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

[Bobjovi]

Homework Statement

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 + a_CA^2/3/(2a_A)

Homework Equations

B(A,Z) = a_V A − a_S A^2/3 − a_CZ²A^-1/3 − a_A(Z − N)²/A + pairing term

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?

 

[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.

 

[Abhishek SandT]

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