$E1$ and $E2\phantom{\rule{0.3em}{0ex}}S$ factors of $^{12}\mathrm{C}$($\ensuremath{\alpha},{\ensuremath{\gamma}}_{0}$)$^{16}\mathrm{O}$ from $\ensuremath{\gamma}$-ray angular distributions with a 4 $\ensuremath{\pi}$-detector array

$E 1$ and $E 2 S$ factors of ${}^{12}C$ ( $α, γ_{0}$ ) ${}^{16}O$ from $γ$ -ray angular distributions with a 4 $π$ -detector array

M. Assunção et al.

Phys. Rev. C 73, 055801 – Published 11 May 2006

Abstract

A new experiment to determine the thermonuclear cross section of the ${}^{12}C$ ( $α, γ$ ) ${}^{16}O$ reaction has been performed in regular kinematics using an intense α-particle beam of up to 340 μA from the Stuttgart DYNAMITRON. For the first time, a 4π-germanium-detector setup has been used to measure the angular distribution of the γ rays at all angles simultaneously. It consisted of an array of nine EUROGAM high-purity Ge detectors in close geometry, actively shielded individually with bismuth germanate crystals. The ${}^{12}C$ targets were isotopically enriched by magnetic separation during implantation. The depth profiles of the implanted carbon in the ${}^{12}C$ targets were determined by Rutherford backscattering for purposes of cross-section normalization and absolute determination of the $E 1$ and $E 2 S$ factors. Angular distributions of the γ decay to the ${}^{16}O$ ground state were measured in the energy range $E_{c . m .} = 1.30 - 2.78$ MeV and in the angular range (lab.) 30°–130°. From these distributions, astrophysical $E 1$ and $E 2 S$ -factor functions vs energy were calculated, both of which are indispensable to the modeling of this reaction and the extrapolation toward lower energies. The separation of the $E 1$ and $E 2$ capture channels was done both by taking the phase value $ϕ_{12}$ as a free parameter and by fixing it using the results of elastic α-particle scattering on ${}^{12}C$ in the same energy range.