The triple-alpha reaction proceeds through the Hoyle state

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear astrophysics and applications · Nuclear astrophysics and applications

Stars from the Inside, Ch Thermonuclear energy generation: reaction rates, burning stages and the elements they make

Problem

The triple-alpha reaction proceeds through the Hoyle state, which sits

Q' = 0.380\,\mathrm{MeV}

above three free alpha particles, so that

r_{3\alpha} \propto n_\alpha^3 T^{-3}e^{-Q'/k_BT}\Gamma_{\rm rad}

and

\nu = Q'/k_BT - 3

. ((a)) Evaluate

\nu

T = 2\times10^{8}\,\mathrm{K}

. ((b)) By what factor does the rate rise for a

5\%

increase in

T

at this temperature?