  Context. Observation of Balmer lines from the region around the forward shock
of supernova remnants (SNR) may provide valuable information on the shock
dynamics and the efficiency of particle acceleration at the shock.
  Aims. We calculated the Balmer line emission and the shape of the broad
Balmer line for parameter values suitable for SNR RCW 86 (G315.4-2.3) as a
function of the cosmic-ray (CR) 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 CR acceleration efficiency in this remnant.
  Methods. We used the recently developed nonlinear theory of diffusive
shock-acceleration in the presence of neutrals. The semianalytical approach we
developed includes a description of magnetic field amplification as due to
resonant streaming instability, the dynamical reaction of accelerated particles
and the turbulent magnetic field on the shock, and all channels of interaction
between neutral hydrogen atoms and background ions that are relevant for the
shock dynamics.
  Results. We derive the CR acceleration efficiency in the SNR RCW 86 from the
Balmer emission. Since our calculation used recent measurements of the shock
proper motion, the results depend on the assumed distance to Earth. For a
distance of 2 kpc the measured width of the broad Balmer line is compatible
with the absence of CR acceleration. For a distance of 2.5 kpc, which is a
widely used value in current literature, a CR acceleration efficiency of 5-30%
is obtained, depending upon the electron-ion equilibration and the ionization
fraction upstream of the shock. By combining information on Balmer emission
with the measured value of the downstream electron temperature, we constrain
the CR acceleration efficiency to be ~20%.
