Explicit expression for the intensity tensor for 3/2-1/2 transitions and solution of the ambiguity problem in Moessbauer spectroscopy

Analytical expressions for the intensity tensor in the case of 3/2-1/2 nuclear transitions are obtained and the properties of the trace, symmetric and antisymmetric parts of the intensity tensor for a single transition are discussed. It is shown that in the principal axis system of the symmetric part of the intensity tensor the angular dependence of absorption of the circularly polarized resonant radiation depends essentially on only one parameter - the maximal degree of circular polarization. The latter parameter is directly connected with the antisymmetric part of the intensity tensor. It is shown that the so-called ambiguity problem, including the sign of the hyperfine magnetic field, can be solved by measuring the antisymmetric part using circularly polarized radiation. Some values typical in circular polarimetry can be measured in a standard experiment and vice versa. Explicit expressions for the line intensities of the powdered absorber are given in the general case of mixed transitions. The symmetry of the shape of the spectra with different signs of the electric field is explained. An experiment is proposed in which all parameters of the I=3/2 spin Hamiltonian can be unambiguously determined. (author)