Variational studies employing the basis functions of the quantal particle-in-a-box model are shown to lead to accurate estimates of eigenvalues, various expectation values and eigenfunctions of the stationary anharmonic oscillator problem. Calculations involve bothzx^2α and (x²⁺zx^2α)-type oscillators, withα=2, 3 and 4, both in weak and strong coupling regime. Apart from its recommendable computational simplicity, convergence of the present recipe has also been demonstrated to be quite fast. Results for the first ten states are reported. A few goodness tests for the approximate wavefunctions and consistency requirements for some properties are also performed.

We have simulated two-dimensional classical XY-model in a microcanonical ensemble using the Monte Carlo technique. Simulations were carried out on a square lattice having 25, 100 or 900-spins with periodic boundary conditions. The nearest neighbour interaction potential was taken to beV(θ)=2J[1−cos¹⁰⁰(θ/2)]. The system energy, mean square magnetization and vortex-density were calculated as functions of temperature. A sudden change in the system energy, vortex density and mean square magnetization was observed at the first-order transition which is associated with this choice of the nearest neighbour interaction potential. The transition temperature increases with decrease in the system size. It is found that the creation of a vortex-antivortex pair costs more energy during the first-order transition than the energy associated with a tightly bound vortex-antivortex pair.

Flavour symmetry breaking is introduced in the approximate formula for quark mass reported earlier. We use SLAC-MIT as well as NMC data to estimate the up, down and strange quark masses from structure functions. Using the approximateQ² evolutions of Altarelli-Parisi equations, we also estimate its perturbative and nonperturbative components.

Mass difference oft-flavored hadrons is calculated using bag model modified for considering heavy quarks inside the bag. Both electric and magnetic contributions to mass differences are evaluated without the assumption of degenerate intermediate state. Mass differences between up and down quarks inside the bag is taken to be a constant in the absence of a dynamical calculations for the same.

An expression for the density of single nucleons in a heavy spherical nucleus is derived using the shell-model and matrix ensembles. It is shown that the theoretical expression gives an excellent fit to the density of nucleons for the nucleus¹⁹⁷Au obtained usinge-scattering data.

Electron impact double ionization cross-sections for Ba and Ba⁺ have been calculated in the binary encounter approximation. Hartree-Fock velocity distribution has been used for the first ejected electron and a hydrogenic velocity distribution for the second. For Ba⁺ the focusing effects of the target ion on the incident electron have been incorporated in the calculations. Contributions from ionization-autoionization to the ionization cross-sections, as observed in experiments, have been included in the present work. The calculated results show structures as observed in recent experiments.

In this preliminary work, using a 3-state diabatic molecular expansion without any excited channels, we have studied within the semiclassical impact parameter approximation the single charge transfer process He²⁺+He(1s²)→He⁺(1s)+He⁺(1s). Our results agree very well with experiment, which demonstrates the usefulness of this type of diabatic molecular basis in doubly charged ion-atom collision systems.