A general analysis of bilinear algebras of creation and destruction operators is performed. Generalizing the earlier work on the single-parameterq-deformation of the Heisenberg algebra, we study two-parameter and four-parameter algebras. Two new forms of quantum statistics called orthofermi and orthobose statistics and aq-deformation interpolating between them have been found. In the Fock representation, quadratic relations among destruction operators, wherever they are allowed, are shown to follow from the bilinear algebra of creation and destruction operators. Postitivity of the Hilbert space for the four-parameter algebra has been studied in the two-particle sector, but for the two-parameter algebra, results are presented up to the four-particle sector.

On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional sextic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. The predicted results are in good agreement with known numerical values.

We present the full set of equations for the solution of the trinucleon problem by the hyperspherical harmonics expansion (HHE) method where nucleons interact via the Reid soft core (RSC) potential. The coupling potential matrix elements are expressed in terms of geometrical structure coefficients (GSC) and potential multipoles (PM). Introduction of GSC greatly simplifies the calculation of the potential matrix and makes the numerical algorithm efficient. A method for calculating all the twelve independent sets of GSC needed, by using the completeness property of the Jacobi polynomials has been presented. A convenient sum rule for each set of GSC has also been derived and precision of the calculated GSC has been checked by the sum rule. Such calculations of GSC are efficient and fast, in view of the complexity of the HHE equations.

A simple model for the adsorption of gas molecules on fractal surfaces is formulated. For surface reactions where adsorption is the rate determining step, considerations based on the probability of adsorption are sufficient to describe the kinetics. Different values of fractal dimension correspond to different values of rate constant for adsorption. A linear relationship between the dynamics and the geometric properties of a solid surface as well as a statistical mechanical relationship between internal partition functions of the gas molecule and the adsorption complex are obtained.

Some cosmological solutions for string model are derived in higher dimensional spherically symmetric space-time, following the techniques used by Letelier. The equations of state for strings have been used for different solutions. Also polynomial relation between the metric coefficients has been assumed in some cases.

The$$qq\bar q$$ model for inclusive processes is reformulated to consider the production of heavy flavours (c, b andt) and higher order flavour exchange effects. Predictions are made in terms of sum rules and inequalities for various inclusive cross-sections. Plausible parametrization of flavour symmetry breaking is also suggested.

Excitation function and mean projected recoil ranges of nuclei produced in theα-particle induced reactions on F, Al, V, Co and Re targets were measured by conventional thick target thick recoil catcher technique for bombarding energiesE_α≤65 MeV. The measured cross-sections are compared with calculations considering equilibrium as well as pre-equilibrium reaction mechanism according to the hybrid and geometry dependent hybrid (GDH) model of Blann using the code Alice/85/300. High energy part of the excitation functions are dominated by pre-equilibrium reaction mechanism whereas the low energy parts are dominated by evaporation with its characteristic peak. In this paper emphasis will be placed on the GDH model, for it provides a potentially better description of the physical process i.e., a higher probability of peripheral collisions to undergo precompound decay than for central collisions. Geometry dependent model with initial exciton numbern₀=4 (n_n=2,n_p=2,n_k=0) gives better fits compared to hybrid model with same initial exciton configuration andmfp parameterk=1.0 forα-induced reactions on F, V, Co and Re. Whereas forα-induced reaction on Al comparatively large initial exciton configurations (8/4/4/0) or (10/5/5/0) were required to fit the excitation functions reasonably well. Recoil ranges were converted into recoil momentum and vice versa using Lindhard, Scharff and Schiott (LSS) and Blaugrund theories. These theories were also used to calculate projected recoil ranges for full momentum transfer pertaining to fusion reactions. The momentum transfer information was used to get clues about some aspect of the interaction from the trends and magnitudes of the observed ranges.

Triple differential cross-sections for ionization of hydrogen atoms by electrons and positrons have been calculated for symmetric coplanar geometry following a multiple scattering method suggested and used earlier by the authors. Results show single binary peaks exactly at 45° and double binary peaks exactly at 135° for higher energies as are expected from an analysis of Briggs [3]. At lower energies there are certain deviations from these values. An analysis of scattering mechanism at peaks are also given. This supports Briggs’ explanation.