  We present a study of the density structure of the protostellar collapse
candidate B335 using continuum observations from the IRAM Plateau de Bure
Interferometer made at wavelengths of 1.2mm and 3.0mm. We analyze these data,
which probe spatial scales from 5000 AU to 500 AU, directly in the visibility
domain by comparison to synthetic observations constructed from models that
assume different physical conditions. This approach allows for much more
stringent constraints to be derived from the data than from analysis of images.
A single radial power law in density provides a good description of the data,
with best fit power law index p=1.65+/-0.05. Through simulations, we quantify
the sensitivity of this result to various model uncertainties, including
assumptions of temperature distribution, outer boundary, dust opacity spectral
index, and an unresolved central component. The largest uncertainty comes from
the unknown presence of a centralized point source. A point source with 1.2mm
flux of F=12+/-7 mJy reduces the density index to p=1.47+/-0.07. The remaining
sources of systematic uncertainty, the most important of which is the
temperature distribution, likely contribute a total uncertainty of < 0.2. We
therefore find strong evidence that the power law index of the density
distribution within 5000 AU is significantly less than the value at larger
radii, close to 2.0 from previous studies of dust emission and extinction.
These results conform well to the generic paradigm of isolated, low-mass star
formation which predicts a power law density index close to p=1.5 for an inner
region of gravitational free fall onto the protostar.
