A general mathematical formulation is developed for calculating the effective electron-electron interaction in layered crystals like YBa₂Cu₃O_7−δ, and for finding the resulting superconducting transition temperatureT_c in such systems within the framework of the conventional BCS pairing arising from various possible excitations in the medium. This differs considerably from the usual case of an effective three-dimensional homogeneous system, and should be relevant in the calculation ofT_c for the new class of high-T_c perovskites in which oxygen deficiencies in Cu-O layers and their distribution in the crystal play a crucial role. The explicit form of the effective interactionV_jj(q_t,ω) in a given layerj in the unit cell of the crystal is found to be determined not only by the true polarization functionπ_j(q_t,ω) of that layer, but also of other layers. The exchange of electronic excitations of a nearby insulating layer by carriers in a conducting layer thus becomes possible to get highT_c, with or without the usual phonon exchange.

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

Pion mass and its decay constant have been studied in a chiral symmetric potential model of independent quarks. The non-perturbative multi-gluon interaction which is responsible for quark confinement in a hadron is phenomenologically represented here by an effective potentialU(r) = 1/2(1 +γ⁰)(ar² +V₀). The residual interactions due to quark-pion coupling arising out of the chiral symmetry preservation and that due to quark-gluon coupling arising out of single-gluon exchange are treated as low order perturbations. The centre of mass correction is also taken into account appropriately. This leads to the$$(q\bar q) - pion$$ mass in consistency with that of the PCAC-pion and the pion decay constant in reasonable agreement with experiment.

In-beam nuclear spectroscopic studies of¹⁸²Re, following the reaction¹⁸¹Ta(α, 3n)¹⁸²Re have been made using gamma-ray and internal conversion electron techniques.K-conversion coefficients for several transitions have been measured and the multi-polarities of the various transitions assigned. In particular, the spin and parity of the four-quasi-particle isomeric level at 2256 keV were determined to be 16⁻. Theg-factor of this level has been measured to beg = 0·32 ± 0·05. On the basis of theg-factor and the decay pattern of this level, a configuration {v9/2⁺ [624↑]v7/2⁻ [514↓]v7/2⁻ [503↑]π9/2⁻ [514↑]}_k^x = 16⁻ has been assigned to this level. The nature of the retardation of the gamma transitions deexciting this level is discussed. It is argued that the measured retardation factors can be explained if the nucleus has a triaxial shape.

The high resolution (³He,α) reaction on²⁰⁶Pb shows the distribution of the 2f_7/2, 1h_9/2 and 1i_{1 3/2} neutron states of²⁰⁵Pb within the 6 MeV excitation energy of²⁰⁵Pb. The spectrum of these three-hole states is obtained within the hole-core vibrational coupling scheme. The shell model energies of the neutron hole states arising from the core-polarization effect are compared with the Bansal-French energy weighted sum rule. The possible implication of the present neutron hole energies has been discussed in the light of the deduced shell model wave functions of the collective states of²⁰⁶Pb.

The lattice parameters of CdF₂ andβ-PbF₂ have been determined over the temperature range 300–670 K. The coefficient of expansion at room temperature is 21·3 × 10⁻⁶ K⁻¹ and 25·4 × 10⁻⁶ K⁻¹ for CdF₂ and PbF₂ respectively and it increases linearly with temperature over the range of temperature covered. The Grüneisen parameter decreases with temperature in both the crystals.