Calculation of C Fusion Reaction Rate and Hindrance Effect

The C reaction is among the most important fusion reactions in stellar evolutions, particularly in stars whose masses are at least six times as large as the sun. Research has shown in the past three decades that stars with initial masses nearly 6–8 times as high as the sun are likely to begin carbon burning in the next stellar evolution stage under electron degeneracy conditions. Fusion hindrance was first observed at under-barrier energy levels for five systems with nuclei of medium mass and has been confirmed for many other heavy-ion systems. Fusion hindrance for the C reaction leads to a peak at nearly 3.6 MeV in the center-of-mass energy in the astrophysical S-factor diagram. The present study evaluates the effect of fusion hindrance on the reaction rate and compares the results with CF88 data. The calculation and comparison of the reaction rate to CF88 data suggested a reduction of order 10 at temperatures around 0.1 GK.