Astrophysical $S$ factor of the ${}^3\mathrm{He}$($\alpha ,\gamma$)${}^7\mathrm{Be}$ reaction measured at low energy via detection of prompt and delayed γ rays

Solar neutrino fluxes depend both on astrophysical and on nuclear physics inputs, namely on the cross sections of the reactions responsible for neutrino production inside the Solar core. While the flux of solar ${}^8\mathrm{B}$ neutrinos has been recently measured at Superkamiokande with a 3.5% uncertainty and a precise measurement of ${}^7\mathrm{Be}$ neutrino flux is foreseen in the next future, the predicted fluxes are still affected by larger errors. The largest nuclear physics uncertainty to determine the fluxes of ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}$ neutrinos comes from the ${}^3\mathrm{He}$($\alpha ,\gamma$)${}^7\mathrm{Be}$ reaction. The uncertainty on its S-factor is due to an average discrepancy in results obtained using two different experimental approaches: the detection of the delayed γ rays from ${}^7\mathrm{Be}$ decay and the measurement of the prompt γ emission. Here we report on a new high precision experiment performed with both techniques at the same time. Thanks to the low background conditions of the Gran Sasso LUNA accelerator facility, the cross section has been measured at $E_{\mathrm{c}.\mathrm{m}.}=170$, 106, and 93 keV, the latter being the lowest interaction energy ever reached. The S-factors from the two methods do not show any discrepancy within the experimental errors. An extrapolated $S(0)=0.560\pm 0.017$ keV barn is obtained. Moreover, branching ratios between the two prompt γ-transitions have been measured with 5–8% accuracy.

Figure 1

Schematic view of the interaction chamber with the position of the HPGe detector and of the 100 μm silicon detector used for ${}^3\mathrm{He}$ density monitoring. The distance between the entrance collimator and the calorimeter is 35 cm. The thickness of the internal collimator is 3 cm for the Lead part and 1.6 cm for the tungsten part.

Figure 2

γ-ray spectrum at $E_{\alpha }=220$, 250, and 400 keV compared with natural laboratory background (in grey) normalized to beam-measurement live times (respectively: 31.2 d, 21.3 d, and 4.8 d). Arrows indicate the primary transition peaks to the first excited state and to the ground state.

Figure 3

Overview of all available S-factor values for the ${}^3\mathrm{He}$($\alpha ,\gamma$)${}^7\mathrm{Be}$ reaction. Filled and open circles: present work. Prompt-γ data: open squares [14], open triangles [15], stars [12], open inverse triangles [16], filled inverse triangles [17], open diamonds [18]. Activation data: filled diamonds [19], crosses [12], filled squares [21], filled triangles [23, 24]. Dashed line: most recent R-matrix fit [34], solid line: fit [34] normalized to present data. In the inset a zoom of prompt γ (filled circles) and activation (open circles) data obtained in this work.