Effect of interatomic electron correlation has been studied in narrow band solids using one-particle Green function method. We follow Hubbard in drawing an analogy with an alloy and find a self-consistent solution which predicts a finite lifetime for pseudoparticles. A specific case of a (non-magnetic) model system with half-filled parabolic band has been considered to calculate the pseudoparticle density of states function. Unlike the result in the presence of intra-atomic correlations alone, we find that this particular system is never an insulator, however large intra-atomic correlations may be.

Some of the cluster extensions of the coherent potential approximation (CPA) based on the effective medium theory have been critically studied with respect to the decoupling schemes involved in them. Their computational tractability has been examined and it has been found that theself-consistent calculations in three-dimensional systems are immensely difficult to perform. A self-consistent calculation has been reported for simple cubic lattices with diagonal and off-diagonal disorder using a pair-CPA method. A significant finding of the paper is that it has been shown thatnon-analyticities are a general feature of extensions of CPA within multiple scattering framework. The non-analyticities were reported several times but a general proof of their existence was not noticed. It was also believed that the so-called molecular—CPA is analytic, this has been shown to be wrong here. The density of states results with off-diagonal randomness have been qualitatively understood to yield some information about the influence of off-diagonal randomness on Anderson localisation of an electron.

Magnetic susceptibility of mixed-valence compounds has been calculated as a function of pressure using Falicov-Kimball model wherein thef-s hybridisation has been taken into account. This model can very well explain the continuous as well as discontinuous transitions from ground states of integral to intermediate valence. Our results for magnetic susceptibility are in qualitative agreement with recent experimental results on some mixed-valence compounds.

It has been shown that an analysis of radial stationary state wave functions of a particle in terms of their loops leads to such continuous, single-valued and finite functions which represent a practically convenient form of the radial wave packets of that particle at various positions. The radial wave packets have been used to investigate target distortion in electron-atom collisions. The distortion of the target is defined in terms of quantum-mechanical probabilities given by the wave packets. A closed expression which depends upon the position of the colliding electron, is obtained for the potential energy of the target in the field of the colliding electron.

Possibility has been explored of periodic time variation of intensity (quanturn beats) of radiation emitted from relativistic electrons channeling along the 〈110〉 axis of a crystal of f.c.c. (diamond) lattice structure.

Poor beam collimation leads to overcompensation of suppression of coherent bremsstrahlung in the axial channelling case. This fact has been used to study the effect of beam divergence on the radiation emitted by relativistic (axially) channelled positrons. It has been found that due to beam divergence in the experiment of Alguard and co-workers in which radiation of 56 MeV positrons channelling along 〈110〉 rows of a silicon crystal is observed, coherent bremsstrahlung becomes an important contributing factor to the high frequency part of the observed spectrum.

Recently, angle-resolved photoemission spectroscopy measurements on Bi₂Sr₂CaCu₂O_8+δ, which possesses two CuO₂ layers in the same unit cell, have yielded very interesting results. For the overdoped samples, these results show a splitting of electronic states near k=(π, 0) point of Brillioun zone. On the other hand, no splitting is observed in the underdoped samples. In view of this, the detailed studies including the doping and temperature dependence of the spectral properties become desirable. In this paper, we consider cuprates possessing two CuO₂ layers per unit cell. Each layer in the system is described by the t-t¹-J model and the two layers are coupled via an intrabilayer hopping term (t_⊥) and an intrabilayer exchange coupling (J_⊥). A self-consistent perturbation approach is used to calculate the electronic spectral function for different values of hole density, hole momentum and temperature. We find that the imaginary part of the self energy is strongly momentum dependent which contradicts the suggestion that the Fermi surface of cuprates may be described by marginal Fermi liquid theory. We have calculated the spectral function for various values of intrabilayer parameters t_⊥ and J_⊥. For larger values of intrabilayer interactions we observe the splitting in the quasi-particle peak at k=(π, 0) which is in agreement with the recent observations. The splitting is also found to be sensitive to the hole concentration as well as the temperature of the system. We have also discussed the reasons why the splitting is absent in underdoped bilayer cuprates at low temperature.

In the present work, we report the interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high-T_c cuprate superconductors. For this we have considered a model Hamiltonian incorporating the intra-planar interactions and the contributions arising due to the coupling between the planes. The interplanar interactions include the single particle tunneling as well as the Josephson tunneling of Cooper pairs between the two layers. The expression of the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state is obtained within a Bardeen-Cooper-Schriefer (BCS) formalism using the Green’s function technique. This correlation is found to be sensitive to the various parameter of the model Hamiltonian. We have calculated the out-of-plane contribution to the superconducting condensation energy. The calculated values of condensation energy are in agreement with those obtained from the specific heat and the c-axis penetration depth measurements on bilayer cuprates.