  Being one of the most abundant atomic/molecular species observed in dense
molecular gas, atomic carbon ($\mathrm{C}^0$) is a potential good tracer of
molecular gas mass in many chemical/physical environments, though the
$\mathrm{C^0}$ abundance variation outside the Galactic disk region is yet to
be fully known. This paper presents a wide-field 500 GHz [CI] map of the
Galactic central molecular zone (CMZ) obtained with the ASTE 10-m telescope.
Principal component analysis and non-LTE multi-transition analysis have shown
that the [CI] emission predominantly originates from the low-excitation gas
component with a 20-50 K temperature and $\sim 10^3\ \mathrm{cm}^{-3}$ density,
whereas $\mathrm{C^0}$ abundance is likely suppressed in the high-excitation
gas component. The average $N(\mathrm{C}^0)$/$N(\mathrm{CO})$ abundance ratio
in the CMZ is 0.3-0.4, which is 2-3 times that in the Galactic disk. The
$N(\mathrm{C}^0)$/$N(\mathrm{CO})$ ratio increases to 0.7 in the innermost 10
pc region and to $\sim2$ in the circumnuclear disk. We discovered
$\mathrm{C^0}$-rich regions distributed in a ring-shape encircling the
supernova remnant (SNR) Sgr A east, indicative that the
$\mathrm{C}^0$-enrichment in the central 10 pc region is a consequence of a
molecular cloud-SNR interaction. In the 15 atom/molecules included in principal
component analysis (PCA), CN is the only other species that increases in the
[CI]-bright ring. The origin of the [CI]-bright ring is likely a cosmic-ray
dominated region created by low-energy cosmic-ray particles accelerated by Sgr
A east or primitive molecular gas collected by the SNR in which the
$\mathrm{C}^0$-to-CO conversion has not reached the equilibrium.
