# 恆星核合成

（重定向自恒星核合成

## 反應速度

"A" 和 "B" 物種之間的每體積反應速率，是由數位密度 "n" "a"、"B" 給出的：

${\displaystyle {\frac {r}{V}}=n_{A}\,n_{B}\,\langle \sigma (v)\,v\rangle }$

${\displaystyle \sigma (E)={\frac {S(E)}{E}}e^{-{\sqrt {\frac {E_{G}}{E}}}}}$

${\displaystyle {\frac {r}{V}}=n_{A}\,n_{B}\int _{0}^{\infty }{\frac {S(E)}{E}}\,e^{-{\sqrt {\frac {E_{G}}{E}}}}{\frac {2}{{\sqrt {\pi }}(kT)^{3/2}}}E^{1/2}e^{-E/kT}\,{\sqrt {\frac {2E}{m_{R}}}}dE}$

${\displaystyle {\frac {\partial }{\partial E}}\left(-{\sqrt {\frac {E_{G}}{E}}}-{\frac {E}{kT}}\right)\,=\,0}$

${\displaystyle E_{0}=\left({\sqrt {E_{G}}}\,kT/2\right)^{2/3}}$

${\displaystyle e^{-{\frac {E}{kT}}-{\sqrt {\frac {E_{G}}{E}}}}\approx e^{-{\frac {3E_{0}}{kT}}}\cdot exp\left(-{\frac {(E-E_{0})^{2}}{4E_{0}kT/3}}\right)}$

${\displaystyle {\frac {r}{V}}\approx n_{A}\,n_{B}\,{\frac {4{\sqrt {2}}}{\sqrt {3m_{R}}}}\,{\sqrt {E_{0}}}{\frac {S(E_{0})}{kT}}e^{-{\frac {3E_{0}}{kT}}}}$

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