Astrophysical reaction rates for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>(<i>p</i>,α<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Be and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>11</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>(<i>p</i>,α<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><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:math>Be from a direct model

The reactions $^{10}\mathrm{B}$(p,\ensuremath{\alpha}${)}^{7}$Be and $^{11}\mathrm{B}$(p,\ensuremath{\alpha}${)}^{8}$Be are studied at thermonuclear energies using DWBA calculations. For both reactions, transitions to the ground states and first excited states are investigated. In the case of $^{10}\mathrm{B}$(p,\ensuremath{\alpha}${)}^{7}$Be, a resonance at ${\mathit{E}}_{\mathrm{res}}$=10 keV can be consistently described in the potential model, thereby allowing the extension of the astrophysical S-factor data to very low energies. Strong interference with a resonance at about ${\mathit{E}}_{\mathrm{res}}$=550 keV require a Breit-Wigner description of that resonance and the introduction of an interference term for the reaction $^{10}\mathrm{B}$(p,${\mathrm{\ensuremath{\alpha}}}_{1}$${)}^{7}$${\mathrm{Be}}^{\mathrm{*}}$. Two isospin T=1 resonances (at ${\mathit{E}}_{\mathrm{res}\mathrm{}1}$=149 keV and ${\mathit{E}}_{\mathrm{res}\mathrm{}2}$=619 keV) observed in the $^{11}\mathrm{B}$+p reactions necessitate Breit-Wigner resonance and interference terms to fit the data of the $^{11}\mathrm{B}$(p,\ensuremath{\alpha}${)}^{8}$Be reaction. S-factors and thermonuclear reaction rates are given for each reaction. The present calculation is the first consistent parametrization for the transition to the ground states and first excited states at low energies. \textcopyright{} 1996 The American Physical Society.