The rotational spectral lines of c-C _ { 3 } H _ { 2 } and two kinds of the ^ { 13 } C isotopic species , c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } ( C _ { 2 v } symmetry ) and c- \mathrm { CC ^ { 13 } CH _ { 2 } } ( C _ { s } symmetry ) have been observed in the 1–3 mm band toward the low-mass star-forming region L1527 .
We have detected 7 , 3 , and 6 lines of c-C _ { 3 } H _ { 2 } , c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } , and c- \mathrm { CC ^ { 13 } CH _ { 2 } } , respectively , with the Nobeyama 45 m telescope , and 34 , 6 , and 13 lines , respectively , with the IRAM 30 m telescope , where 7 , 2 , and 2 transitions , respectively , are observed with the both telescopes .
With these data , we have evaluated the column densities of the normal and ^ { 13 } C isotopic species .
The [ c-C _ { 3 } H _ { 2 } ] / [ c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } ] ratio is determined to be 310 \pm 80 , while the [ c-C _ { 3 } H _ { 2 } ] / [ c- \mathrm { CC ^ { 13 } CH _ { 2 } } ] ratio is determined to be 61 \pm 11 .
The [ c-C _ { 3 } H _ { 2 } ] / [ c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } ] and [ c-C _ { 3 } H _ { 2 } ] / [ c- \mathrm { CC ^ { 13 } CH _ { 2 } } ] ratios expected from the elemental ^ { 12 } C/ ^ { 13 } C ratio are 60–70 and 30–35 , respectively , where the latter takes into account the statistical factor of 2 for the two equivalent carbon atoms in c-C _ { 3 } H _ { 2 } .
Hence , this observation further confirms the dilution of the ^ { 13 } C species in carbon-chain molecules and their related molecules , which are thought to originate from the dilution of ^ { 13 } C ^ { + } in the gas-phase C ^ { + } due to the isotope exchange reaction : ^ { 13 } \mathrm { C } ^ { + } + \mathrm { CO } \rightarrow { } ^ { 13 } \mathrm { CO } + \mathrm { C } ^ { + } .
Moreover , the abundances of the two ^ { 13 } C isotopic species are different from each other .
The ratio of c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } species relative to c- \mathrm { CC ^ { 13 } CH _ { 2 } } is determined to be 0.20 \pm 0.05 .
If ^ { 13 } C were randomly substituted for the three carbon atoms , the [ c- \mathrm { { } ^ { 13 } CCCH _ { 2 } } ] / [ c- \mathrm { CC ^ { 13 } CH _ { 2 } } ] ratio would be 0.5 .
Hence , the observed ratio indicates that c- \mathrm { CC ^ { 13 } CH _ { 2 } } exists more favorably .
Possible origins of the different abundances are discussed .