What influences the binding energy of nucleons in a nucleus?

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Homework Help Overview

The discussion revolves around the binding energy of nucleons in a nucleus, specifically focusing on the strong interaction's contribution to the energy of the nucleus as described by a formula involving parameters related to the number of nucleons (A) and protons (Z).

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the parameters r and p in the energy formula, considering the constraints of the strong interaction. Questions arise about how varying the number of protons and neutrons affects the binding energy and the implications of contact forces in this context.

Discussion Status

Several hints have been provided to guide the exploration of the problem, with participants attempting to derive values for r and p based on specific cases. There is an ongoing examination of the implications of the strong interaction and how it applies to nucleons in the nucleus.

Contextual Notes

Participants express uncertainty about how to apply the given constraints and the theoretical background necessary for the problem. The discussion reflects a need for clarification on the nature of the strong interaction and its effects on binding energy.

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?
 
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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?
 
I don't know how to use the constraints, maybe I miss some theory..
 
See the two hints I gave.
 
mfb said:
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 said:
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
 
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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