The angular distribution of γ-radiation from an assembly of nuclei oriented by the magnetic h.f.s. method can be very much modified by interactions between the radioactive ions and other paramagnetic ions in the crystal. In order to calculate the effect of these interactions, an operator Γ is derived which represents the angular distribution of γ-rays from a radioactive nucleus. The angular distribution at any temperature is given by Spur(Γρ), where ρ is the statistical matrix [Formula: see text], [Formula: see text] being the Hamiltonian for the whole crystal. For a high temperature approximation, ρ is expanded in powers of 1/T. It is found that, for alignment by the magnetic h.f.s. method, the first term which contains interaction parameters is that in 1/T4, and an expression is given for the contribution of interactions to this term.At very low temperatures, perturbation theory is used to estimate the effect of interactions on the lowest nuclear energy state, and hence on the angular distribution of γ-rays. It is found that, if an external magnetic field is applied along a principal axis of the g-tensor of the radioactive ions, interactions have no influence on the angular distribution of γ-rays in the limit of large fields. It is also shown that Bleaney's restriction, that for a successful nuclear orientation experiment the broadening of the levels should be less than the hyperfine splitting, is not necessary in this case.
Expanding commodity frontiers and the emergence of customary land markets: A case study of tree-crop farming in Venda, South Africa
