Quadrupole splitting interaction energy level

Fig. 7.4 Top Nuclear energy levels of Fe as shifted by electrical monopole (left), or as split by electrical quadrupole (center) or by magnetic dipole interaction (right), schematized for hematite at room temperature (5 > 0 vs. a-Fe, EQ < 0, Bhf 0). Bottom Schematic Mossbauer spectra corresponding to the energy levels schematized on top (J. FriedI, unpubl.).

Figure 2 Schematic description of some 57 Fe Mossbauer spectra showing original nuclear energy levels (A) slightly perturbed through interaction with S electron density (B) giving rise to a chemical shift (8) resulting from quadrupole interactions (C) and magnetic splitting of the ground and excited states (D). Arrows indicate transitions responsible for one,...

Figure 1 Nuclear energy levels responsible for one-, two-, and six-line iron Mossbauer spectra I, original energy levels II, small perturbation via interaction with s-electron density III, quadrupole interaction splitting IV, magnetic splitting of the ground and excited states...

Figure 1. Hyperfine interactions for Fe nuclei, showing the nuclear energy level diagram for (a) an unperturbed nucleus (b) electric monopole interaction (isomer shift) (c) electric quadrupole interaction (quadrupole splitting) and (d) magnetic dipole interaction (hyperfine magnetic splitting). Each interaction is shown individually, accompanied by the resulting Mossbauer spectrum.

The interaction of the nuclear quadrupole moment Q with the local electric field gradient (EFG) at the nuclear site causes a splitting of the nuclear energy levels. Table lc illustrates the situation for an Fe57 absorber atom embedded in a crystal with lower than cubic point symmetry for the iron lattice site. Since the nuclear ground state of Fe57 has zero quadrupole moment it remains unsplit. The excited state of Fe57, characterized by Q>0, however, splits into two sublevels. 

Starting with the simplest case, when no electric quadrupole interaction is present and when either an externally controllable magnetic field, Ho, is applied or, as in the case of metallic iron, when there is an internal magnetic field, Hint, we shall be concerned with Zeemann splittings of the nuclear levels as indicated in Table 1. The energy level positions Em are then dependent upon the effective magnetic field etf =i o + int ... 

Fig. 21. Crystal field results for the temperature dependent quadrupole splitting in Hb, involving spin-orbit interaction between energetically low lying levels r>Bg, 3E, Mi, and 5E. Their energies relative to the groundstate 5B2 are (for E (3E), E (Mi), and E (s ) in cm-1) ...

The magnetic dipole interaction and the electric quadrupole interaction, in an atom with nuclear spin I, will cause a level with angular momentum J to split into different energy levels denoted by the total angular momentum F (F=I+J), according to the Casimir formula [11],... 

Of the NMR-active nuclei around three-quarters have / > 1 so that the quadrupole interaction can affect their spectra. The quadrupole inter action can be significant relative to the Zeeman splitting. The splitting of the energy levels by the quadrupole interaction alone gives rise to pure nuclear quadrupole resonance (NQR) spectroscopy. This chapter will only deal with the case when the quadrupole interaction can be regarded as simply a perturbation of the Zeeman levels. 

Next, consider the energy levels of a spin-3/2 nucleus in a single crystal in the presence of an applied magnetic field and an electric field gradient so that the perturbation provided by the quadrupole interaction with the applied EFG is small a first order perturbation. We already considered this case in II.D.l. where we saw that the quadrupole interaction split the single line into three by shifting the 3/2<- l/2 and the -3/2 ->-1/2 lines in opposite directions. We state without... 

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