We present the results of $^{12}$CO($J$=1-0) and $^{13}$CO($J$=1-0) simultaneous mappings toward the nearby barred spiral galaxy NGC 4303 as a part of the CO Multi-line Imaging of Nearby Galaxies (COMING) project. Barred spiral galaxies often show lower star-formation efficiency (SFE) in their bar region compared to the spiral arms. In this paper, we examine the relation between the SFEs and the volume densities of molecular gas $n(rm{H}_2)$ in the eight different regions within the galactic disk with CO data combined with archival far-ultraviolet and 24 $mu$m data. We confirmed that SFE in the bar region is lower by 39% than that in the spiral arms. Moreover, velocity-alignment stacking analysis was performed for the spectra in the individual regions. The integrated intensity ratios of $^{12}$CO to $^{13}$CO ($R_{12/13}$) range from 10 to 17 as the results of stacking. Fixing a kinetic temperature of molecular gas, $n(rm{H}_2)$ was derived from $R_{12/13}$ via non-local thermodynamic equilibrium (non-LTE) analysis. The density $n(rm{H}_2)$ in the bar is lower by 31-37% than that in the arms and there is a rather tight positive correlation between SFEs and $n(rm{H}_2)$, with a correlation coefficient of $sim 0.8$. Furthermore, we found a dependence of $n(rm{H}_2)$ on the velocity dispersion of inter-molecular clouds ($Delta V/ sin i$). Specifically, $n(rm{H}_2)$ increases as $Delta V/ sin i$ increases when $Delta V/ sin i < 100$ km s$^{-1}$. On the other hand, $n(rm{H}_2)$ decreases as $Delta V/ sin i$ increases when $Delta V/ sin i > 100$ km s$^{-1}$. These relations indicate that the variations of SFE could be caused by the volume densities of molecular gas, and the volume densities could be governed by the dynamical influence such as cloud-cloud collisions, shear and enhanced inner-cloud turbulence.
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