${}^3\mathrm{He}+{}^4\mathrm{He}$ $\to$ ${}^7\mathrm{Be}$ astrophysical $S$ factor

We present precision measurements of the ${}^3\mathrm{He}+{}^4\mathrm{He}$ $\to$ ${}^7\mathrm{Be}$ reaction in the range $E_{\mathrm{c}.\mathrm{m}.}=0.33$ to 1.23 MeV using a small gas cell and detection of both prompt γ rays and ${}^7\mathrm{Be}$ activity. Our prompt and activity measurements are in good agreement within the experimental uncertainty of several percent. We find $S(0)=0.595\pm 0.018$ keV b from fits of the Kajino theory to our data. We compare our results with published measurements, and we discuss the consequences for Big Bang Nucleosynthesis and for solar neutrino flux calculations.

Figure 1

Energy level diagram.

Figure 2

Gas cell and beam collimation geometry.

Figure 3

Absolute online Ge photopeak detection efficiency vs $E_{\gamma }$. Solid points are measurements. Error bars are statistical. The curve is the fit to the data of the function $\epsilon (E_{\gamma })={\mathit{aE}}_{\gamma }^b(1+{\mathit{cE}}_{\gamma }^2)$, with $a,b,$ and $c$ parameters. (Bottom panel) Fractional fit residuals.

Figure 4

Solid (blue) circles are measured online Ge detector efficiency vs position for a ${}^{137}\mathrm{Cs}$ source on the axis of the gas cell. Solid (red) squares are PENELOPE simulations. The curve is to guide the eye. The center of the cell is at 2.63 cm, the simulated end points are located at positions near the ends of the cell, and the position scale has an arbitrary offset.

Figure 5

Gas cell and detector geometry used in PENELOPE simulations. The beam enters from the left, passing through the collimator mounting tube and electron suppressor. The Ge detector is shown with its carbon fiber window and Plexiglass absorber.

Figure 6

$E_{\mathrm{c}.\mathrm{m}.}=0.43$ MeV ($E_{\alpha }=1.7$ MeV) prompt background-subtracted γ spectrum (points) and PENELOPE simulation (curve) in the region of the ${\gamma }_0$ peak.

Figure 7

Prompt γ spectra measured at $E_{\alpha }=1.7$ MeV ($E_{\mathrm{c}.\mathrm{m}.}=0.43$ MeV). (Top panel, from top to bottom) ${}^4\mathrm{He}+{}^3\mathrm{He}$ (black), ${}^4\mathrm{He}+{}^4\mathrm{He}$ (red), and beam-off background (blue) spectra. (Bottom panels) Background subtracted spectra in the region of the 429 keV line and ${\gamma }_0$. The window used to determine the ${\gamma }_0$ yield is indicated.

Figure 8

Prompt γ spectra measured at $E_{\alpha }=3.5$ MeV ($E_{\mathrm{c}.\mathrm{m}.}=1.23$ MeV). The colors correspond to those used in Fig. 7. See legend to Fig. 7 for additional information.

Figure 9

$E_{\mathrm{c}.\mathrm{m}.}=1.23$ and 0.43 MeV ($E_{\alpha }=1.7$ and 3.5 MeV) offline activity spectra. (Top panels) ${}^4\mathrm{He}+{}^3\mathrm{He}$ irradiation. (Middle panels) ${}^4\mathrm{He}+{}^4\mathrm{He}$ irradiation. (Bottom panels) Source-out background. Counting periods (in d) are shown.

Figure 10

Solid (blue) points are $S_{\mathrm{act}}$($E_{\mathrm{c}.\mathrm{m}.}$) vs $E_{\mathrm{c}.\mathrm{m}.}$. The curve is the fit of Kajino's function. (Bottom panel) Fractional fit residuals.

Figure 11

Solid (blue) points are $S_{\mathrm{prompt}}(E_{\mathrm{c}.\mathrm{m}.})$ vs $E_{\mathrm{c}.\mathrm{m}.}$, for the isotropic ${\gamma }_0$ assumption. The curve is the fit of Kajino's function. (Bottom panel) Fractional fit residuals.

Figure 12

$S_{\mathrm{prompt}}$/S${}_{\mathrm{act}}$ vs $E_{\mathrm{c}.\mathrm{m}.}$. (Solid blue circles) Assuming ${\gamma }_0$ isotropic. (Red x's) ${\gamma }_0$ corrected for theoretical anisotropy as given in Table . The crosses have been displaced from the circles for clarity.

Figure 13

(Left panel) Red points, $S_{\mathrm{act}}(0)$. (Right panel) Blue points, $S_{\mathrm{prompt}}(0)$. The horizontal lines are the fits to the activity values (left panel) and prompt values (right panel) as given in Table .

Figure 14

Recently measured $S(0)$ values. Points, from left to right: Ref. [13] and Ref. [14] activity values, Ref. [15], and present activity + prompt values. Horizontal line—fit to Ref. [13] values, Ref. [15] total, and present total as given in Table .