivalent configurations A and B are then high enough for the splitting of energy levels due to the tunneling to be detected experimentally. 

With this understanding, the spectra of Eu could probe the microstructure of nanomaterials, because the Dq to Fi transition was very sensitive to the site symmetry. Yan et al. used laser selective excitation technique to research the high-resolution spectra of f-YV04 Eu NPs (Yan et al., 2003a). When the Eu dopants approach the NPs surface, the D2d symmetry is broken. In emission spectra this is reflected by several points the increased number of emission lines the shortened luminescent lifetime, the enhanced splitting of energy levels, and the broadened emission peaks. 

Figure 3. Energy levels of 3d electrons in (a) regnlar octahedron (b) highly distorted octahedron. The splitting of energy levels in the gronnd state are given by Ai and A2 (adapted from Bnms 1993).

The interaction of magnetic moments with a magnetic field gives rise to a splitting of energy levels. It is called Zeeman interaction. For this reason the index Z is used in (2.2.3). 

Relativistic effects in atoms and molecules are commonly separated in kinematical effects, which do not cause a splitting of energy levels due to the spin degrees of freedom, and the effects of spin-orbit coupling. This separation is not unambiguously defined (Visscher and van Lenthe 1999), but is nevertheless extremely convenient when discussing effects on phenomenology. 

The HCp operator represents the nonspherically symmetric components of the one-electron CF interactions, i.e. the perturbation of the Ln3+ 4fN electron system by all the other ions. The states arising from the 4fN configuration are well-shielded from the oscillating crystalline field (so that spectral lines are sharp) but a static field penetrates the ion and produces a Stark splitting of energy levels. The general form of the CF Hamiltonian Hcf is given by... 

Describe the importance of the spin quantum number (m,) and the exclusion principle for populating an orbital understand how shielding and penetration lead to the splitting of energy levels into sublevels ( 8.2) (EPs 8.4-8.13)... 

For systems with spin 5 > 1 the zero-field splitting of energy levels appears. These substances may exhibit a step increase of the magnetisation (the temperature should be low and the magnetic field high). Consequently the mean and differential magnetic susceptibilities differ substantially. 

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... 

Hyperfine structure - Splitting of energy levels and spectral lines into several closely spaced components as a result of interaction of nuclear spin angular momentum with other angular momenta in the atom or molecule. 

This phenomenon must not be confused with spin-spin coupling, which is transmitted through bonds and which leads to the splitting of energy levels. Only relaxation times are involved. 

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