Paramagnetic relaxation line shape in the Mössbauer spectroscopy of 1/2 → 3/2 transitions in axial symmetry

Hirst's theory for the line shape of Mössbauer spectra in the presence of paramagnetic relaxation phenomena is applied to the case of 1/2 → 3/2 transitions. A detailed procedure for obtaining the lineshape is given for the case of axial symmetry, including off-diagonal terms in the hyperfine Hamiltonian. This is applicable for example, to the 14.4-keV transition in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ or the 66.7-keV transition in ${}_{}{}^{171}{}_{}{}^{}\mathrm{Yb}$. The theory is used to analyze the data for ${}_{}{}^{171}{}_{}{}^{}\mathrm{Yb}$ in the cubic compound ${\mathrm{Cs}}_2$NaYb${\mathrm{Cl}}_6$. The hyperfine parameter $A=-38.7\mathrm{}\pm 2.0$ mm/sec and relaxation rate $W=185\mathrm{}\pm 24$ MHz are in good agreement with previous measurements utilizing the resonance of ${}_{}{}^{170}{}_{}{}^{}\mathrm{Yb}$ in this material.