Elastic α-¹²C Scattering and the ¹²C(α,γ)¹⁶O E2 S Factor

Angular distributions of ¹²C(α,α)¹²C have been measured for E_α = 2.6–8.2MeV, at angles from 24° to 166°, yielding 12 864 data points. R-matrix analysis of the ratios of elastic scattering yields a reduced width amplitude of γ₁₂ = 0.47±0.06 MeV^1/2 for the E_x = 6.917MeV(2⁺) state in ¹⁶O(a = 5.5fm). The dependence of the χ² surface on the interaction radius a has been investigated and a deep minimum is found at a = 5.42_-0.27^+0.16fm. Using this value of γ₁₂, radiative α capture and ¹⁶N β-delayed α-decay data, the S factor is calculated at E_c.m. = 300keV to be S_E2(300) = 53_-18⁺¹³keVb for destructive interference between the subthreshold resonance tail and the ground state E2 direct capture.