As an improvement over the Hartree-Fock approximation, we investigate a Green’s Function method—theΣ perturbation method—for molecular calculations. The method is applied to hydrogen molecule and to theπ-electron system of ethylene under PPP approximation. When the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits.

We have applied the Krieger-James approximation to a description of short range order effects in both ferro- and antiferromagnetism. In this method, a mechanical consistency condition is imposed on the probability distribution of a pair of near neighbours in a cluster of (Z+1) ions. The resulting theory is analytically equivalent to the familiar constant coupling approximation, thus ensuring thermodynamic equilibrium of the system.

Integrated intensities of Bragg reflections of CdO, PbS and MnS have been measured at room temperature using an x-ray powder diffractometer. From a least square treatment of the intensity data the mean Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. Calculations were made using scattering factors pertaining to neutral atoms as well as doubly ionised ions. The results from the two sets of calculations agreed within limits of errors.

Various symmetry relations developed between neutrino-neutron and antineutrino-proton elastic scattering cross sections are surveyed and an identity between scattering amplitudes and a symmetry between cross sections of these processes established by consideringCPT andG conjugation invariance of current matrix elements. A symmetry is obtained giving rise to a theorem on the nature of contribution of form factors to terms in the cross sections.

Energy levels and electromagnetic transitions in⁶²Zn have been calculated using band-mixing formalism in the framework of deformed Hartree-Fock theory. Matrix elements of Adjusted-Surface Delta Interaction (ASDI) and of Tabakin interaction have been used. Detailed structure of various nuclear states in terms of bands has been discussed. Although the calculated spectra for both the interactions are somewhat compressed as compared to the observed spectra, the ASDI results are in substantially better agreement with experiments. Several additional states of high spin (J>4) have been predicted.B(E2) transitions between inter-band as well as some of the intraband states are calculated to stimulate further experiments.

The differential cross section for the reactionD(d, t)H has been calculated in the distorted wave Born approximation including finite range effects. All 6 interactions between the 4 nucleons are explicitly evaluated. It has been found that the interactions neglected by earlier work are significant. Distortions are necessary to reproduce the minimum at 37.5° observed at an incident energy of 25.3 MeV in the cross section. The absolute cross section at 14.3° is predicted by theory to be 23.5 mb/sr as against the experimental 16.4 mb/sr. Better agreement with experiment at backward angles may be obtained with the use of an expanded deuteron and the inclusion ofd-state effects.

Collective bands of the positive parity states in odd-A f_7/2 shell nuclei are described in the framework of deformed Hartree-Fock theory by projecting states from lowest energy intrinsic states with (d₃^2/−1f₇^2/n+1) one hole configurations. In the calculation empirical (d_3/2 −f_7/2)² effective matrix elements have been used to test the tacit assumptions of the Bansal and French model.

Measurement of magnetic susceptibility of the powder samples of heavy rare-earth (Tb, Dy, Ho, Er, Tm and Yb) sesquioxides have been reported in the temperature range 300 to 900 K. Curie-Weiss law behaviour has been observed for all samples. The Curie constant, the paramagnetic Curie temperature and the magneton number for magnetic ions in each material have also been evaluated.

Using the Green function method of lattice statics, the lattice distortion in the neighborhood of a vacancy in magnesium has been calculated in three different axially-symmetric (AS) host lattice models and also in a model derived from an empirical interatomic pair potential. The variations in the lattice distortion and the relaxation energy of the vacancy are studied as the size of the defect space is allowed to vary from two to four surrounding neighbors. The perfect static lattice Green functions are computed up to 19 neighbors in the 4 models and the values obtained are shown to be not very sensitive to the model chosen. The lattice relaxation is found to be negligible in all models except in a four-neighbor AS model. The relaxation energies in these four models are computed to be 0.0027 eV, 0.034 eV, 0.28 eV and 0.0069 eV respectively. Results for the monovacancy formation energy, the elastic dipole tensor and the volume change of the crystal due to the vacancy are also presented.

Approximate analytic solutions to the self similar equations of gas dynamics for a plasma, treated as an ideal gas with specific heat ratioγ = 5/3, are obtained for the implosion and subsequent reflection of various types of shock sequences in spherical and cylindrical geometries. This is based on the lowest-order polynomial approximation, in the reduced fluid velocity, for a suitable nonlinear function of the sound velocity and the fluid velocity. However, the method developed here is powerful enough to be extended analytically to higher order polynomial approximations, to obtain successive approximations to the exact self-similar solutions. Also obtained, for the first time, are exact asymptotic solutions, in analytic form, for the reflected shocks. Criteria are given that may enable one to make a choice between the two geometries for maximising compression or temperature of the gas. These solutions should be useful in the study of inertial confinement of a plasma.

The nonlinear Schrödinger equation describing the evolution of the plane wave solutions of the Hirota equation and of the Boussinesq equation are obtained. The conditions for modulational instability and the localised stationary solutions are derived.