$E2$ Interference Effects in the ${}^{12}\mathbf{C}(\alpha ,{\gamma }_0{)}^{16}\mathbf{O}$ Reaction

The $E1\mathrm{\text{−}}E2$ interference sign between the $E_{\mathrm{c}.\mathrm{m}.}=2.68-\mathrm{MeV}$ $E2$ resonance and an underlying $E1$ strength has been measured for the first time. An $E1\mathrm{\text{−}}E2$ asymmetry parameter of $a=0.07\pm 0.05$ was extracted from the thick-target $\gamma$-ray yields of the narrow resonance at angles of 45° and 135°. The positive sign of $a$ corresponded to constructive interference at forward angles and, further, allowed the interference between the resonance and an $E2$ background to be identified as constructive below the resonance energy. The $E2\mathrm{\text{−}}E2$ interference was then used to evaluate the global $S_{E2}$ data within the vicinity of the resonance $2.5\le E_{\mathrm{c}.\mathrm{m}.}\le 3.0\mathrm{MeV}$. An analysis of the global $S_{E2}$ data that agreed with the interference scenario has determined the $E2\mathrm{\text{−}}E2$ interference scheme of the 4.34-MeV resonance and background, resulting in a value of $S_{E2}(300)={62}_{-6}^{+9}\mathrm{keV}\mathrm{b}$.

Figure 1

A fit to the 135° $\gamma$-ray yield from the first ${}^{12}\mathrm{C}(\alpha ,\gamma {)}^{16}\mathrm{O}$ experiment. The solid (red) curve was the sum of three contributions: an ambient room background shown as a long dashed (blue) curve, a beam-induced background given by the short dashed (green) curve, and a Monte Carlo signal that corresponds to the dash-dot (black) curve.

Figure 2

Fits (a) (top panel) and (b) (bottom panel) to the global $S_{E2}$ data. The solid (dashed) line represents the fit assuming the opposite (same) interference signs for the 4.34-MeV and subthreshold resonances.