The subthreshold 1 ^ { - } _ { 1 } state at an excitation energy E _ { x } = 7.12 MeV in ^ { 16 } O has been believed to enhance the S -factor of ^ { 12 } C ( \alpha , \gamma ) ^ { 16 } O .
The enhancement seems to originate from strong interference between 1 ^ { - } _ { 1 } and 1 ^ { - } _ { 2 } ( E _ { x } \approx 9.6 MeV ) in the vicinity of the \alpha -particle threshold .
However , weak interference between them and a resulting small E 1 S -factor are exemplified with R -matrix theory .
Including a higher-order correction of the resonance parameters , the present example appears to reproduce the experimental data consistently .
It would therefore be possible that the E 1 S -factor is reduced at low energies .