The $$^{12}$$C$$(\alpha ,\gamma )^{16}$$O reaction, in the laboratory and in the stars

Abstract The evolutionary path of massive stars begins at helium burning. Energy production for this phase of stellar evolution is dominated by the reaction path 3 $$\alpha \rightarrow ^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:msup> <mml:mo>→</mml:mo> <mml:mn>12</mml:mn> </mml:msup> </mml:mrow> </mml:math> C $$(\alpha ,\gamma )^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <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>16</mml:mn> </mml:msup> </mml:math> O and also determines the ratio of $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C/ $$^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>16</mml:mn> </mml:mmultiscripts> </mml:math> O in the stellar core. This ratio then sets the evolutionary trajectory as the star evolves towards a white dwarf, neutron star or black hole. Although the reaction rate of the 3 $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> process is relatively well known, since it proceeds mainly through a single narrow resonance in $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C, that of the $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C $$(\alpha ,\gamma )^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <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>16</mml:mn> </mml:msup> </mml:math> O reaction remains uncertain since it is the result of a more difficult to pin down, slowly-varying, portion of the cross section over a strong interference region between the high-energy tails of subthreshold resonances, the low-energy tails of higher-energy broad resonances and direct capture. Experimental measurements of this cross section require herculean efforts, since even at higher energies the cross section remains small and large background sources are often present that require the use of very sensitive experimental methods. Since the $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C $$(\alpha ,\gamma )^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <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>16</mml:mn> </mml:msup> </mml:math> O reaction has such a strong influence on many different stellar objects, it is also interesting to try to back calculate the required rate needed to match astrophysical observations. This has become increasingly tempting, as the accuracy and precision of observational data has been steadily improving. Yet, the pitfall to this approach lies in the intermediary steps of modeling, where other uncertainties needed to model a star’s internal behavior remain highly uncertain.