We have performed C ^ { 18 } O ( J =1–0 ) mapping observations of a 20 ^ { \prime } \times 20 ^ { \prime } area of the OMC-1 region in the Orion A cloud .
We identified 65 C ^ { 18 } O cores , which have mean radius , velocity width in FWHM , and LTE mass of 0.18 \pm 0.03 pc , 0.40 \pm 0.15 km s ^ { -1 } , and 7.2 \pm 4.5 M _ { \odot } , respectively .
All the cores are most likely to be gravitationally bound by considering the uncertainty in the C ^ { 18 } O abundance .
We derived a C ^ { 18 } O core mass function , which shows a power-law-like behavior above 5 M _ { \odot } .
The best-fit power-law index of -2.3 \pm 0.3 is consistent with those of the dense core mass functions and the stellar initial mass function ( IMF ) previously derived in the OMC-1 region .
This agreement strongly suggests that the power-law form of the IMF has been already determined at the density of \sim 10 ^ { 3 } cm ^ { -3 } , traced by the C ^ { 18 } O ( J =1–0 ) line .
Consequently , we propose that the origin of the IMF should be searched in tenuous cloud structures with densities of less than 10 ^ { 3 } cm ^ { -3 } .