The young A0V star HR 4796A is host to a bright and narrow ring of dust, thought to originate in collisions between planetesimals within a belt analogous to the Solar Systems Edgeworth-Kuiper belt. Here we present high spatial resolution 880$mu$m continuum images from the Atacama Large Millimeter Array. The 80au radius dust ring is resolved radially with a characteristic width of 10au, consistent with the narrow profile seen in scattered light. Our modelling consistently finds that the disk is also vertically resolved with a similar extent. However, this extent is less than the beam size, and a disk that is dynamically very cold (i.e. vertically thin) provides a better theoretical explanation for the narrow scattered light profile, so we remain cautious about this conclusion. We do not detect $^{12}$CO J=3-2 emission, concluding that unless the disk is dynamically cold the CO+CO$_2$ ice content of the planetesimals is of order a few percent or less. We consider the range of semi-major axes and masses of an interior planet supposed to cause the rings eccentricity, finding that such a planet should be more massive than Neptune and orbit beyond 40au. Independent of our ALMA observations, we note a conflict between mid-IR pericenter-glow and scattered light imaging interpretations, concluding that models where the spatial dust density and grain size vary around the ring should be explored.
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