Experimental determination of the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction cross section  above the ${}^7\mathrm{Be}$ proton separation threshold

Background: The ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction plays a major role both in the big bang nucleosynthesis producing the majority of the primordial ${}^7\mathrm{Li}$, and in the $pp$ chain of solar hydrogen burning, where it is the branching point between the $pp$-I and $pp$-II,-III chains. As a few-nucleon system, this reaction is often used to validate ab initio theoretical calculations and/or test $R$-matrix theory and code implementations. For the latter, experimental data in an extended energy range is of crucial importance to test the fit and extrapolation capabilities of the different codes.

Purpose: The ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction cross section has been measured by several groups up to the first resonance ($E_{\mathrm{c}.\mathrm{m}.}\approx 3$ MeV) in the reaction. However, only one data set exists above the ${}^7\mathrm{Be}$ proton separation threshold measured in a narrow energy range ($E_{\mathrm{c}.\mathrm{m}.}=4.0–4.4$ MeV). In this work we extend the available experimental capture cross section database to the energy range of known ${}^7\mathrm{Be}$ levels, where only particle scattering experiments are available for testing the models.

Method: The activation method was used for the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction cross section determination. The experiment was performed using a thin-window gas cell with two high-purity Al foils as entrance and exit windows. The activity of the ${}^7\mathrm{Be}$ nuclei implanted in the exit/catcher foil was measured by detecting the yield of the emitted $\gamma$ rays using shielded high-purity germanium detectors.

Results: New experimental ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction cross section data were obtained for the first time in the $E_{\mathrm{c}.\mathrm{m}.}=4.3–8.3$ MeV energy region, corresponding to $E_x=5.8–10$ MeV excitation energies of ${}^7\mathrm{Be}$. The new data set with about 0.2 MeV step covers the energy range of known levels and particle separation thresholds. No prominent structures are observer around the ${}^7\mathrm{Be}$ levels.

Conclusions: The measured reaction cross section is slowly increasing with increasing energy in the range of $E_x=6–8$ MeV from $10\mu \mathrm{b}$ to $13\mu \mathrm{b}$. Above the ${}^6\mathrm{Li}+p_1$ threshold, a decrease starts in the cross section trend and reaches a value of about $8\mu \mathrm{b}$ around $E_x=10$ MeV. The overall structure of the cross section suggest a broad resonance peaking around $E_x=7.5$ MeV ${}^7\mathrm{Be}$ excitation energy, with a width of 8 MeV.

Figure 1

Cutaway technical drawing of the gas-cell used for the irradiations. The complete cell is surrounded by the beam-line vacuum. See text for details.

Figure 2

Efficiency determination of the ULB $\gamma$-ray detector at 27 cm source-detector distance. The extrapolation and interpolation to 477.6 keV is shown in the inset together with the averaged value finally used in the analysis. The shaded areas are the $1\sigma$ confidence intervals of the fits.

Figure 3

On the top, in (a), a typical spectrum taken by the LEGe detector, in the middle (b) another one taken by the ULB on samples from lower energy irradiations, while on the bottom, in (c), a typical spectrum after a higher energy irradiation is shown. In all cases the peak from ${}^7\mathrm{Be}$ is clearly separable, even though in the high energy irradiation more parasitic activity was created in the exit foil. See text for details.

Figure 4

In the bottom panel (a) the present reaction cross sections together with data from previous works [15, 19] are displayed. Only the statistical uncertainty of the data points is plotted. In (b) the ${}^7\mathrm{Be}$ levels are shown with dashed central lines, and shaded total widths taken from the most recent compilation [35]. The proton separation thresholds are indicated with solid lines. Each of the energies are shifted for the plot with the reaction $Q$ value to match the experimental energy scale. On the top panels selected differential cross section data from the literature for the ${}^3\mathrm{He}(\alpha ,p){}^6\mathrm{Li}$ reaction [54] (c) and for the elastic scattering [54] (d) are plotted. The lines are just to guide the eye.

Figure 5

The present data (a) compared to the ${}^3\mathrm{H}(\alpha ,\gamma ){}^7\mathrm{Li}_{\mathrm{g}.\mathrm{s}.}$ reaction cross section (b) from [27, 29, 57]. The $x$ axes are aligned to account for the $Q$-value difference of the reactions.

Figure 6

In (a) the present results and literature data sets from Refs. [15, 19] together with $R$-matrix calculations from previous works [25, 26] and with the adjusted parameters from this work are displayed. [(b)–(d)] show elastic scattering excitation functions from Ref. [54] at selected angles together with the $R$-matrix fits.