Direct measurements of the $$^{12}$$C+$$^{12}$$C reactions cross-sections towards astrophysical energies
L. Morales-Gallegos, M. Aliotta, L. Gialanella, A. Best, C. G. Bruno, R. Buompane, T. Davinson, M. De Cesare, A. Di Leva, Antonio D’Onofrio, J. G. Duarte, L. R. Gasques, G. Imbriani, Giuseppe Porzio, D. Rapagnani, M. Romoli, F. Terrasi
Abstract
Abstract Carbon fusion reactions $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>12</mml:mn> </mml:msup> </mml:math> C( $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>12</mml:mn> </mml:msup> </mml:math> C,p) $$^{23}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>23</mml:mn> </mml:msup> </mml:math> Na and $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>12</mml:mn> </mml:msup> </mml:math> C( $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>12</mml:mn> </mml:msup> </mml:math> C, $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> ) $$^{20}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>20</mml:mn> </mml:msup> </mml:math> Ne play a key role in the evolution of massive stars and in explosive scenarios such as type-Ia supernovae and super-bursts in binary stars. A direct determination of their cross sections is extremely challenging and discrepancies exist between different data sets in the literature. Here we report the results of a direct measurement performed at the CIRCE Tandem Accelerator Laboratory in Caserta (Italy), using $$\varDelta E-E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>E</mml:mi> <mml:mo>-</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> detectors for unambiguous charge identification. Cross sections were measured in the energy range $$E_{\mathrm{c.m.}} =2.51-4.36$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>.</mml:mo> <mml:mi>m</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.51</mml:mn> <mml:mo>-</mml:mo> <mml:mn>4.36</mml:mn> </mml:mrow> </mml:math> MeV with energy steps between 10 and 25 keV in the centre of mass. To our knowledge these represent the finest energy steps to date. Results are presented in the form of partial and summed astrophysical $${\tilde{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>S</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> -factors for individual proton- and $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -particle channels. Branching ratios of individual proton- and $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -particle groups were found to vary significantly with energy. Angular distributions, albeit limited to three angles, were also found to be non-isotropic, which could be a potential explanation for the discrepancies observed among different data sets. Further efforts are ongoing to extend measurements to lower energies.