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

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1. Feb 19, 2017

### Bobjovi

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. Feb 19, 2017

### TSny

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
3. Jun 22, 2017

### Abhishek SandT

I think your asymmetric Energy term is an error in the above mentioned B.E formula ..
replace (Z-N) By (N-Z)