Astrophysical $S$ factors and reaction rates of the direct radiative capture processes $^{3}{rm He}(alpha, gamma)^{7}{rm Be}$ and $^{3}{rm H}(alpha,gamma)^{7}{rm Li}$, as well as the primordial abundance of the $^{7}{rm Li}$ element, are estimated in the framework of a modified two-body potential model. It is shown that suitable modification of phase-equivalent $alpha-^{3}{rm He}$ potentials in the $d$ waves can improve the description of the astrophysical $S$ factor for the direct $^{3}{rm He}(alpha, gamma)^{7}{rm Be}$ radiative capture reaction at energies above 0.5 MeV. An estimated $^{7}{rm Li/H}$ abundance ratio of $(4.89pm 0.18 )times 10^{-10}$ is in very good agreement with the recent measurement of $(5.0pm 0.3) times 10^{-10}$ by the LUNA collaboration.
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