Pseudopotential is used as a formal operator to write the exact time-dependence of a pseudoexciton and hence that of an initial excitation spatially localized in a crystal. The exponential operator where pseudopotential occurs at the argument is readily evaluated using the property of projection operators. Migration of an initially localized excitation is of considerable experimental importance and can be of conceptual use since it should eventually generate the characteristics of a migrating exciton. From the formal time-dependence of a localized excitation, its spread with time can be calculated with relative ease. In a concurrent discussion, the previous work of Merrifield (1958) on the propagation of excitation is criticized and an error is pointed out. The spread, however, remains wavelike and is not dissipative in the absence of a collisional mechanism.

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr₀. It is observed from the behaviour ofr₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E_exp−E_cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.

TheL shell x-ray intensity ratios have been measured for the elements Ta and W by photoionization ofL shell electrons in the photon energy region 14⩽E⩽44 keV. The experimental results are compared with those calculated at the photon energies used in the present measurements. The measured values show fairly good agreement with the calculated values within the experimental uncertainties.

L-shell photoelectric cross-sections have been measured at 6 keV for eight elements in the range 40⩽Z⩽53. The measurements agree with theoretical calculations.

Dispersion relation for plasma waves in the presence of magnetic monopoles of electron mass and electron charge, is derived. It is shown that magnetic monopole charges, in general, dominate the dispersion. When monopoles form a fraction of the main body of plasma, there are two dominant oscillations. It is suggested that there can be electromagnetic emissions at these frequencies by nonlinear conversions. Possible application to the pulsar neighbourhood is envisaged.

A model of the proton with its constituent quarks bound in a colour polarizable medium with dielectric constant varying as (a/r−b²) from a fixed centre, is presented. The Dirac equation modified by the colour polarization is solved and the analytic expression for the wavefunction of the quarks obtained shows that quarks with higher energy lie closer to the fixed centre. The energy spectrum is equispaced without any continuum. A semiclassical approximation scheme yields closed orbits for quarks which have smaller size for higher energies and no orbits with size bigger than a certain maximum, thereby rendering the quarks permanently confined. The wavefunctions of the three quarks constituting the proton are used to calculate physical parameters of the proton such as its mass, charge radius and weak coupling constant which with suitable choice of the constantsa andb appearing in the dielectric constant agree fairly well with experimental results.

The existence of a ‘hole’ in the local field distributionP(H) in canonical spin glasses is proved in the framework of Mookerjee and Chowdhury’s percolation model of spin glass transition.

The nonlinear differential equation resulting from the use of the ’t Hooft-Corrigan-Fairlie-Wilczek ansatz in SU(2) Yang-Mills gauge theory is solved by the bilinear operator method. The solutions which are singular are interpreted as fluctuations involving no flux transport. However, these objects may play a tunnelling role similar to that of merons.

The presence of a continuum bound state for the nucleon-nucleon (nn) scattering by a nonlocal potential in which Yamaguchi potential enters as an attractive part is examined. It is well-known that an extra node in the radial wave function is directly related to the existence of a continuum bound state in the scattering spectrum. The extra nodes of the wave functions occur in conjunction with the zeros of the Fredholm determinants associated with the physical and regular wave functions of the radial equation for the nonlocal potential. Here we have observed that the extra nodes also occur in conjunction with the zeros of the transition matrix.