  Measurements of the cross section for exclusive virtual-photoproduction of
rho^0 mesons from hydrogen are reported. The data were collected by the HERMES
experiment using 27.5 GeV positrons incident on a hydrogen gas target in the
HERA storage ring. The invariant mass W of the photon-nucleon system ranges
from 4.0 to 6.0 GeV, while the negative squared four-momentum Q^2 of the
virtual photon varies from 0.7 to 5.0 GeV^2. The present data together with
most of the previous data at W > 4 GeV are well described by a model that
infers the W-dependence of the cross section from the dependence on the Bjorken
scaling variable x of the unpolarized structure function for deep-inelastic
scattering. In addition, a model calculation based on Off-Forward Parton
Distributions gives a fairly good account of the longitudinal component of the
rho^0 production cross section for Q^2 > 2 GeV^2.
