In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

New experimental results to demonstrate that the annoying DC in the reconstructed wavefronts from in-line holograms could be successfully eliminated are presented in this paper. The complete elimination of DC has been achieved by making proper use of a Mach-Zehnder interferometer. The results for an in-line hololens and an in-line Fourier transform hologram are discussed.

The propagation of ion-acoustic K-dV solitary waves in weakly inhomogeneous, collisionless plasmas with gradients both in the density and the temperature of the ions has been considered. The electrons are assumed to be hot and isothermal, and the ions to be warm and adiabatic. The reductive perturbation analysis of the fluid equations is then carried out. The zero order quantities existing in the system due to the presence of the inhomogeneities are taken into account consistently and a set of ‘stretched coordinates’ appropriate for the inhomogeneous system is employed. A more general modified K-dV equation has been derived and its soliton solution is obtained explicitly. It is shown that as the soliton propagates along the temperature gradient, its amplitude and the velocity decrease, and the width increases. Further, it is found that when the two gradients are in opposite directions, the amplitude of the soliton remains constant.

Interaction of electromagnetic waves penetrating into anisotropic semi-infinite collisional plasma embedded in a uniform external magnetic field is studied using half range Fourier transforms. General field equations are developed for fractionally accommodating boundary and a particular case of specular reflection is discussed both for right handed as well as left handed circularly polarized modes. Anisotropy effects are found to be more prominent in the continuum mode of field component. Anisotropy as well as collisions make the field to attain a constant value at a shorter distance. Left handed polarized modes are found to be more penetrating than right handed modes. Surface impedance is calculated and effects of collisions as well as anisotropy are discussed.

The thermal instability of a finitely conducting hydromagnetic composite and compressible medium is studied to include the frictional effects with neutrals. The effect of compressibility is found to be stabilizing. In contrast to the nonoscillatory modes for (C_p/g)β > 1 in the absence of a magnetic field;C_v, β andg being specific heat at constant pressure, uniform adverse temperature gradient and acceleration due to gravity respectively, the presence of magnetic field introduces oscillatory modes in the system. The overstable case is also discussed. The magnetic field is found to have a stabilizing effect on the system for (C_p/g)β > 1.

A Bose type of classical Hamilton algebra, i.e., the algebra of the canonical formalism of classical mechanics, is represented on a linear space of functions of phase space variables. The symplectic metric of the phase space and possible algorithms of classical mechanics (which include the standard one) are derived. It is shown that to each of the classical algorithms there is a corresponding one in the phase space formulation of quantum mechanics.

A general method of obtaining wavefunctions for empirical diatomic molecular potential functions has been given. Efficacy of the method has been tested by computing Franck-Condon factors for some bands of a new system of SiO using Morse oscillator model and these have been compared with the ones obtained using exact Morse wavefunctions. It is concluded that the method is satisfactory at low quantum numbers.

The design and fabrication of an indigenous on-line computer controlled four-circle neutron diffractometer at the CIRUS reactor in Trombay are described. The diffractometer has an 18 in dia full-circle crystal-orienter which is sturdy enough to carry a cryostat. Three crystal orientation angles χ, φ and ω and the detector angle 2θ can be set to an accuracy of 0·01°. The four angle shafts are driven through precision worm-gears by SCR-controlled DC motors and their instantaneous positions sensed by optical digitizers. The diffractometer is interfaced to an ECIL TDC-312 computer system consisting of the CPU with 4K-memory, ASR-35 teletype, X-Y plotter and the digital input/output system (DIOS). The DIOS which operates under program control is a real-time peripheral device used to exchange information in digital form between the computer and the diffractometer. A software package consisting of over 40 useroriented teletype commands has been developed for on-line control and automatic data-acquisition.

Spectral shapes of bremsstrahlung were measured when³²P and⁴⁵Ca beta rays were absorbed in several elements Al, Cu, Sn and Pb of different thicknesses. While in aluminium, the experimental values and Bethe-Heitler theory agree for all thicknesses, in the case of the other elements an increase in the experimental value is observed which increases with Z of the target material and thickness of the target.

General expressions for the interlattice displacements of the A-15 structure compounds are obtained in terms of the strain components making use of the deformation theory. The nature of the interlattice displacements of all the 8 atoms in the unit cell is discussed. It is found that the interlattice displacements occur in such a way that the pair of atoms along any linear chain move in opposite directions with equal magnitudes. Expression for the strain energy of these compounds is developed using deformation theory and this is compared with the strain energy expression from continuum theory to obtain the elastic constants. The theoretical values of the elastic constants fairly agree with the experimental values for V₃ Si, V₃Ge and Nb₃ Sn.

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ_f/Γ_n)₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.

The total (α, n) reaction cross section for¹⁹F has been measured as a function of alpha energy in the energy range 2·6 to 5·1 MeV with a thin target. The excitation function exhibits a large number of resonances. The prominent amongst these for which theJ^π values are known have been analysed to extract the partial widthsΓ^α and Γ_n. Statistical analysis of the data in terms of strength function and average level spacing distribution has also been performed.