  The Berezinskii-Kosterlitz-Thouless theory for superfluid films is
generalized in a straightforward way that (a) corrects for overlapping
vortex-antivortex pairs at high pair density and (b) utilizes a dielectric
approximation for the polarization of the vortex system and a local field
correction. Generalized Kosterlitz equations are derived, containing higher
order terms, which are compared with earlier predictions. These terms cause the
total pair density to remain finite for temperatures above the transition so
that it is not necessary to introduce an ad hoc cut-off, as opposed to the
original Berezinskii-Kosterlitz-Thouless theory. The low-temperature bound pair
phase is destabilized for small vortex core energy. The behaviour of the
stiffness constant and of the correlation length close to the transition is not
affected by the higher order terms. A first-order transition as suggested by
other authors is not found for any values of the parameters. The pair density
is calculated for temperatures below and above the transition. Possible
experiments and the applicability of the extended approach are discussed. The
approach is found to be applicable even in a significant temperature range
above the transition.
