We have made the first detection of circumstellar absorption lines of the ^ { 12 } C ^ { 13 } C { A } ^ { 1 } \Pi _ { u } - { X } ^ { 1 } \Sigma _ { g } ^ { + } ( Phillips ) system 1-0 band and the ^ { 12 } C ^ { 16 } O { X } ^ { 1 } \Sigma ^ { + } first-overtone 2-0 band in the spectrum of the post-AGB star HD 56126 ( IRAS 07134+1005 ) .
All current detections of circumstellar molecular absorption lines towards HD 56126 ( ^ { 12 } C _ { 2 } , ^ { 12 } C ^ { 13 } C , ^ { 12 } C ^ { 14 } N , ^ { 13 } C ^ { 14 } N , and ^ { 12 } C ^ { 16 } O ) yield the same heliocentric velocity of v _ { CSE } = 77.6 \pm 0.4 km s ^ { -1 } .
The ^ { 12 } C _ { 2 } , ^ { 12 } C ^ { 13 } C , and ^ { 12 } C ^ { 16 } O lines give rotational temperatures and integrated column densities of T _ { rot } = 328 \pm 37 K , \log N _ { int } = 15.34 \pm 0.10 cm ^ { -2 } , T _ { rot } = 256 \pm 30 K , \log N _ { int } = 13.79 \pm 0.12 cm ^ { -2 } , and T _ { rot } = 51 \pm 37 K , \log N _ { int } = 18.12 \pm 0.13 cm ^ { -2 } respectively .
The rotational temperatures are lower for molecules with a higher permanent dipole moment .
Derived relative column densities ratios are ^ { 12 } C _ { 2 } / ^ { 12 } C ^ { 13 } C = 36 \pm 13 , and ^ { 12 } C ^ { 16 } O/ ( ^ { 12 } C _ { 2 } + ^ { 12 } C ^ { 13 } C ) = 606 \pm 230 .
Combined with data from Paper III we find relative column densities of ^ { 12 } C ^ { 16 } O/ ( ^ { 12 } C ^ { 14 } N+ ^ { 13 } C ^ { 14 } N ) = 475 \pm 175 and ^ { 12 } C ^ { 14 } N/ ^ { 13 } C ^ { 14 } N = 38 \pm 2 .

Under chemical equilibrium conditions , ^ { 12 } C ^ { 13 } C is formed twice as easily as ^ { 12 } C _ { 2 } .
The isotopic exchange reaction for ^ { 12 } C _ { 2 } is too slow to significantly alter the ^ { 12 } C _ { 2 } / ^ { 12 } C ^ { 13 } C ratio and the ^ { 12 } C _ { 2 } to ^ { 12 } C ^ { 13 } C ratio a good measure of half the carbon isotope ratio : ^ { 12 } C/ ^ { 13 } C= 2 \times ^ { 12 } C _ { 2 } / ^ { 12 } C ^ { 13 } C= 72 \pm 26 .
This is in agreeement with our prediction that the isotopic exchange reaction for ^ { 12 } C ^ { 14 } N is efficient and our observation in Paper III of ^ { 12 } C ^ { 14 } N/ ^ { 13 } C ^ { 14 } N = 38 \pm 2 .

A fit of the C _ { 2 } excitation model of van Dishoeck & Black ( [ 1982 ] ) to the relative population distribution of C _ { 2 } yields n _ { c } \sigma / I = 3.3 \pm 1.0 \times 10 ^ { -14 } .
At r \simeq 10 ^ { 16 } cm this translates in n _ { c } = 1.7 \times 10 ^ { 7 } cm ^ { -3 } and \dot { M } \simeq 2.5 \times 10 ^ { -4 } M _ { \odot } yr ^ { -1 } .

\keywords line : identification – molecular data – molecular processes – stars : AGB and post-AGB – stars : circumstellar matter– individual stars : HD 56126