We performed a search of star-forming sites influenced by external factors, such as SNRs, HII regions, and cloud-cloud collisions, to understand the star-forming activity in the Galactic center region using the NRO Galactic Center Survey in SiO $v=0, J=2-1$, H$^{13}$CO$^+ J=1-0$, and CS $J=1-0$ emission lines obtained by the Nobeyama 45-m telescope. We found a half-shell like feature (HSF) with a high integrated line intensity ratio of $ int T_{ mathrm B}$(SiO $v=0, J=2-1$)$dv$/$ int T_{ mathrm B}$(H$^{13}$CO$^+ J=1-0$)$dv sim6-8$ in the 50 km s$^{-1}$ molecular cloud, which is a most conspicuous molecular cloud in the region and harbors an active star-forming site seen as several compact HII regions. The high ratio in the HSF indicates that the cloud contains huge shocked molecular gas. The HSF is also seen as a half-shell feature in the position-velocity diagram. A hypothesis explaining the chemical and kinetic properties of the HSF is that the feature is originated by a cloud-cloud collision (CCC). We analyzed the CS $J=1-0$ emission line data obtained by Nobeyama Millimeter Array to reveal the relation between the HSF and the molecular cloud cores in the cloud. We made a cumulative core mass function (CMF) of the molecular cloud cores within the HSF. The CMF in the CCC region is not truncated at least up to $ sim2500M_ odot$ although the CMF of the non-CCC region reaches the upper limit of $ sim1500M_ odot$. Most massive molecular cores with $M_{ mathrm{gas}}>750 M_{ odot}$ are located only around the ridge of the HSF and adjoin the compact HII region. These may be a sign of massive star formation induced by CCC in the Galactic center region.
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