In the present work, we have studied the properties of the αγ He( , ) Be2 3 4 7 reaction. The direct radiative capture nuclear reactions in the Big-Bang nucleosynthesis mainly, are done in the external areas of inter-nuclear interaction range and play an essential role in nuclear astrophysics. Among of these reactions, the αγ He( , ) Be2 3 4 7 reaction with Q=1.586 MeV is the main part of the Big-Bang nucleosynthesis chain reactions. This reaction can be used to understand the physical and chemical properties of the sun as well as can be justified the lake of the observed solar neutrino in the detector of the Earth. Since product neutrino fluxes are predicated in the center of the sunbythedecay of 7Beand 8B,andalmost areproportional totheastrophysical S-factor forthe αγ He( , ) Be2 3 4 7 reaction, S34.The αγ He( , ) Be2 3 4 7 reactionis consideredthekey tosolve thesolarneutrino puzzle.Finally, wehave astrophysical S-factor obtained for the ground S1,3/2-, first excited S1,1/2-and total S34 states by modern nucleonnucleon two-body local potential models. We have also compared the obtained S-factor with experimental data and other theoretical works.
