# Energy component of a nucleus

#### Bestfrog

1. 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?

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#### mfb

Mentor
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

Mentor
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 $p=0$.

Mentor
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

Mentor
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?

"Energy component of a nucleus"

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