Time-Reversal Measurement of the $p$-Wave Cross Sections of the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ Reaction for the Cosmological Li Problem

The cross sections of the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction for $p$-wave neutrons were experimentally determined at $E_{\mathrm{c}.\mathrm{m}.}=0.20–0.81\mathrm{MeV}$ slightly above the big bang nucleosynthesis (BBN) energy window for the first time on the basis of the detailed balance principle by measuring the time-reverse reaction. The obtained cross sections are much larger than the cross sections for $s$-wave neutrons inferred from the recent measurement at the n_TOF facility in CERN, but significantly smaller than the theoretical estimation widely used in the BBN calculations. The present results suggest the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction rate is not large enough to solve the cosmological lithium problem, and this conclusion agrees with the recent result from the direct measurement of the $s$-wave cross sections using a low-energy neutron beam and the evaluated nuclear data library ENDF/B-VII.1.

Figure 1

Neutron energy spectra in the ${}^4\mathrm{He}(\alpha ,n){}^7\mathrm{Be}$ reaction measured at $E_{\alpha }=39.30\mathrm{MeV}$ and ${\theta }_{\text{lab}}=0°$. (a) Open and hatched spectra were taken using the He gas-filled and empty cells, respectively. (b) Background-free spectrum obtained by subtracting the background spectrum taken from the empty-cell measurement.

Figure 2

Angular distribution of the differential cross sections for the ${}^4\mathrm{He}(\alpha ,n){}^7\mathrm{Be}$ reaction. The solid circles and squares show the differential cross sections for the ground and first excited states in ${}^7\mathrm{Be}$, respectively. The solid and dashed lines are series of the even-order Legendre polynomials to fit the experimental data.

Figure 3

Measured total cross sections of the ${}^4\mathrm{He}(\alpha ,n){}^7\mathrm{Be}$ reaction for the ground (solid squares) and first excited (solid triangles) states. The sum of the two states is shown by solid circles. Previous results from Ref. [13] are shown by the open circles. The solid lines interpolating the data points are drawn for a guide to the eye.

Figure 4

Measured total cross sections for the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction on the ground (solid circles) and first excited (solid squares) states. The cross sections for the first excited state are larger than those for the ground state, but those for the first excited state make no sizable contribution to the destruction rate of ${}^7\mathrm{Be}$ at the BBN temperature. The solid line, dotted line, open triangles, and dashed line in the bottom panel are the previous evaluations from Refs. [8, 11, 14], and [17], respectively. The solid line in the top panel shows the Maxwell-Boltzmann distribution at $T_9=0.7$. The shaded area presents the effective-energy window for the $p$-wave reaction at $T_9=0.6–0.8$.