High-energy breakup of ${}^6\mathrm{Li}$ as a tool to study the Big Bang nucleosynthesis reaction ${}^2\mathrm{H}$($\alpha$,$\gamma$)${}^6\mathrm{Li}$

The recently claimed observations of non-negligible amounts of ${}^6\mathrm{Li}$ in old halo stars have renewed interest in the Big Bang nucleosynthesis (BBN) of ${}^6\mathrm{Li}$. One important ingredient in the predicted BBN abundance of ${}^6\mathrm{Li}$ is the low-energy ${}^2\mathrm{H}$($\alpha$,$\gamma$)${}^6\mathrm{Li}$ cross section. Up to now, the only available experimental result for this cross section showed an almost constant astrophysical $S$ factor below $400$ keV, contrary to theoretical expectations. We report on a new measurement of the ${}^2\mathrm{H}$($\alpha$,$\gamma$)${}^6\mathrm{Li}$ reaction using the breakup of ${}^6\mathrm{Li}$ at 150 $A\hspace{0.5em}$ MeV. Even though we cannot separate experimentally the Coulomb contribution from the nuclear one, we find clear evidence for Coulomb-nuclear interference by analyzing the scattering angular distributions. This is in line with our theoretical description, which indicates a drop of the $S_{24}$ factor at low energies as predicted also by most other models. Consequently, we find even lower upper limits for the calculated primordial ${}^6\mathrm{Li}$ abundance than before.

Figure 1

Phase-shift data measured for low-energy $\alpha$-${}^2\mathrm{H}$ scattering as a function of the relative $\alpha$-${}^2\mathrm{H}$ energy in the c.m. system, $E_{\mathrm{rel}}$. Data points are from Jenny et al. (circles, [25]), McIntyre and Haeberli (squares, [26]), and Grüebler et al. (diamonds, [27]). The results of the model calculations (full lines) were obtained with the potential parameters described in the text.

Figure 2

Center-of-mass angular distributions for (a) 55 and 70 $A\hspace{0.5em}$MeV ${}^2\mathrm{H}$, (b) 120 and 175 $A\hspace{0.5em}$MeV $\alpha$, and (c) 100 $A\hspace{0.5em}$MeV ${}^6\mathrm{Li}$ on ${}^{208}\mathrm{Pb}$. The full lines represent fits to the measured data using the optical-model potentials as described in the text. Note that the angular distributions for $E_d=140$ MeV in (a) and for $E_{\alpha }=699$ MeV in (b) have been scaled by a factor of ${10}^{-2}$.

Figure 3

Expected distribution of the differential cross section $d\sigma /d{\theta }_6$ as a function of the scattering angle ${\theta }_6$ of the excited ${}^6\mathrm{Li}$${}^{*}$ before breakup, in arbitrary units. The full (red) curve represents the total distribution, whereas the nuclear and Coulomb contributions are depicted by the dot-dashed (blue) and dashed (green) histograms, respectively. Note that the different curves have been normalized to the same total cross section. All distributions were summed over ${}^2\mathrm{H}$-$\alpha$ c.m. energies $E_{\mathrm{rel}}$ up to 1.5 MeV.

Figure 4

The experimental setup shows the fragment-tracking SSD behind the Coulomb-breakup target followed by a 16-strip $\Delta$$E$ detector and a beam stopper. Deuteron and $\alpha$ positions were measured near the focal plane of the KaoS QD spectrometer by two successive large-area multiwire proportional chambers (MWPCs) followed by a scintillator-paddle TOF wall used for trigger purposes.

Figure 5

(a) Relative-energy resolution ($1\sigma$ widths) as determined by simulating ${}^6\mathrm{Li}$ breakup with geant. The data points can be approximated by the fitted function ${\sigma }_E=0.1645\times \sqrt{E_{\mathrm{rel}}}$. (b) Combined geometrical and analysis efficiency of determining $E_{\mathrm{rel}}$ from the ${}^2\mathrm{H}$ and $\alpha$ momentum vectors. The intrinsic efficiency of the MWPC detectors has been assumed to be unity in this graph.

Figure 6

Opening angles ${\theta }_{24}$ between the outgoing fragments ${}^2\mathrm{H}$ and $\alpha$. Full circles correspond to measured data. The dash-dotted histogram (blue) denotes simulations with pure nuclear interaction, whereas the pure CD contribution is shown by the dashed histogram (green). Combined (CD$+$nuclear) contributions are shown by the full red line. Note that the numbers of simulated counts in each spectrum were normalized to the experimental ones.

Figure 7

Angular distribution of the excited ${}^6\mathrm{Li}$${}^{*}$ nuclei after the reaction (${\theta }_6$). The panels represent three different bins of $E_{\mathrm{rel}}$: (a) $0.0⩽E_{\mathrm{rel}}<0.5$ MeV; (b) $0.5⩽E_{\mathrm{rel}}<0.9$ MeV; (c) $0.9⩽E_{\mathrm{rel}}<1.5$ MeV. The measured data points are shown in comparison with simulations with pure nuclear and pure CD as well as with (CD$+$nuclear) interactions. Line types and color codes are identical to the ones in Fig. 6.

Figure 8

Differential cross sections as a function of the energy $E_{\mathrm{rel}}$ in the $\alpha$-${}^2\mathrm{H}$ c.m. system. Black points indicate the experimental data; the histogram corresponds to the geant simulation using the (CD$+$nuclear) interaction as described in the text and a binning of 100 keV (note that the vertical error bars result from a quadratic sum of statistical and systematical uncertainties).

Figure 9

(a) Theoretical $E1$, $E2$, and total $S_{24}$ factors that describe well the present experimental data, together with data points from the previous CD experiment by Kiener et al. [21] and from direct measurements (Robertson et al. [17] and Mohr et al. [18]). See Sec. 5 for an interpretation of the data of Ref. [21]. (b) Comparison of various theoretical predictions for the summed $E1$ and $E2$ contributions to $S_{24}(E)$ [18, 24, 39, 40, 41].

Figure 10

Ratio of nuclear and Coulomb differential dissociation cross sections for ${}^6\mathrm{Li}$ at 150 $A\hspace{0.5em}$MeV (full line) and at 26 $A\hspace{0.5em}$MeV (dashed line). Both curves were calculated with the same model described in detail above in Sec. 2b.

Figure 11

Predicted BBN production ratios for ${}^{6,7}\mathrm{Li}$ over hydrogen as a function of $\eta$, the baryon-to-photon ratio in the early Universe. The solid red line represents the result for ${}^6\mathrm{Li}$ from the $S_{24}$ values obtained in the present work, based on theoretical values for the $E1$ and $E2$ components. The dashed red line represents a very conservative but safe upper limit where all observed events are assumed to result from Coulomb breakup. The blue band denotes the range of predicted ${}^7\mathrm{Li}$ yields [4]. Observational data are indicated by horizontal green-hatched areas: the upper one has been derived from the recent review of lithium observations by Spite and Spite [5]; the lower one corresponds to the largest ${}^6\mathrm{Li}$ yield reported for the star HD 84937 [13]. The yellow vertical band shows the WMAP $\eta$ value [1].