A simple parametric form for the static local field factor G(q) which appears in the dielectric screening theory of an electron gas is proposed. A very accurate fit of Ceperley-Alder data of electron correlation energy in the entire density range using Levin-Weniger interpolant is obtained and used for the calculation of G(q). Both the short-and longwavelength limits of G(q) are satisfied exactly in the present formulation which ensures fulfilment of a number of other legitimate criteria and produces some interesting results. A comparative study of the various static local field factors derived so far vis-a-vis the present work is made. Even within the approximations of a static self-consistent theory, reasonable prediction regarding Wigner Crystallization is obtained in the present work.PACS Number(s): 71.00, 71.45G * B. K. Girls' College,

Computation of reliable effective interionic pair interaction for simple metals has been discussed on the basis of localised ab initio pseudopotential within linear screening approximation. The influence of different commonly used screening functions on the shape of pair potential is examined and the temperature dependence of the interaction is also investigated. Various features of the potential are studied and compared with empirical and available first principle results. Importance of the present study and some related problems are also analysed.

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In the most general case, the calculation of the static local field factor G(q) for the unpolarised electron gas requires the knowledge of exchange--correlation energy functionals for both the parallel and antiparallel relative spin orientations of the electron gas system. Accurate density interpolation formulae using the quantum Monte Carlo data of Ceperley-Alder for the correlation energy of electron gas in both the "para" and "ferro" states, respectively, in the given density range are used for the calculation of G(q). Fulfilment of relevant consistency criteria is ensured and the local field factor so obtained renders significant improvement of ab initio pseudopotential calculation of effective interaction of Al. The Levin like interpolant of the correlation energy Ceperley-Alder data has been further used to study the ground state properties of the electron gas. It is also noted that a better understanding of the interacting electron gas properties requires a more accurate spin interpolation formula for the correlation energy than the existing ones.

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