We study the astrophysical reaction rate for the formation of ^ { 9 } Be through the three body reaction \alpha ( \alpha n, \gamma ) .
This reaction is one of the key reactions which could bridge the mass gap at A = 8 nuclear systems to produce intermediate-to-heavy mass elements in alpha- and neutron-rich environments such as r-process nucleosynthesis in supernova explosions , s-process nucleosynthesis in asymptotic giant branch ( AGB ) stars , and primordial nucleosynthesis in baryon inhomogeneous cosmological models .
To calculate the thermonuclear reaction rate in a wide range of temperatures , we numerically integrate the thermal average of cross sections assuming a two-steps formation through a metastable ^ { 8 } Be , \alpha + \alpha \rightleftharpoons ^ { 8 } Be ( n , \gamma ) ^ { 9 } Be .
Off-resonant and on-resonant contributions from the ground state in ^ { 8 } Be are taken into account .
As input cross section , we adopt the latest experimental data by photodisintegration of ^ { 9 } Be with laser-electron photon beams , which covers all relevant resonances in ^ { 9 } Be .
Experimental data near the neutron threshold are added with \gamma -ray flux corrections and a new least-squares analysis is made to deduce resonance parameters in the Breit-Wigner formulation .
Based on the photodisintegration cross section , we provide the reaction rate for \alpha ( \alpha n, \gamma ) ^ { 9 } Be in the temperature range from T _ { 9 } =10 ^ { -3 } to T _ { 9 } =10 ^ { 1 } ( T _ { 9 } is the temperature in units of 10 ^ { 9 } K ) both in the tabular form and in the analytical form for potential usage in nuclear reaction network calculations .
The calculated reaction rate is compared with the reaction rates of the CF88 and the NACRE compilations .
The CF88 rate , which is based on the photoneutron cross section for the 1/2 ^ { + } state in ^ { 9 } Be by Berman et al . , is valid at T _ { 9 } > 0.028 due to lack of the off-resonant contribution .
The CF88 rate differs from the present rate by a factor of two in a temperature range T _ { 9 } \geq 0.1 .
The NACRE rate , which adopted different sources of experimental information on resonance states in ^ { 9 } Be , is 4–12 times larger than the present rate at T _ { 9 } \leq 0.028 , but is consistent with the present rate to within \pm 20 \% at T _ { 9 } \geq 0.1 .