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The 16 O( 3 He,d) 17 F reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of 17 F. The coefficients provide the normalization for the tails of the overlap functions for 17 F→ 16 Oϩp and allow us to calculate the S factors for 16 O(p,␥) 17 F at astrophysical energies. The calculated S factors are compared to measurements and found to be in very good agreement. This provides a test of this indirect method to determine astrophysical direct capture rates using transfer reactions. In addition, our results yield S(0) for capture to the ground and first excited states in 17 F, without the uncertainty associated with extrapolation from higher energies. ͓S0556-2813͑99͒00702-5͔ PACS number͑s͒: 25.40. Lw, 25.55.Hp, 26.20.ϩf, 27.20.ϩn

Asymptotic normalization coefficients ͑ANCs͒ for 8 Li→ 7 Liϩn have been extracted from the neutron transfer reaction 13 C(7 Li, 8 Li) 12 C at 63 MeV. These are related to the ANCs in 8 B→ 7 Beϩp using charge symmetry. We extract ANCs for 8 B which are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the p 1/2 and p 3/2 components in the transfer. We find the astrophysical factor for the 7 Be(p,␥) 8 B reaction to be S 17 (0)ϭ17.6Ϯ1.7 eV b. This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.