Astrophysical<i>S</i>factor for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><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:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:math>

The ${}^{9}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{10}\mathrm{B}$ reaction plays an important role in primordial and stellar nucleosynthesis of light elements in the p shell, but the energy dependence of $S(E)$ has not been well understood. We reanalyze the existing ${}^{9}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{10}\mathrm{B}$ experimental data within the framework of the R-matrix method. The direct capture part of the S factor is calculated using the experimentally measured asymptotic normalization coefficients for ${}^{10}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}^{9}\mathrm{Be}+p.$ The fitted parameters of the low-lying ${}^{10}\mathrm{B}$ resonances are also required to be consistent with previous measurements of ${}^{6}\mathrm{Li}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{10}\mathrm{B}.$ A good simultaneous fit to both radiative capture reactions is found, in contrast to previous analyses. These results demonstrate that experimentally measured asymptotic normalization coefficients, coupled to the R-matrix method, can provide a reasonable determination of direct radiative capture rates, even when the captured proton is tightly bound in the final nucleus.

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