Energy Levels: Why Do Spacings Get Smaller as Excitation Increases?

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SUMMARY

The discussion focuses on the phenomenon of decreasing energy level spacings in nuclear energy levels as excitation increases, specifically referencing Nickel-64 and its magic number of protons. Participants highlight the relevance of the nuclear shell model and the role of quantum numbers, such as principal quantum number (n) and orbital angular momentum (l), in determining energy states. As excitation energy increases, the interactions become weaker, leading to smaller differences between energy levels. This behavior is consistent with the principles of quantum mechanics and the harmonic oscillator model.

PREREQUISITES
  • Nuclear shell model
  • Quantum mechanics principles
  • Understanding of quantum numbers (n, l, m, s)
  • Basic knowledge of energy levels in atomic and nuclear physics
NEXT STEPS
  • Study the nuclear shell model in detail
  • Explore the implications of magic numbers in nuclear physics
  • Learn about the harmonic oscillator model in quantum mechanics
  • Investigate the effects of weak interactions on energy levels
USEFUL FOR

Students of nuclear physics, physicists specializing in quantum mechanics, and anyone interested in the behavior of energy levels in atomic and nuclear systems.

Martin89
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TL;DR
Why does nuclear energy level spacing decrease as the nucleus gets more excited?
Nuclear energy levels.png


Hi All. For the above energy level diagram, why do the energy levels spacings proceed to get smaller and smaller as the excitation energy increases?
 
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Gaussian97 said:
Have you ever read about Bohr model?
Yes, but I'm asking about nuclear energy levels not atomic energy levels
 
Oh, sorry my fault, I didn't read correctly 😅 I apologise. Have you ever read about the nuclear shell model? It may be a good start point.
 
Yeah I've been studying it this semester. I believe this particular diagram is for Nickel-64 which has a magic number of protons which explains why the spacing between the ground state and the first excited state is so large. The gaps in the higher levels are due to magic numbers also, but I don't know how to explain why the spacings get smaller?
 
This may be a little clumsy. Consider the principle quantum number n. As it increases the other available quantum number as orbital angular momentum l increase along with its various projections m . These quantum numbers in the presence of relevant interactions along with the spin s lead to different energy states whose differences are smaller (closer) because these interactions are relatively weak.
 
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The levels are at equal intervals in a harmonic oscillator.
If in a nucleus, excited levels are at decreasing intervals, this suggests that the excited levels reach potential tails of some sort.
 
gleem said:
This may be a little clumsy. Consider the principle quantum number n. As it increases the other available quantum number as orbital angular momentum l increase along with its various projections m . These quantum numbers in the presence of relevant interactions along with the spin s lead to different energy states whose differences are smaller (closer) because these interactions are relatively weak.

Thanks for the reply, I guess that makes some sense
 

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