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We investigate the energy dependence of the astrophysical $S$ factor for thereaction $^7$Be$(p,\gamma)^8$B, the primary source of high-energy solarneutrinos in the solar $pp$ chain. Using simple models we explore the modeldependence in the extrapolation of the experimental data to the region ofastrophysical interest near 20 keV. We find that below approximately 400 keVthe energy dependence is very well understood and constrained by the data forthe elastic scattering of low energy neutrons from $^7$Li. Above 400 keVnuclear distortion of the wave function of the incident proton introduces asignificant model dependence. This is particularly important for the s-wavecontribution to the $S$ factor. The extracted value of S(0) is $19.0 \pm 1.0\pm 0.2$~eVb. The first error is experimental while the second is an estimateof the theoretical error in the extrapolation.Comment: 30 pages, 12 figures, 6 table

physical review. c. nuclear physics/physical review. c, nuclear physics

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></…

Extrapolation of the astrophysicalSfactor for7Be(p,γ)8B