Context : In comets the atomic oxygen green ( 5577 Å ) to red-doublet ( 6300 , 6364 Å ) emission intensity ratio ( G/R ratio ) of 0.1 has been used to confirm H _ { 2 } O as the parent species producing forbidden oxygen emission lines .
The larger ( > 0.1 ) value of G/R ratio observed in a few comets is ascribed to the presence of higher CO _ { 2 } and CO relative abundances in the cometary coma .

Aims : We aim to study the effect of CO _ { 2 } and CO relative abundances on the observed G/R ratio in comets observed at large ( > 2 au ) heliocentric distances by accounting for important production and loss processes of O ( ^ { 1 } S ) and O ( ^ { 1 } D ) atoms in the cometary coma .

Methods : Recently we have developed a coupled chemistry-emission model to study photochemistry of O ( ^ { 1 } S ) and O ( ^ { 1 } D ) atoms and the production of green and red-doublet emissions in comets Hyakutake and Hale-Bopp .
In the present work we applied the model to six comets where green and red-doublet emissions are observed when they are beyond 2 au from the Sun .

Results : The collisional quenching of O ( ^ { 1 } S ) and O ( ^ { 1 } D ) can alter the G/R ratio more significantly than that due to change in the relative abundances of CO _ { 2 } and CO .
In a water-dominated cometary coma and with significant ( > 10 % ) CO _ { 2 } relative abundance , photodissociation of H _ { 2 } O mainly governs the red-doublet emission , whereas CO _ { 2 } controls the green line emission .
If a comet has equal composition of CO _ { 2 } and H _ { 2 } O , then \sim 50 % of red-doublet emission intensity is controlled by the photodissociation of CO _ { 2 } .
The role of CO photodissociation is insignificant in producing both green and red-doublet emission lines and consequently in determining the G/R ratio .
Involvement of multiple production sources in the O ( ^ { 1 } S ) formation may be the reason for the observed higher green line width than that of red lines .
The G/R ratio values and green and red-doublet line widths calculated by the model are consistent with the observation .

Conclusions : Our model calculations suggest that in low gas production rate comets the G/R ratio greater than 0.1 can be used to constrain the upper limit of CO _ { 2 } relative abundance provided the slit-projected area on the coma is larger than the collisional zone .
If a comet has equal abundances of CO _ { 2 } and H _ { 2 } O , then the red-doublet emission is significantly ( \sim 50 % ) controlled by CO _ { 2 } photodissociation and thus the G/R ratio is not suitable for estimating CO _ { 2 } relative abundance .