Evaluation of modern ${}^3\mathrm{He}$($\alpha$, $\gamma$)${}^7\mathrm{Be}$ data

In both the Sun and the early universe, the ${}^3\mathrm{He}$($\alpha$, $\gamma$)${}^7\mathrm{Be}$ reaction plays a key role. The rate of this reaction is the least certain nuclear input needed to calculate both the primordial ${}^7\mathrm{Li}$ abundance in big-bang nucleosynthesis and the solar neutrino flux. Taking advantage of several recent highly precise experiments, we analyze modern ${}^3\mathrm{He}$($\alpha$, $\gamma$)${}^7\mathrm{Be}$ data using a robust and minimally model-dependent approach capable of handling discrepant data sets dominated by systematic rather than statistical errors. We find $S_{34}(0)=0.580\pm 0.043(0.054)$ keV b at the 68.3(95.4)% confidence level.

Figure 1

(a) Theoretical $S_{34}$ calculations of Tombrello and Parker[22] (solid) and of Kajino[27] (dashed) are plotted relative to their values at $E=0$. (b) The deviation relative to the Kajino calculation. In both plots, the dotted lines delineate the uncertainty due to the ±6% theoretical uncertainty in the zero-energy $S$ factor and logarithmic derivative estimated in Ref. [25].

Figure 2

The best fit $S$ factor for the ${}^3\mathrm{He}$($\alpha$, $\gamma$)${}^7\mathrm{Be}$ reaction (solid curve). Also shown are the central $68.3\%$ confidence level limits (dashed curves). The experimental data and their total uncertainties are plotted [Activity (open points), Prompt (solid points)].

Figure 3

The best fit branching ratio $S_1/S_0$ for the ${}^3\mathrm{He}$($\alpha$, $\gamma$)${}^7\mathrm{Be}$ reaction (solid curve). Also shown are the central 68.3% confidence level limits (dashed curves). The experimental data and their total uncertainties are plotted.

Figure 4

This figure shows the fitted contributions of various partial waves to the $S$ factor. The $s$-wave (short dashed), $d$-wave (dotted), and total (solid) $S$ factors for capture into the ground state and the $s$-wave (long dash-dotted), $d$-wave (short dash-dotted), and total (long dashed) $S$ factors for capture into the first excited state are all shown.

Figure 5

(a) The $S_{34}$ calculation of Kajino[27] (dashed) and of this evaluation (solid) are plotted relative to their values at $E=0$. (b) The deviation relative to the Kajino calculation.