Extrapolation of the astrophysical<b><i>S</i></b>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>7</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>8</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:math>to solar energies

We investigate the energy dependence of the astrophysical S factor for the reaction ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$, the primary source of high-energy solar neutrinos in the solar $\mathrm{pp}$ chain. Using simple models we explore the model dependence in the extrapolation of the experimental data to the region of astrophysical interest near 20 keV. We find that below approximately 400 keV the energy dependence is very well understood and constrained by the data for the elastic scattering of low-energy neutrons from ${}^{7}\mathrm{Li}$. Above 400 keV nuclear distortion of the wave function of the incident proton introduces a significant model dependence. This is particularly important for the s-wave contribution to the S factor. The extracted value of $S(0)$ is $19.0\ifmmode\pm\else\textpm\fi{}1.0\ifmmode\pm\else\textpm\fi{}0.2$ eV b. The first error is experimental while the second is an estimate of the theoretical error in the extrapolation.

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