Analytical lineshapes for integer spins

To deduce an analytical expression for this asymmetrical lineshape we define 

In their subsequent analysis Baker and Bleaney (ibidem) decided to ignore the last term on the assumption that gdl 3b hv. Although this is a reasonable approximation for lanthanide and actinide integer-spin ions doped in single crystals, it is not usually an acceptable assumption for the broad-line spectra from metalloproteins. Furthermore, the assumption of a A-distribution around zero (i.e., D 0 but all other zero-field interaction parameters are zero) is equally untenable for biomolecules. Therefore, we go for a later extension of the theory, based on a full Equation 12.9 and on (A) 0, for application to metalloproteins (Hagen 1982b). 

If the intradoublet splitting is distributed around a nonzero value A i.e., if a rhombic E-term and/or higher order cubic terms (cf. Section 8.1) are nonzero, then we have 

The signal is maximal for 0 = 0, and rotating B (and / ,) away from the molecular z-axis causes a rapid divergence of linewidth and intensity. Thus, the powder spectrum is obtained as the integral 

Inclusion of this factor in Equation 12.15 affords the normal-mode powder spectrum. 

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