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...

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present...

The Gross–Pitaevskii régime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii...

A re-examination has been made of the form and the role of equivalent operators which are used to represent the effects of intersite electron-electron interactions. The approach takes into account the relativistic character of both the interaction operator and the electronic wavefunctions. The...

In this paper we discuss the various approaches to the problem of off-diagonal operators in atomic and nuclear physics. Most of these approaches have been based on the Schwinger algebra. Here, we propose a different way of incorporating generators of transitions between configurations. This is a...

The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution...

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...