A new analysis of the modern astrophysical S factors for the direct-capture 3 He(α, γ ) 7 Be reaction, precisely measured in recent works [B.S. Nara Singh et al., Phys. Rev. Lett. 93, 262503 (2004); D. Bemmerer et al., ibid. 97, 122502 (2006); F. Confortola et al., Phys. Rev. C 75, 065803 (2007), Gy. Gyrky et al., ibid. 75, 035805 (2007), T. A. D. Brown et al., ibid. 76, 055801 (2007), and A. Di Leva, et al., Phys. Rev. Lett. 102, 232502], has been carried out within the modified two-body potential approach. New estimates are obtained for the "indirectly determined" values of the asymptotic normalization constants and the respective nuclear vertex constants for 3 He + α → 7 Be(g.s.) and 3 He + α → 7 Be(0.429 MeV) as well as the astrophysical S factors S 34 (E) at E 90 keV, including E = 0. The values of asymptotic normalization constants have been used to obtain the values of the ratio of the α-particle spectroscopic factors for the mirror ( 7 Li 7 Be) pair.