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In the present work, the results of the analysis of the experimental astrophysical $S$ factors (AS) $S^{\exp}(E)$ [1,2] for the nuclear-astrophysical $d(\alpha,\gamma){}^6{\rm Li}$ reaction directly measured at extremely low energies E are presented. One notes that the $d(\alpha,\gamma){}^6{\rm Li}$ reaction is of great interest as one of the sources of the 6Li creation in the early Universe [1].
The analysis is performed within the modified two-body potential method [3]. The method involves two additional conditions that verify the peripheral character of the direct radiative capture reaction $d(\alpha,\gamma){}^6{\rm Li}$: 1) $R(E,b)= const$ for arbitrary variation of the free model parameter b for each fixed experimental value of the energy $E$; 2) the ratio $C_d^2 = S^{\exp}(E)/R(E,b)$ must not depend neither from b and nor from the energy E for each experimental point $ E=E_i$, where $R(E,b)=S^{(sp)}(E;b)/b^2$ and $i=1,2,…N (N =4)$ is a number of experimental points for $S^{\exp}(E_i)$. Here $S^{(sp)}(E;b)$ is a single-particle astrophysical $S$ factor and $b$ is the amplitude of the tail of the radial $s$-component wave function of the bound ${}^6Li (=\alpha+d)$ state, which is calculated in the framework of the shell model using the phenomenological Woods-Saxon potential with the geometric parameters (a radius $r_o$ and a diffuseness a). The value of $b$ strongly changes as a function $(r_o, a)$-pair, i.e., $b= b (r_o, a)$. Fulfilment of the conditions, firstly, it makes it possible to remove the model dependence of the calculated direct $S(E)$ on the geometric parameters $r_o$, and a both for the two-body bound $(\alpha + d)$ state and the $d$-scattering one in minimum being within the experimental errors. It allows, secondly, us to determine “experimental” value of $C_d^2 [=(C_d^{\exp})^2]$ and its uncertainty by model-independent way. The obtained $(C_d^{exp})^2$ values can be implemented in the expression $S(E)= (C_d^{\exp})^2 R(E,b)$ for obtaining the extrapolated values of S(E) and its uncertainties within the energy range $E< E_1$, including $E=0$.
Variation of values of the parameters ro, and a is done in the wide range (1.13≤ r0 ≤1.37 fm, 0.58≤ a ≤0.72 fm, 2.37≤b≤ 2.86 fm$^{-1/2}$ ) and is shown that the reaction is strongly peripheral. As a result, the ANC $(C_d^{exp})^2$, NVC $|C_d^{exp}|^2$ and $S(0)$ values were obtained. They are equal to $(C_d^{exp})^2 = 5.33\pm 0.35 {\rm fm}^{-1}$, $|C_d^{\exp}|^2 =0.43\pm 0.03$ fm and $S(0)= 1.32\pm 0.09$ MeV·nb, which can be considered as determined from the direct measured data of the $S^{\exp}(E)$ for the first time. The obtained results are compared with those from other authors.
This work has been supported in part by the Ministry of Innovations and Technologies of the Republic of Uzbekistan (grant No. HE F2-14).
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