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Nucleus Ratio of nucleons between surface and core

  1. May 21, 2010 #1
    1. The problem statement, all variables and given/known data

    We suppose the nucleon density of a spherical nucleus where r<R1 is constant, and where R1<r<R2 the density linearly decreases to 0 at R2.

    We call the surface nucleons (Number Ns) the number of nucleons contained in the volume R1<r<R2 and core nucleons (Nc) the number of nucleons in the volume r<R1.

    It is easy to represent graphically the density (ρ) from 0 to R2 however,

    to calculate the proportion of surface nucleons as a function of R2/R1 for Al27 and Po219 is proving more difficult.


    2. Relevant equations

    R1 = 1.1 A^1/3 -1.5
    R2 = 1.1 A^1/3 +1.5

    (the +/- 1.5 is not in the power!)

    also

    a^3-b^3 = (a-b).(a^2-b^2+ab)

    and

    a^4-b^4 = (a-b).(a^3-b^3+ab.(a+b))


    3. The attempt at a solution


    Nc + Ns = A

    (ρ)c = Nc / V = 3Nc / 4π R1^3

    (ρ)s = Ns / V = 3Ns / 4π ∫1/R^3 dR where the integral is from R1 to R2



    Ns/N is the fraction being looked for and that is where we are stuck.

    Were having problems relating Ns to R

    If anyone could guide us through this it would be greatly appreciated.


    Thanks


    Ash + Aaron
     
  2. jcsd
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