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The direct ${}^3$He(α,γ)${}^7$Be radiative capture reaction is studied in the framework of two- and three-body potential cluster models [1,2]. E1 and E2 transitions are described at the long-wavelength approximation. The two-body model is based on a simple Gaussian form $α^{3}$He-potential of Dubovichenko $V_{D}^{a}$ from Ref.[1], with a modification in d waves. The new potential parameters are $V_{0}$=-180 MeV, α=0.4173 $fm^{-2}$ and $V_{0}$=-190 MeV, α=0.4017 $fm^{-2}$ in the $d_{3/2}$ and $d_{5/2}$ partial waves, respectively. The potential describes correctly the phase shifts in the $s$, $p$, $d$ and $f$ waves and binding energies of the ground $p_{3/2}$ and the first excited $p_{1/2}$ bound states. As can be seen in Fig.1, the modification of the potential in $d$ waves allows to improve the description of the astrophysical S factor for the direct ${}^3$He(α,γ)${}^7$Be radiative capture reaction at intermediate energies E>0.5 MeV in comparison with the results of Ref.[1]. In the three-body model the ${}^7$Be nucleus is described as a bound state of α+p+d in the Hyperspherical Lagrange mesh method. The initial state is factorized into the p+d bound state and the α+${}^3$He scattering state. The αd-potential is from Ref.[2], while αN-potential was taken from Ref.[3]. The pd-potential of the Gaussian form [4] with parameters $V_0$=-34.92 MeV, α=0.15 $fm^{-2}$ and $V_0$=2.4 MeV, α=0.01 ${fm}^{-2}$ are used in the even and odd partial waves, respectively. The α${}^3$He-potential is the same as in the two-body model. The three body bound state wave functions of ${}^7$Be was corrected at R=6 fm with the help of the Whittaker asymptotics.

Fig. 1. (a) Astrophysical S factor within the two- and three-body models in comparison with the available experimental data. Panel (b) highlights the low energy region.

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