Astrophysical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>factor of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>3</mml:mn></mml:msup></mml:math>He<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>7</mml:mn></mml:msup></mml:math>Be

Background: The ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\gamma})}^{7}$Be reaction is important for the neutrino production in the sun's core and the production of ${}^{7}$Li during big bang nucleosynthesis. The reaction mechanism is characterized by a strong direct capture component and nearby broad unbound resonance levels.Purpose: Recent experiments have opened up a new energy window into the reaction mechanism and it becomes more and more evident that, in order to understand the shape of the $S$ factor, theoretical calculations need to take into account possible resonance contributions from higher energies as well.Method: In the present work, a relatively wide energy window was investigated, ${E}_{c.m.}=300$--1460 keV, by detecting the prompt $\ensuremath{\gamma}$ rays from the reaction. An extensive $R$-matrix analysis was performed, utilizing all modern literature capture data, as well as elastic scattering data, which are important in constraining some $R$-matrix parameters.Results: The new experimental data agree very well with the modern literature data. The final result from the $R$-matrix fit gives a zero-energy $S$ factor of $S(0)=0.554(20)$ keV b. A table with the newly calculated reaction rate is given.Conclusions: The simultaneous $R$-matrix analysis of the ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\gamma})}^{7}$Be and ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\alpha})}^{3}$He channels yielded a reliable fit, consistent with all the included experimental data sets. In order to further constrain the reaction rate within the $R$-matrix framework, additional high-energy capture data, $\ensuremath{\gamma}$-ray angular distributions, and the inclusion of other relevant reaction channels are necessary.

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