Measurement of $d+{}^7\mathrm{Be}$ Cross Sections for Big-Bang Nucleosynthesis

The cross sections of nuclear reactions between the radioisotope ${}^7\mathrm{Be}$ and deuterium, a possible mechanism of reducing the production of mass-7 nuclides in big-bang nucleosynthesis, were measured at center-of-mass energies between 0.2 and 1.5 MeV. The measured cross sections are dominated by the $(d,\alpha )$ reaction channel, towards which prior experiments were mostly insensitive. A new resonance at 0.36(5) MeV with a strength of $\omega \gamma =1.7(5)\mathrm{keV}$ was observed inside the relevant Gamow window. Calculations of nucleosynthesis outcomes based on the experimental cross section show that the resonance reduces the predicted abundance of primordial ${}^7\mathrm{Li}$, but not sufficiently to solve the primordial lithium problem.

Figure 1

Comparison of beam-particle energies reconstructed with two methods, the “sum method” ($E_{\mathrm{sum}}$) and the “tracking method” ($E_{\text{track}}$), see text. Events between the two red lines were accepted for analysis.

Figure 2

Dalitz-plot analysis of $p+2\alpha$ events at $E_{\text{c}\mathrm{.}\text{m}\mathrm{.}}=1.15\pm 0.20\mathrm{MeV}$, characterized according to the squared invariant masses of the $\alpha +\alpha$ and $\alpha +p$ systems. The lower of the two possible ${\alpha }_{1,2}+p$ invariant-mass values was selected.

Figure 3

Cross section as a function of the $d+{}^7\mathrm{Be}$ center-of-mass energies, with statistical errors. The events are separated into $(d,p)$ and $(d,\alpha )$ reactions, according to their location on the Dalitz-plot of Fig. 2. Shown for comparison are differential cross sections from Kavanagh [15], multiplied by $4\pi$. The average detection efficiency (dashed line) and the Gamow window for $T=0.8$ GK are also shown.

Figure 4

$S$-factor representation of the experimental data for the $(d,\alpha )$ and the $(d,p_1)$ channels. The continuous line represents the $R$-matrix fit including the $100{\mathrm{keV}}_{\mathrm{FWHM}}$ experimental resolution. The dashed line is an $R$-matrix calculation using the same resonance parameters without the experimental resolution included. Data points from Angulo et al. [16] are shown for comparison.

Figure 5

Thermal reaction rates of $d+{}^7\mathrm{Be}$ reactions as a function of temperature, calculated from $R$-matrix fit in this work, and in dashed lines “high” and “low” values from systematic uncertainties. Rates calculated from Kavanagh [15] and Angulo et al. [16] are shown for comparison.

Figure 6

BBN outcome for light isotopes as a function of baryon-to-photon ratio $\eta$. The relative ${}^7\mathrm{Li}$ abundance was calculated using the experimental $d+{}^7\mathrm{Be}$ reaction rate and its uncertainty range, which is compared to a BBN network without the $d+{}^7\mathrm{Be}$ reaction. Horizontal dashed lines show range of observations [7].