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$\quad$ Knowledge of the asymptotic normalization coefficients (ANC) for the resulting single-particle bound configurations in the final nucleus (or nuclear vertex constants which differ only by a multiplier from ANCs) [1], plays a crucial role in the calculations of direct nuclear-astrophysical processes of radiative capture [2].
$\quad$ Particularly, to extrapolate the astrophysical S factor $S_{1\,16}(E)$ of the $^{16}$O(p,γ)$^{17}$F reaction, which plays an important role in cold CNO cycle of hydrogen burning, it is required to know the corresponding ANCs for $^{16}$O+p→$^{17}$F. These values can be conveniently and reliably extracted from the analysis of nucleon transfer in reactions with heavy ions at near-barrier energies.
$\quad$ The differential cross sections (DCS) of the reaction $^{16}$O($^{10}$B,$^{9}$Be)$^{17}$F measured at $^{10}$B ions beam of the C-200P cyclotron of the Heavy Ion Laboratory (University of Warsaw) with the energy $E_{10B}$=41.3 MeV have been analyzed using the modified DWBA method [3,4]. Domination of the peripheral proton transferring was found to both proton bound states in $^{17}$F nucleus and the ANC for bound $^{17}$F→$^{16}$O+p configurations were extracted for the ground (5/2+) and first excited (E*=0.495 MeV, ½+) states. At that the squared ANC ($C_{^{10}B→^{9}Be+p})^{2}$ [5] was used as the DCS of the reaction should be normalized by the product of the ANCs squares $(C_{^{10}B→^{9}Be+p})^{2}×(C_{^{17}F→^{16}O+p})^{2}$.
$\quad$ Since the reaction 16O(p,γ)17F occurs through the direct radiative capture of protons at energies below $E_p$ = 2.5 MeV (lab), the modified two body potential approach [6] was used to calculate the astrophysical S-factor $S_{1\,16}$. The obtained value of total $S_{1\,16}(0)$ within the margin of error consistent with the value obtained in [7].
[1] L.D. Blokhintsev, I.Borbely, E.I. Dolinskii // Sov. J. Part. Nucl. 8, 485 (1977)
[2] Tribble R.E., et al. // Rep.Prog.Phys.77. –2014. – 106901. – P.1– 49.
[3] S. V. Artemov, et al. // Phys. At. Nucl. 59, 428 (1996).
[4] A. M. Mukhamedzhanov, et al. // Phys. Rev. C 56, 1302 (1997).
[5] R. Yarmukhamedov, K.I. Tursunmakhatov, and N. Burtebayev, Int.J. Mod. Phys.: Conf. Series. 49, 1960016(2019).
[6] S.B. Igamov, R.Yarmukhamedov. Nucl. Phys. A781 (2007) 247.
[7] S.V. Artemov, et al. // Bull. Rus. Academy of Sci.: Physics, 2009, Vol. 73, No. 2, p. 165.
