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Semi-empirical mass formula: most stable isobar for odd A

  1. Feb 19, 2017 #1
    1. The problem statement, all variables and given/known data
    Using the Semi-empirical Mass Formula show that for fixed odd atomic mass
    number, A, the most stable isobar has a neutron to proton ratio given by
    N/Z = 1 + aCA2/3/(2aA)

    2. Relevant equations
    B(A,Z) = aV A − aS A2/3 − aCZ2A-1/3 − aA(Z − N)2/A + pairing term

    3. The attempt at a solution
    I computed dB/dZ = 0 because the most stable means the one with the maximum binding energy. I get the formula but missing the factor of a half. The fact A is odd means that we don't have a pairing term.

    My question is where does the half come from? What am I doing wrong?
     
  2. jcsd
  3. Feb 19, 2017 #2

    TSny

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    Gold Member

    We would need to see your computation of dB/dZ to find your mistake. One thing to keep in mind, you cannot treat N as constant while taking the derivative with respect to Z.
     
    Last edited: Feb 19, 2017
  4. Jun 22, 2017 #3
    I think your asymmetric Energy term is an error in the above mentioned B.E formula ..
    replace (Z-N) By (N-Z)
     
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