s-process nucleosynthesis in low-mass AGB stars by the $$^{13}$$C($$\alpha $$,n)$$^{16}$$O neutron source

Abstract In this review we outline the temporal growth of our knowledge on slow neutron captures (the so-called s-process), concentrating on its main part occurring during the final stages of stellar evolution for low or intermediate-mass stars when they approach for the second time the Red Giant Branch and are therefore called Asymptotic Giant Branch , or AGB, stars. In particular, we focus our attention on how, in this field, studies passed from a first era of inquiries based on nuclear systematics (now often referred to as the the phenomenological approach ), to numerical nucleosynthesis computations performed in stellar codes. We then discuss how these last were forced, by observational constraints, to almost abandon, for the synthesis of nuclei between Sr and Pb (i.e. the main component ), the rather naturally activated $$^{22}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>22</mml:mn> </mml:mmultiscripts> </mml:math> Ne( $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> ,n) $$^{25}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>25</mml:mn> </mml:mmultiscripts> </mml:math> Mg neutron source (operating efficiently at T $${\gtrsim }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>≳</mml:mo> </mml:math> 3.5 $${\cdot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>·</mml:mo> </mml:math> 10 $$^8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>8</mml:mn> </mml:mmultiscripts> </mml:math> K, i.e. 30 keV, and producing a neutron density $$n_n \gtrsim 5 \cdot 10^8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>≳</mml:mo> <mml:mn>5</mml:mn> <mml:mo>·</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>8</mml:mn> </mml:msup> </mml:mrow> </mml:math> $$\hbox {cm}^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>cm</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> ). This implied considering the alternative reaction $$^{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>13</mml:mn> </mml:mmultiscripts> </mml:math> C( $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> ,n) $$^{16}$$ <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, that can be activated locally after each of the recurring mixing episodes from the envelope (collectively referred to as the Third Dredge Up , or TDU ). The mentioned crucial reaction occurs at a relatively low temperature ( $$T \simeq 8-9 \cdot 10^7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>8</mml:mn> <mml:mo>-</mml:mo> <mml:mn>9</mml:mn> <mml:mo>·</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>7</mml:mn> </mml:msup> </mml:mrow> </mml:math> K., i.e. less than 8 keV), in the time intervals separating two subsequent thermal instabilities of the He shell (also named Thermal Pulses , or TP ). The layers where $$^{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>13</mml:mn> </mml:mmultiscripts> </mml:math> </jats:alternativ