Statistical Properties of Molecular Clumps in the Galactic Center 50 km s$^{-1}$ Molecular Cloud

We present the statistical properties of molecular clumps in the Galactic center 50 km s$^{-1}$ molecular cloud (GCM-0.02-0.07) based on observations of the CS $J=1-0$ emission line with the Nobeyama Millimeter Array. In the cloud, 37 molecular clumps with local thermal equilibrium (LTE) masses of $2\times10^2-6\times10^3 M_\odot$ were identified by using the {\it clumpfind} algorithm. The velocity widths of the molecular clumps are about five-fold those of Galactic disk molecular clouds with the same radius. The virial-theorem masses are three-fold the LTE masses. The mass and size spectra can be described by power laws of $dN/dM\propto M^{-2.6\pm0.1}$ ($M\gtrsim 900M_\odot$) and $dN/dR\propto R^{-5.9\pm0.3}$ ($R\gtrsim 0.35$ pc), respectively. The statistical properties of the region interacting with the Sgr A East shell and those of the non-interacting part of the cloud are significantly different. The interaction probably makes the mass function steeper, from $dN/dM\propto M^{-2.0\pm0.1}$ in the non-interacting part to $dN/dM\propto M^{-4.0\pm0.2}$ in the interacting region. On the other hand, the interaction presumably truncates the size spectrum on the larger side of $R\sim 0.4$ pc.