Many-body statistical tensors for the nuclear-ordered state

Abstract

The problem of calculating statistical tensors rho qn(I) for the nuclear-ordered state in enhanced compounds such as HoVO4, PrNi5 etc., is examined within the framework of both a simple effective-field model and more sophisticated many-body theories, such as the RPA. It is shown that for simple ferromagnets and the anti-ferromagnets, a result, originally due to Callen and Shtrikman (1965), can be used to show that there is a one-to-one relationship between the rho qn(I) calculated using many-body Green function theories and the simple effective-field model. In addition a new recursion relationship is derived, linking statistical tensors of differing rank. This relationship holds for a wide class of renormalised collective excitation theories and is far more convenient to use in practice than either the moment-generating function of Callen (1963) or the methods of Tahir-Kheli and ter Haar (1962). Using first-order perturbation theory it is also shown that the Callen and Shtrikman result breaks down in the presence of a small axially symmetric quadrupole interaction. Thus it is unlikely that a simple check on the accuracy of 'simple effective-field statistical tensors' can be devised in the spirit of the Callen and Shtrikman result. Some comments are also made concerning the nuclear statistical tensors used to describe the gamma -ray emission patterns from the enhanced nuclear magnet HoVO/sub /(Allsop et al.).