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Energy component of a nucleus

  • Thread starter Bestfrog
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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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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..
 
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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##.
 

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
 
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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?
 

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