Coefficients of fractional parentage, which arise in the calculation of “crystal fields” in metals, have been calculated explicitly and compared with an earlier study where they were left undetermined but specific assumptions were made about them to reach conclusions about the “crystal...

The interaction of conduction electrons with host ions are shown to give rise to “crystal fields”, VC, which act on the magnetic ion in some dilute magnetic alloys. Crystal fields, VN, arising directly from ions neighbouring the magnetic ion have been compared with VC to show that the...

Application of the recently formulated theory of spin-correlated crystal fields is made to the Gd3+ ion in ethysulphate lattices. Detailed calculations of the spin-correlated crystal field contribution to the zero field splitting are found to be of the correct sign but its magnitude is too...

This paper revisits the fundamental statistical properties of the crucial model in critical phenomena i.e., the Ising model, guided by our knowledge of the energy values of the Ising Hamiltonian and aided by numerical estimation techniques. We have obtained exact energies in 2D and 3D and nearly...

Effective operators of the spin correlated crystal field have been derived using a second order perturbation mechanism which couples an exchange interaction with the crystal field. We have taken into account the effect of excited configurations involving np and np orbitals. Relativistic...

We consider a class of quantum many-body systems which are coupled by one- and two-body interactions. Following our earlier work on deriving nonlinear field equations of motion for such systems, we incorporate the effects of finite temperature through a semiclassical free energy functional. We...

A second quantised operator approach has been used to calculate formulae for one-body fractional parentage coefficients (fpc) for a system of many spinless bosons. A number of examples have been discussed and compared with some of those already calculated by a different technique when used to...

A method is described for calculating crystal fields for rare-earth ions in non-magnetic hosts. Screening is included by performing a Bohm-Pines-like unitary transformation on the starting Hamiltonian which contains kinetic-energy and Coulombic energies of electrons in the presence of fixed...

We develop a field theoretical formalism for describing the non-linear dynamics of interacting nuclear, atomic and molecular species. Specifically, four simple types of reaction are considered all of which involve up to two reactants and two products. The equations of motion for space- and...

The equivalent operator method has been extended and applied to anisotropic intersite electron-electron interactions between a central paramagnetic ion and its ligand neighbours. The relativistic character of both the interaction operator, in Breit-Pauli form, as well as the electronic...