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

[Martin89]

TL;DR Summary

Why does nuclear energy level spacing decrease as the nucleus gets more excited?

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?

 

[Gaussian97]

Have you ever read about Bohr model?

 

[Martin89]

Have you ever read about Bohr model?

Yes, but I'm asking about nuclear energy levels not atomic energy levels

 

[Gaussian97]

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.

 

[Martin89]

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?

 

[gleem]

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.

 

[snorkack]

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.

 

[Martin89]

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