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Nuclear fusion cross sections

  1. Jul 14, 2011 #1

    I am inquiring as to what the theorem function is for the mean product of cross section and velocity for stellar fusion reactions? [tex]\langle \sigma v \rangle[/tex]

    Mean product of nuclear fusion cross section and velocity. [tex]\langle \sigma v \rangle[/tex]

    Maxwell–Boltzmann probability density function:
    [tex]f(v) = \sqrt{\frac{2}{\pi}\left(\frac{m}{kT}\right)^3}\, v^2 \exp \left(- \frac{mv^2}{2kT}\right)[/tex]

    The mean speed is the mathematical average of the speed distribution:
    [tex]\langle v \rangle = \int_0^{\infty} v \, f(v) \, dv = \sqrt{\frac{8kT}{\pi m}}[/tex]

    For a mono-energy beam striking a stationary target, the cross section probability is:
    [tex]P = n_2 \sigma_2 = n_2 \pi r_2^2[/tex]

    And the reaction rate is:
    [tex]f = n_1 n_2 \sigma_2 v_1[/tex]
    Reactant number densities:
    [tex]n_1, n_2[/tex]
    Target total cross section:
    [tex]\sigma_2 = \sigma_\text{A} + \sigma_\text{S} + \sigma_\text{L} = \pi r_2^2[/tex]
    Mono-energy beam velocity:
    Aggregate area circle radius:

    Stellar nuclear fusion reaction rate (fusions per volume per time):
    [tex]f = n_1 n_2 \langle \sigma v \rangle[/tex]

    What is the theorem and solution for the mean cross section in stellar nuclear fusion? [tex]\langle \sigma \rangle[/tex]

    Is the mean cross section the mathematical average of the cross section distribution?:
    [tex]\langle \sigma \rangle = \int_0^{\infty} \sigma \, f(\sigma) \, d\sigma = \, \text{???}[/tex]

    http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution" [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
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