Shell Model: Filling g9/2 Shell w/ 5 Protons

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SUMMARY

The discussion focuses on the filling of the g9/2 shell with 5 protons in the shell model of nuclear structure. It is established that the Pauli exclusion principle allows the first four protons to occupy the shell in anti-parallel pairs, while the fifth proton can occupy the shell in either an up or down spin state. The participant seeks clarification on the assumptions necessary for calculating the state of minimal energy for the last proton, specifically questioning the validity of the independent particle model in this context.

PREREQUISITES
  • Understanding of the shell model in nuclear physics
  • Familiarity with the Pauli exclusion principle
  • Knowledge of proton configurations in nuclear shells
  • Basic concepts of nuclear energy states
NEXT STEPS
  • Research the implications of the Pauli exclusion principle in nuclear configurations
  • Study the independent particle model in nuclear physics
  • Learn about energy minimization techniques for nucleon configurations
  • Explore the concept of spin states in nuclear shells
USEFUL FOR

Students and researchers in nuclear physics, particularly those studying nuclear shell models and proton configurations, will benefit from this discussion.

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Homework Statement


How do 5 protons fill a g9/2 shell in the shell model?
There are 10 spots in the g9/2 shell.

Homework Equations





The Attempt at a Solution


Pauli principle dictates the first four to be in anti-parallel pairs. But the last can be either up or down. Am I missing something or is this really all there is to it?
 
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I will try to go a little further in hope that someone picks it up and can help me.
I think I need to find the state of minimal energy for the last neutron. What are the assumptions I need to make to calculate this? Is it good enough to assume the complete independent particle model?

I really could use some help on this one. I can do the opposite, get total spin of nucleus in the groundstate by the nucleonconfiguration, but the reverse is not so clear for me...
 
I am still wondering btw... :p
 

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