Measurements of branching ratios from the 7.12-MeV state in ${}^{16}\mathrm{O}$ and the ${}^{12}\mathrm{C}$($\alpha ,\gamma$)${}^{16}\mathrm{O}$ reaction cross section

Gamma-ray branching ratios of the 7.12-MeV state in ${}^{16}\mathrm{O}$ have been measured using the $\gamma \text{−}\gamma$ coincidence technique. The extrapolations of several components of the important ${}^{12}\mathrm{C}$($\alpha ,\gamma$)${}^{16}\mathrm{O}$ cross section to helium-burning energies are dependent upon the $7.12\to 6.92$ MeV branching ratio. An experimental upper limit has been placed on this transition; the $7.12\to 6.13$ MeV branching ratio has also been measured. Relative cross sections and $\gamma$-ray angular distributions have been measured for the ${}^{19}\mathrm{F}$($p,\alpha \gamma$) reaction at several energies near $E_p=2$ MeV, leading to the 6.13-, 6.92-, and 7.12-MeV states of ${}^{16}\mathrm{O}$. Monte Carlo simulations of the various detectors have been developed and the simulated detector efficiencies have been compared and adjusted to experimental measurements. The available experimental data relating to the ${}^{12}\mathrm{C}$($\alpha ,\gamma$)${}^{16}\mathrm{O}$ cross section have been fitted with the $R$-matrix formalism. The new upper limit on the $7.12\to 6.92$ MeV branching ratio impacts the extrapolation of both the $E2$ ground-state cross section and the cascade cross section through the 6.92-MeV state.

Figure 1

Experimental setup for the angular distribution measurements.

Figure 2

HPGe spectrum at $0^{°}$ and 2.00-MeV proton energy. Peaks attributed to 7.12-, 6.92-, and 6.13-MeV transitions are shown. Numbers in parentheses indicate whether a peak is a full-energy loss peak (0), a one-escape peak (1), or a double-escape peak (2).

Figure 3

Angular distribution for the 6.13-MeV state decay at $E_p=2.00$ MeV.

Figure 4

Angular distribution of the 7.12-MeV radiation at 2.00-MeV proton energy. The solid curve is a least-square fit with Legendre polynomials.

Figure 5

Angular distribution of the 6.92-MeV radiation at 2.00-MeV proton energy. The solid curve is a least-square fit with Legendre polynomials.

Figure 6

Relative intensities of the 7.12-, 6.92-, and 6.13-MeV transitions corrected for efficiency.

Figure 7

Schematic view of the experimental setup. The beam enters from the left.

Figure 8

Interactive GEANT simulation of the experimental setup. Dotted straight lines are $\gamma$ rays; solid lines are charged particles.

Figure 9

The NaI(Tl) singles spectrum. The gate on the NaI(Tl) detector was set on the 4–8 MeV region.

Figure 10

HPGe spectrum in coincidence with the 4–8 MeV region in NaI(Tl). The 0.99-MeV peak from the $7.12\to 6.13$ MeV transition is indicated.

Figure 11

HPGe spectrum in coincidence with the 4–8 MeV region in NaI(Tl), showing expanded 200-keV region with the 197-keV peak from the ${}^{19}\mathrm{F}$($p,p^{\prime }$) reaction and the position of a possible $7.12\to 6.92$ MeV transition.

Figure 12

The best $R$-matrix fit to the cascade $S$-factor data (△ [3], ◯ [4]) with a $7.12\to 6.92$ MeV branching ratio of $2\times {10}^{-5}$. The solid line represents the $S$ factor for the cascade through the 6.92-MeV state.

Figure 13

${\chi }^2$ minimization for the $\alpha$ reduced width.