The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating it by a sphere, by making use of simple coordinate axes transformations and lattice symmetry in the case of f.c.c. and b.c.c. structures. It is shown that there are several alternative ways of expressing the interference factor,S(q) and the different expressions given by Sharan and others and Bross and Bohn are just two of these equivalent expressions. By comparing these expressions in the symmetry directions with those obtained under spherical approximation their apparent differences are discussed.

The Pippard-Janovec relations are derived for correlating the anomalous elastic coefficient and the anomalous specific heat near the phase transitions of ferroelectric crystals. These relations are verified in the case of ferroelectric triglycine selenate crystal.

Coherent inelastic neutron scattering techniques are employed to measure several branches of the phoon dispersion relation in KNO₃ in its orthorhombic (α-phase or phase II) form at room temperature. Group theoretical selection rules for external modes of the crystal have been used in the measurements along the three symmetry directions Σ(ξ00), Δ(0ξ0) and Λ(00ξ).

Theoretical investigation of the lattice dynamics of the crystal is carried out on the basis of a rigid molecular-ion model using the external mode formalism. A two-body potential consisting of the Coulombic interaction and the Born-Mayer type short range interaction is assumed. The effective charges and radii of different atoms are determined by applying the stability criterion for the crystal. Dispersion curves are calculated, representation by representation, making use of group theoretical information. Comparison of theoretical results with experimental information on elastic constants, optical data and neutron results are made. Agreement between theoretical and the various experimental results may be considered very satisfactory.

The dielectric constant and loss tangent of BaTiO₈ with ZrO₂ additives have been studied. The loss tangent was less ranging between 0.16 for pure BaTiO₃ and 0.05 for samples containing 5% ZrO₂. The dielectric constant at Curie temperature decreased with increasing ZrO₂ concentration up to 0.4%. The volume resistivity measurements illustrate a peak value at a certain range of temperatures for each composition.

The signal-to-noise improvement ratio (SNIR) of a Box-Car averager is calculated for various noise sources such as random white noise, exponentially correlated noise, etc. For a time constant (RC), and a sampling time ε, the quoted value of SNIR as (2RC/ε)^1/2 is shown to be strictly correct only when the noise is white and deviation from this law is expected for other non-white noise sources. The validity of some of the calculated expressions is established by direct measurement of noise output.

By means of refinements in the modulated molecular beam technique the signal-to-noise ratio can be greatly improved, and differential cross-sections, for collision of molecuies of the same species, can be measured. This was accomplished by combining beam modulation and phase sensitive detection with very sharp turning on the front end of the lock-in-amplifier and long integration times on the output. In addition, the signal-to-noise ratio of the Ar-Ar system as a function of integration time was investigated using two different types of electron bombardment detectors an Aberth ion-source and a quadrupole mass filter. With an integration time of 40 min the estimated upper limit to the signal-to-noise ratio is 1500 to 1 for the Aberth ion-source. Using quadrupole mass filter with an integration time of 60 min the estimated upper limit to the signal-to-noise ratio is 5 × 10⁴ to 1. For chemical kinetics studies this ratio may be two orders of magnitude higher.

An initial value problem is set up to describe propagation of a low-frequency wave-field interacting with two almost transparent wave-fields in a dispersive medium. With no linear loss, perfect phase-matching, and equal group velocities for the two high-frequency wave-packets, it is shown how the solution of the above problem can evolve to well-known soliton solutions of the sine-Gordon equation. Other attempts for solving the more general problem in which all the group velocities are different are also discussed.

Multiparticle production data on proton-nucleus collisions have been analyzed taking the number of ‘created’ charged particles instead of the observed number of shower particles as the variable. The mean normalized multiplicity,R_A, has been found to be independent of energy in the energy range (7–8000) GeV and its mass number dependence has been obtained. The modified analysis introduces some more regularities in the experimental results onp-nucleus collisions like the invariance with respect to energy of the relationshipR_A = α + βN_h and the KNO-like scaling of the multiplicity distributions of the created charged particles. The functional form of the scaling function has been calculated.

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8)_w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ*₃⁺⁺ and Θ⁻ are also discussed. SU(8)_w symmetry predictsα$$(\Omega \bar k) = 0$$, which is consistent with the experimental value.

Recent experimental data on thermal conductivity and viscosity are used to calculate values of rotational collision numbers and diffusion coefficients for oxygen in the temperature range 400–1600 K.