The differential cross sections for the reactions ${}^9\mathrm{Be}{(}^{10}\mathrm{B}{,}^{10}\mathrm{B}{)}^9\mathrm{Be}$ and ${}^9\mathrm{Be}{(}^{10}\mathrm{B}{,}^9\mathrm{Be}{)}^{10}\mathrm{B}$ have been measured at an incident energy of 100 MeV. The elastic scattering data have been used to determine the optical model parameters for the ${}^9\mathrm{Be}{+}^{10}\mathrm{B}$ system at this energy. These parameters are then used in distorted-wave Born approximation (DWBA) calculations to predict the cross sections of the ${}^9\mathrm{Be}{(}^{10}\mathrm{B}{,}^9\mathrm{Be}{)}^{10}\mathrm{B}$ proton exchange reaction, populating the ground and low-lying states in ${}^{10}\mathrm{B}$. By normalizing the theoretical DWBA proton exchange cross sections to the experimental ones, the asymptotic normalization coefficients (ANC's), defining the normalization of the tail of the ${}^{10}\mathrm{B}$ bound state wave functions in the two-particle channel ${}^9\mathrm{Be}+p$, have been found. The ANC for the virtual decay ${}^{10}\mathrm{B}(\mathrm{g}.\mathrm{s}.\mathrm{}){\to }^9\mathrm{Be}+p$ will be used in an analysis of the ${}^{10}\mathrm{B}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^9\mathrm{Be}$ reaction to extract the ANC's for ${}^8\mathrm{B}{\to }^7\mathrm{Be}+p$. These ANC's determine the normalization of the ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ radiative capture cross section at very low energies, which is crucially important for nuclear astrophysics.

• Received 13 March 1997

DOI:https://doi.org/10.1103/PhysRevC.56.1302