Asymptotic normalization coefficients for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">B</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>→</mml:mo></mml:mrow><mml:mrow><mml:mn>9</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">Be</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:math>

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 ${}^{10}\mathrm{B}(\mathrm{g}.\mathrm{s}.){\ensuremath{\rightarrow}}^{9}\mathrm{Be}+p$ 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 ${}^{8}\mathrm{B}{\ensuremath{\rightarrow}}^{7}\mathrm{Be}+p$. These ANC's determine the normalization of the ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$ radiative capture cross section at very low energies, which is crucially important for nuclear astrophysics.

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