  Context: Observation of Balmer lines from the region around the forward shock
of supernova remnants may provide precious information on the shock dynamics
and on the efficiency of particle acceleration at the shock.
  Aims: We calculate the Balmer line emission and the shape of the broad Balmer
line for parameter values suitable for SNR 0509-67.5, as a function of the
cosmic ray acceleration efficiency and of the level of thermal equilibration
between electrons and protons behind the shock. This calculation aims at using
the width of the broad Balmer line emission to infer the cosmic ray
acceleration efficiency in this remnant.
  Methods: We use the recently developed non-linear theory of diffusive shock
acceleration in the presence of neutrals. The semi-analytical approach that we
developed includes a description of magnetic field amplification as due to
resonant streaming instability, the dynamical reaction of both accelerated
particles and turbulent magnetic field on the shock, and all channels of
interaction between neutral atoms and background plasma that change the shock
dynamics.
  Results: We achieve a quantitative assessment of the CR acceleration
efficiency in SNR 0509-67.5 as a function of the shock velocity and different
levels of electron-proton thermalization in the shock region. If the shock
moves faster than ~4500 km/s, one can conclude that particle acceleration must
be taking place with efficiency of several tens of percent. For lower shock
velocity the evidence for particle acceleration becomes less clear because of
the uncertainty in the electron-ion equilibration downstream. We also discuss
the role of future measurements of the narrow Balmer line.
