  We present new observations of HCN and HCO+in the circumnuclear disk (CND) of
the Galaxy, obtained with the APEX telescope. We have mapped emission in
rotational lines of HCN J = 3-2, 4-3, and 8-7, as well as HCO+ J = 3-2, 4-3,
and 9-8. We also present spectra of H13CN and H13CO+ toward four positions in
the CND. Using the intensities of all of these lines, we present an excitation
analysis for each molecule using the non-LTE radiative transfer code RADEX. The
HCN line intensities toward the northern emission peak of the CND yield log
densities (cm^-3) of 5.6 +0.6/-0.6, consistent with those measured with HCO+,
as well as with densities recently reported for this region from an excitation
analysis of highly-excited lines of CO. These densities are too low for the gas
to be tidally stable. The HCN line intensities toward the CND's southern
emission peak yield log densities of 6.5 +0.5/-0.7, higher than densities
determined for this part of the CND with CO (although the densities measured
with HCO+, log [n] = 5.6 +0.2/-0.2, are more consistent with the CO-derived
densities). We investigate whether the higher densities we infer from HCN are
affected by mid-infrared radiative excitation of this molecule through its 14
micron rovibrational transitions. We find that radiative excitation is
important for at least one clump in the CND, where we additionally detect the J
= 4-3, v2=1 vibrationally-excited transition of HCN, which is excited by dust
temperatures of > 125-150 K. If this hot dust is present elsewhere in the CND,
it could lower our inferred densities, potentially bringing the HCN-derived
densities for the Southern part of the CND into agreement with those measured
using HCO+ and CO. Additional sensitive, high-resolution submillimeter
observations, as well as mid-infrared observations, would be useful to assess
the importance of the radiative excitation of HCN in this environment.
