  Supernova remnants exhibit shock fronts (shells) that can accelerate charged
particles up to very high energies. In the past decade, measurements of a
handful of shell-type supernova remnants in very-high-energy gamma rays have
provided unique insights into the acceleration process. Among those objects,
RX$~$J1713.7-3946 (also known as G347.3-0.5) has the largest surface
brightness, allowing us in the past to perform the most comprehensive study of
morphology and spatially resolved spectra of any such very-high-energy
gamma-ray source. Here we present extensive new H.E.S.S. measurements of
RX$~$J1713.7-3946, almost doubling the observation time compared to our
previous publication. Combined with new improved analysis tools, the previous
sensitivity is more than doubled. The H.E.S.S. angular resolution of
$0.048^\circ$ ($0.036^\circ$ above 2 TeV) is unprecedented in gamma-ray
astronomy and probes physical scales of 0.8 (0.6) parsec at the remnant's
location.
  The new H.E.S.S. image of RX$~$J1713.7-3946 allows us to reveal clear
morphological differences between X-rays and gamma rays. In particular, for the
outer edge of the brightest shell region, we find the first ever indication for
particles in the process of leaving the acceleration shock region. By studying
the broadband energy spectrum, we furthermore extract properties of the parent
particle populations, providing new input to the discussion of the leptonic or
hadronic nature of the gamma-ray emission mechanism.
