What influences the binding energy of nucleons in a nucleus?

[Bestfrog]

Homework Statement

The component of nucleus' energy due to the strong interaction (with $Z,A >>1$) can be written as $U_f = E_f A^r Z^p$, ($E_f$ is a constant with the dimension of a energy). Find $r,p$ knowing that
(i) strong interaction doesn't distinguish between protons and neutrons
(ii) strong interaction is a force of contact
Can you give me a hint to start?

 

[mfb]

Did you try different values and see if they fit to the constraints?

In particular, what happens if you keep A constant and change Z?

What can you say about the energy per nucleus if there is no long-range contribution?

 

[Bestfrog]

I don't know how to use the constraints, maybe I miss some theory..

 

[mfb]

See the two hints I gave.

 

[Bestfrog]

See the two hints I gave.

I have an idea. If $N$ is the number of neutrons, then $U_f = E_f (Z+N)^r Z^p$. For the constraint (i) if I first put $Z=1$ and so $N=1$, then I put $Z=2$ with $Z+N$ constant (N=0), I have $$E_f 2^r \cdot 1 = E_f 2^r 2^p$$ so $p=0$.

 

[mfb]

Right.

 

[Bestfrog]

What can you say about the energy per nucleus if there is no long-range contribution?

Can you explain this in other words? I don't get what you say

 

[mfb]

If nucleons are only influenced by nucleons directly around them, and every nucleon always has nucleons directly around it, what can influence the binding energy for this particular nucleon?