Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.

A general solution is obtained for the lattice dynamics of a cluster ofn-impurity atoms using the double-time Green’s function formalism. The cluster is characterized byn-mass defect andm-force constant change parameters. It is shown that this general solution for the Green’s function for then-impurity cluster can also be expressed in terms of the Green’s function for the (n−1)-impurity cluster. As an application, the cluster impurity modes for a pair are calculated using the Debye model for the host lattice dynamics. The splitting of the high frequency local modes and nearly zero frequency resonant modes due to pairs show an oscillatory behaviour on varying the distance of separation between the two impurity atoms. These oscillations are most prominent for two similar impurities and get damped for two dissimilar impurities or if one of the impurities produces a force constant change. The predictions of the calculation provide qualitative explanation of the data obtained from the infrared measurements of the resonant modes in mixed crystal system of KBr_1−c Cl_c: Li⁺ and KBr_1−c I_c: Li⁺.

Raman intensity analysis of LaCl₃ on lines adopted earlier for crystals like LiNO₃, KNO₃ or YVO₄ is found to be unsuitable for LaCl₃. The rotation of the LaCl₃ pyramids in the unit cell of this crystal is represented by high frequencies, comparable to the internal oscillations of LaCl₃ molecule. The intensity ofR_z, rotation about the symmetry axis of the crystal, is higher than the total symmetric line. These two factors show that the two molecules in the unit cell cannot be treated separately. Also, the polarisability of the bonds between atoms connecting the molecules cannot be neglected. The intensity formulae have been derived for this crystal and using the directional Raman spectra, electro-optical constants of the LaCl and Cl-Cl bonds have been evaluated. It is found that while the polarisability of Cl-Cl bond between the molecules, is about 0·4 times that of LaCl bonds, in crystals like LiNO₃ the polarisability of bonds like Li-O is found to be negligible.

X-ray and ultraviolet photoelectron spectroscopy have been employed to investigate the high temperature metal-insulator transitions in V₂O₃ and (V_0.99Cr_0.01)₂O₃. The high temperature transitions are associated with more gradual changes in the 3d bands compared to the low-temperature transitions.

Brightness waves due to sinusoidal excitations for ZnO:Nd electroluminor have been investigated for a temperature range 93°K to 363°K. During each cycle of excitation it consists of two primary waves each associated with a secondary wave, which grow and disappear twice in this temperature range. These results have been discussed in terms of existing models.

Electron spin resonance studies have been carried out on Cu²⁺ ion doped in single crystals of cadmium maleate dihydrate at 303 and 77K. It has been found that Cu²⁺ enters this lattice interstitially. The spin Hamiltonian parameters have been evaluated and the ground state wave function is found to be predominantly |X² −Y²〉 with a slight admixture of |3Z² −r²〉.

The interaction second virial coefficient of a binary polar-quadrupolar gas mixtures of non-spherical molecules of arbitrary symmetry has been calculated for a set of unlike force parameters which is obtained from the force parameters for like interactions by using empirical combination rules. In the calculation the influence of anisotropic interactions has been considered. The relative contribution of each branch of interactions has been evaluated as a function of temperature. The theoretical results have been compared with the experimental data of CH₃F + N₂, CH₃F + CO₂ and CH₃Cl + CS₂. The agreement between theory and experiment is satisfactory.

The low-lying collective bands of positive parity states in (fp) shell nuclei are described in the deformed Hartree-Fock method by projecting states of definite angular momenta from ‘the lowest energy intrinsic states in (sd)⁻¹ (fp)ⁿ⁺¹ configurations. The modified Kuo-Brown effective interaction for (fp) shell and modified surface delta interaction (MSDI) for a hole in (sd) shell with a particle in (fp) shell have been used.

The collective bands of states are in general well reproduced by the effective interactions. The excitation energies of the band head states are however off by about one MeV. The calculated magnetic moments of the band headj=3/2⁺ states are in reasonable agreement with experiment. Using effective chargese_p=1.33e ande_n=0.64e we get fairly good agreement forE(2) transitions. The hinderedM(1) transition strengths are reproduced to the correct order however they are slightly higher compared to experiment.