The electronic band structure of f.c.c. phase of the rare earth metal cerium (α-cerium) has been calculated using a formulation of the crystal potential where correlation also has been included in addition to exchange. We use the prescription of Cohn and Sham as well as that of Overhauser. The Green’s function method of Korringa-Kohn and Rostoker has been used for obvious advantages in the calculation. The calculations indicate that the s—d bands are hybridized with the f-levels but the f-bands are fairly narrow and lie slightly above the Fermi level. The structure of the bands is qualitatively similar to those of calculations by others except for a general shift of the entire set of bands by about 0·1 Ryd. The density of states has been calculated from the bands obtained. The spin susceptibility ofα-cerium has also been calculated using the Kohn-Sham method. However, the calculated additional contributions to the band structure values cannot still explain the large experimental values reported in the literature.

From the computation of self-avoiding walks on the kagomé lattice, its connectivity constant is found to be 2·569 ± 0·008.

Energy bands of dysprosium have been calculated considering the effects of correlation and spin-polarisation. The exchange and correlation contributions to the spherically symmetric crystalline potential have been taken in the forms suggested by (i) Kohn and Sham and (ii) Overhauser. The exchange and correlation potential of von Barth and Hedin has been used to study the effect of spin-polarisation on the band structures. The resulting bandwidth, density of states, magnetic moment and spin-splitting have been computed and compared with experimental results. Some discrepancies remain; theoretical calculations done so far agree reasonably among themselves, so accurate experimental data are probably called for.

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.

A green shale from the Precambrian banded iron formation of the Bonai Range, Eastern India, is examined by transmission Mössbauer spectroscopy. The constituent phases are identified to be chlorite, siderite and magnetite. The fractional resonance area of each constituent is computed and the ferrous-ferric ratio determined. The variation of this ratio over the sample is examined. Intensity of the magnetite lines reveals that deviation from stoichiometry is negligible. The observations suggest a transition within short range from silicate-rich facies to carbonate-oxide-rich facies in the studied section.