The recovery of cosmic ray Carbon nuclei of energy ~20-125 MeV/nuc in solar cycle #23 from 2004 to 2010 has been followed at three locations, near the Earth using ACE data and at V2 between 74-92 AU and also at V1 beyond the heliospheric termination shock at between 91-113 AU. To describe the observed intensity changes and to predict the absolute intensities measured at all three locations we have used a simple spherically symmetric (no drift) two-zone heliospheric transport model with specific values for the diffusion coefficient in both the inner and outer zones. The diffusion coefficient in the outer zone is determined to be ~5-10 times smaller than that in the inner zone out to 90 AU. For both V1 and V2 the calculated C nuclei intensities agree within an average of pm 10% with the observed intensities. Because of this agreement between V1 and V2 observations and predictions there is no need to invoke an asymmetrical squashed heliosphere or other effects to explain the V2 intensities relative to V1 as is the case for He nuclei. The combination of the diffusion parameters used in this model and the interstellar spectrum give an unusually low overall solar modulation parameter phi = 250 MV to describe the Carbon intensities observed at the Earth in 2009. At all times both the observed and calculated spectra are very closely ~ E1.0 as would be expected in the adiabatic energy loss regime of solar modulation.
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