Line shape function nucleus

Recently, the stochastic models for the Mossbauer line shape problem have been discussed by several investigators.20 Such models can be treated in a systematic way as we have described in the above. For example, in a 57Fe nucleus, the spin in the excited state is / = and that in the ground state is / = i, so that the Hamiltonian is a 6 x 6 matrix. If a two-state-jump model is adopted, the dimension of the matrix equation, Eq. (63), is 6 x 2 = 12. If the stochastic operator is of the type (26), then the equation is a set of six differential equations. These equations can be solved, if necessary, by computers to yield the line shape functions for various values of parameters. 

Fig. 3. Line shape function of the central transition of a quadrupole nucleus with a half-integer nuclear spin, calculated for /Jq=0 in the limiting case of rapid magic angle spinning assuming that the electric quadrupole interaction is the dominating line broadening interaction...

As was discussed qualitatively in Section II,A,2, the local magnetic fields produced at a nucleus in a solid by the magnetic dipole moments of nuclei around it are often responsible for the observed line widths. Van Vleck (73) has derived, in a rigorous manner, an expression for the second moment of the absorption curve of the nuclei in terms of the magnetic moments, spins, and internuclear distances of the nuclei. The second moment ((AH )) of the shape function g(H — Ho) normalized to unit area is... 

Figure 3 (A) Powder pattern line shape of an I nucleus coupled to a quadrupolar (S= 1) nucleus when fe/vos) = 1, J so = 0. The frequency axis is in units of the dipolar coupling constant D. (B) Frequencies (in units of D) of the three lines expected for an l,S pair S= 1) as a function of the ratio / os- The line positions marked with symbols have been obtained by full-matrix Hamiltonian calculations. The solid lines are the values given by Equation [6].

Figure 6.5 Simulated static-powder (left column) and MAS (right column Vr = 1500 Hz) spectra for a spin / = 1/2 nucleus influenced only by the CSA interaction for the Larmor frequency Vi = 79.43 MHz (i.e. Si at 9.4 T) and 6 so = 0.0 ppm, illustrating the variation in line shape/spinning sideband intensities as a function of the CSA parameters, and...

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