Primordial $\alpha +d\to {}^6\mathrm{Li}+\gamma$ reaction and second lithium puzzle

During the Big Bang, ${}^6\mathrm{Li}$ was synthesized via the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction. After almost 25 years of the failed attempts to measure the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction in the laboratory at Big Bang energies, just recently the LUNA Collaboration presented the first successful measurements at two different Big Bang energies [Anders et al., Phys. Rev. Lett. 113, 042501 (2014)]. In this paper we will discuss how to improve the accuracy of the direct experiment. To this end the photon's angular distribution is calculated in the potential model. It contains contributions from electric dipole and quadrupole transitions and their interference, which dramatically changes the photon's angular distribution. The calculated distributions at different Big Bang energies have a single peak at $\sim {50}^{\circ }$. These calculations provide the best kinematic conditions to measure the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction. The expressions for the total cross section and astrophysical factor are also derived by integrating the differential cross section over the photon's solid angle. The LUNA data are in excellent agreement with our calculations using a potential approach combined with a well established asymptotic normalization coefficient for ${}^6\mathrm{Li}\to \alpha +d$. Comparisons of the available experimental data for the $S_{24}$ astrophysical factor and different calculations are presented. The Big Bang lithium isotopic ratio ${}^6\mathrm{Li}/{}^7\mathrm{Li}=(1.5\pm 0.3)\times {10}^{-5}$ following from the LUNA data and the present analysis are discussed in the context of the disagreement between the observational data and the standard Big Bang model, which constitutes the second lithium problem.

Figure 1

Angular distributions of the photons emitted in the direct radiative capture ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ at $E=70$ keV (a), $E=100$ keV (b), $E=200$ keV (c) and $E=400$ keV (d). All red (green) lines are obtained using method $M1$ $\left(M2\right)$. The red dashed line (sparsely dotted green line): the angular distribution calculated for the $E1$ transition; the red dotted line (densely dotted green line): the $E2$ transition; the solid red line (dashed-dotted green line): the total photon differential cross section, which is the sum of the electric dipole and quadrupole terms and their interference term.

Figure 2

Astrophysical $S_{24}\left(E\right)$ factors for the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction. Black dots are data from Ref. [13]; green crosses are data from Ref. [12]; black triangles are data from Ref. [11]. Two blue boxes are the LUNA experimental data reported at $E=94$ and 134 keV [16] shown together with their uncertainties. The purple long dashed-dotted line is the $S_{24}\left(E\right)$ astrophysical factor from Ref. [19]. The black dashed-dotted line is the $S_{24}\left(E\right)$ factor from Ref. [15]. All the red (green) lines are our calculations obtained using model $M1$ $\left(M2\right)$. The red dotted (green dotted), red long dashed (green dashed), and red solid (green dashed-dotted) lines are the dipole, quadrupole and total $S_{24}\left(E\right)$ factors, correspondingly, from the present calculations. Notations in the inset are the same.