  Exclusive rho^0-meson electroproduction is studied in the HERMES experiment,
using a 27.6 GeV longitudinally polarized electron/positron beam and
unpolarized hydrogen and deuterium targets in the kinematic region 0.5 GeV^2 <
Q^2 < 7.0 GeV^2, 3.0 GeV < W < 6.3 GeV, and -t' < 0.4 GeV^2. Real and imaginary
parts of the ratios of the natural-parity-exchange helicity amplitudes T_{11}
(\gamma^*_T --> \rho_T), T_{01} (\gamma^*_T --> \rho_L), T_{10} (\gamma^*_L -->
\rho_T), and T_{1-1} (\gamma^*_{-T} -->\rho_T) to T_{00} (\gamma^*_L -->
\rho_L) are extracted from the data. For the unnatural-parity-exchange
amplitude U_{11}, the ratio |U_{11}/T_{00}| is obtained. The Q^2 and t'
dependences of these ratios are presented and compared with perturbative QCD
predictions.
