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

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Discussion Overview

The discussion revolves around the phenomenon of energy level spacings in nuclear energy levels, specifically why these spacings decrease as excitation energy increases. Participants explore theoretical frameworks and models related to nuclear physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the decreasing spacings of energy levels with increasing excitation energy.
  • Another participant suggests the relevance of the Bohr model, but clarifies that the discussion pertains to nuclear energy levels rather than atomic ones.
  • A participant mentions studying the nuclear shell model and references Nickel-64, noting that the large spacing between the ground state and the first excited state is due to magic numbers, but expresses uncertainty about the decreasing spacings at higher levels.
  • One participant proposes that as the principal quantum number n increases, the associated quantum numbers (orbital angular momentum l and its projections m) also increase, leading to smaller differences in energy states due to relatively weak interactions.
  • Another participant compares the energy levels in a nucleus to those in a harmonic oscillator, suggesting that decreasing intervals in excited levels indicate reaching potential tails.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the reasons behind the decreasing energy level spacings, with no consensus reached on a definitive explanation. Some ideas are explored, but uncertainty remains regarding the underlying mechanisms.

Contextual Notes

Participants reference different models and concepts, such as the nuclear shell model and harmonic oscillators, but the discussion does not resolve the complexities or assumptions involved in these frameworks.

Who May Find This Useful

Individuals interested in nuclear physics, energy level theories, and the nuclear shell model may find this discussion relevant.

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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