Astrophysical $S$ factor for the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ and ${}^6\mathrm{Li}{(d,p_0/p_1)}^7\mathrm{Li}$ reactions and their astrophysical implications

In this work, three astrophysical $S\left(E\right)$ factors of the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}, {}^6\mathrm{Li}{(d,p_0)}^7\mathrm{Li}$, and ${}^6\mathrm{Li}(d,p_1{)}^7\mathrm{L}{\mathrm{i}}^{*}$ reactions have been presented, and the value of screening potential was also deduced, where the subsequent two $S\left(E\right)$ factors were reported for the first time. The present extracted astrophysical $S\left(E\right)$ factors result in $S_{\mathrm{bare}}\left(0\right)=19.20\pm 0.52,20.46\pm 0.63$, and $3.79\pm 0.18\mathrm{MeV}\mathrm{b}$ for the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}, {}^6\mathrm{Li}{(d,p_0)}^7\mathrm{Li}$, and ${}^6\mathrm{Li}(d,p_1{)}^7\mathrm{L}{\mathrm{i}}^{*}$ reactions, respectively. The deduced screening potential $\left(U_s\right)\mathrm{is}478\pm 42\mathrm{eV}$ in the liquid lithium $(\sim 530\mathrm{K})$ host which is much larger than the expected value of 186 eV calculated by adiabatic approximation. Using these results, the stellar reaction rates for the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ and ${}^6\mathrm{Li}{(d,p_0+p_1)}^7\mathrm{Li}$ reactions for temperatures up to $T=3\times {10}^9\mathrm{K}$ were calculated, so as to estimate the abundances of ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ in the solar proton-proton burning process.

Figure 1

Charged-particle spectra for the (a) 70-, (b) 50-, and (c) 30-keV deuteron bombardments on liquid enriched ${}^6\mathrm{Li}$ target, respectively. Four peaks, protons $\left(p\right)$ from the $D(d,p)t$ reaction, protons $(p_1$ and $p_0)$ from the ${}^6\mathrm{Li}(d,p_1/p_0{)}^7\mathrm{Li}$ reactions, and α particles from the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ reaction, are indicated.

Figure 2

Thick-target yields of charged particles emitted from the ${}^6\mathrm{Li}(d,p_1/p_0{)}^7\mathrm{Li}$ and ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ reactions as a function of the bombarding energy of deuterons.

Figure 3

$S$ factor for the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ reaction as a function of c.m. energy. The solid circles are obtained by thin-target yield. The open circles and crosses are the experimental data for molecular target and atomic target from Engstler 1992 [15]. The dashed and short dashed curves representing the $S$ factor include screening potential contribution of this work and Barker 2002 [16]. The solid and dashed-dotted curves are the corresponding and bare $S$ factors, respectively.

Figure 4

$S$ factor for the ${}^6\mathrm{Li}{(d,p_0)}^7\mathrm{Li}$ reaction as a function of c.m. energy. The solid circles are obtained by thin-target yield. The open circles are the experimental data obtained by Elwyn 1977 [23]. The dashed curve represents the $S$ factor taking screening potential contribution into account, and the solid curve is the corresponding bare $S$ factor. The dashed-dotted curve shows the result estimated from Czerski 1993 [21].

Figure 5

$S$ factor for the ${}^6\mathrm{Li}(d,p_1{)}^7\mathrm{L}{\mathrm{i}}^{*}$ reaction as a function of c.m. energy. The crosses are the experimental data obtained by Czerski 1993 [21]. The rest of the descriptions are the same as in Fig. 4.

Figure 6

Stellar reaction rates for the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ reaction. Dashed curve: Czerski 1997 [37]; solid curve: this work; shadow region: uncertainty of reaction rate.

Figure 7

Stellar reaction rates for the ${}^6\mathrm{Li}(d,p{)}^7\mathrm{Li}$ reaction. The dashed curve represents the rate of ReaclibV2.0 [35]. The dashed-dotted and short dashed curves are the rate of ${}^6\mathrm{Li}{(d,p_0)}^7\mathrm{Li}$ and ${}^6\mathrm{Li}{(d,p_1)}^7\mathrm{Li}$ reactions, respectively, which are obtained based on the present work. The solid curve is the total contribution of the two reactions, with the shadow region (as detailed shown in the inset) corresponding to the uncertainty of reaction rate.

Figure 8

The behaviors of ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ abundances in solar proton-proton burning. Six simulations were included, though there seem to be only two curves due to overlapping.