The structure factor, pair distribution function, screened impurity potential, density of
screening charge, and exchange and screened exchange energies have been theoretically
investigated for a semiconductor quantum wire using an improved random phase
approximation that takes into account the local field corrections within the Hubbard
approximation. Our approach enabled us to obtain approximate analytical results on some
of the aspects and to greatly simplify the computation task on others. However,
computed results from our simple approach show very good agreement with those
obtained by performing cumbersome numerical solutions for the structure factor,
density–density response function and the static local field corrections, within the
Singwi–Tosi–Land–Sjölander approximation. Our investigations suggest that: (i) the
magnitude of the screened impurity potential and the average distribution of
electrons about an electron at larger distances are enhanced on reducing the width of
quantum wire, and (ii) the exchange interactions strengthen on narrowing the
quantum wire and on increasing the carrier density. Friedel oscillations are seen
in both our computed screened potential and the density of screening charge.