The dynamics of a crystal containing a rigid, isolated substitutional molecular impurity is discussed using the Green’s function method. The dynamical matrix for the problem is set up, and the various constraints on the force constants are pointed out. The application of the matrix partitioning technique is then indicated, and the possibility of a resonance mode arising from molecular librations is pointed out. Comparison is made with the earlier work of Wagner, and finally the relevance of the present formalism to the interpretation of a recent neutron scattering experiment is discussed.

The dynamics of a crystal containing a molecular impurity is discussed with allowance for the effects of internal vibrations of the molecule. Cartesian co-ordinates are introduced to describe internal vibrations, angular oscillations and centre of mass motions of the impurity, and the displacements of the atoms of the host crystal. Next the Hamiltonian is set up and the equations of motion derived. In this process, use is made of Dirac brackets when dealing with coordinates having redundancy and constraints. From the dynamical matrix, some of the familiar results of the crystal-field approximation are recovered. The application of the partitioning technique is then discussed, and finally comparison is made with results of other approaches.

A telescope of area 4 m², consisting of horizontal layers of plastic scintillators, neon flash tubes and absorbers was operated at a depth of 754 hg/cm² in the Kolar Gold Mines. New values for the vertical intensities of muons have been obtained from observations of the angular distribution over the slant depths ∼ 750–2300 hg/cm² and are compared with the existing measurements. From the angular distribution observed, we conclude that muons are produced wholly through the decay of pions and kaons up to energies of the order of 1 TeV. A value of 0.3±0.2 is estimated for theK/π ratio at production, for muon energies around 500 GeV. A decoherence distribution has been obtained for parallel muon events up to distances of the order of 10 m. From this we conclude that the averageP_t of the parents of muons of energy ∼ 250 GeV is of the order of 0.3 GeV/c. From an analysis of rock showers, we obtain the cross section for inelastic interaction of muons of mean energy 100 GeV as (3.8±1.5)×10⁻³⁰ cm²/nucleon.

The reaction matrix elements needed to study the ground state properties of normal liquid Helium 3 are obtained by a matrix inversion method in momentum space within the Brueckner-Goldstone formalism. Fully self-consistent calculations of the hole-line potential and the two-body interaction energies are performed with self-consistent occupation probabilities for Frost-Musulin potential.