Predicting spin and parity of excited states from shell mode

In summary, the conversation discusses the prediction of spin and parity for F(A=17,Z=9) in its ground state and first two excited states using the shell model. The ground state is determined to be (5/2)^+ by promoting one proton from the (1p 1/2) level. The first excited state can have a spin of either (1/2)^- or (0)^+ depending on whether the spin and parity come from the hole created or the new filled level. The second excited state can have a spin of (2)^-, (3)^-, (0)^+, (1)^+, (2)^+, (3)^+, (4)^+ or (5)^+ depending on the same
  • #1
pondzo
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Homework Statement

Consider the following example from a previous exam. We are to predict the spin and parity for F(A=17,Z=9), Florine, in the ground state and the first two excited states using the shell model.

Ground state:
Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2

Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 (1d 5/2)^1

Thus J^P = (5/2)^+

First excited state: Promote one proton from the (1p 1/2) level
Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2

Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^1 (1d 5/2)^2

Does the spin and parity come from (a) the hole created or (b) the new filled level. If (a) then J^P = (1/2)^-. If (b) then J^P = (0)^+.
Second excited state: Promote one neutron from the (1p 1/2) level
Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^1 (1d 5/2)^1

Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 (1d 5/2)^1

Does the spin and parity come from (a) the hole created or (b) the new filled level. If (a) then the possible J values range from |1/2 - 5/2| to (1/2 + 5/2) in steps of one, so J=2 or 3. The parity multiplies so we have a minus from the l=1 neutron and a positive from the l=2 proton thus parity is minus and J^P = (2)^- or (3)^-. If (b) then J ranges from |5/2 - 5/2| to (5/2 + 5/2) in steps of one so J = 0,1,2,3,4 or 5. The parities both come from the same l level (d) so is positive. Thus J^P = (0)^+, (1)^+, (2)^+, (3)^+, (4)^+ or (5)^+.

So how do we get the spin's and parities from the excited states? Is it determined by the hole created or the new excited level?

Also how do I know which would be the first excited level and which would be the second? And is there a way to figure out which levels get filled up first when calculating the ground state, or should I just remember the order of the levels?

We are not expected to know the Nordheim rules.
 
  • #3
I have come to the conclusion that any unpaired nucleons will contribute to the spin/parity, not just the ones from the hole created or the new level filled. And if it so happens that an excited state yields three or more unpaired nucleons, then the shell model is no longer reliable in predicting the spin and parity of the nucleus.
 

1. What is "shell model" in the context of predicting spin and parity of excited states?

The shell model is a theoretical framework used to describe the arrangement of protons and neutrons in an atomic nucleus. It is based on the idea that nucleons (protons and neutrons) occupy different energy levels, or "shells", within the nucleus, similar to how electrons occupy different energy levels in an atom. This model helps predict the behavior and properties of nuclei, including the spin and parity of excited states.

2. How does the shell model help predict the spin and parity of excited states?

The shell model takes into account the interactions between individual nucleons and the overall nuclear structure to predict the spin and parity of excited states. The number of nucleons in each shell, as well as their energy levels and interactions, contribute to the overall spin and parity of the nucleus. By understanding the arrangement of nucleons within the nucleus, scientists can make predictions about the spin and parity of excited states.

3. Can the shell model accurately predict the spin and parity of all excited states?

The shell model is a powerful tool, but it is not perfect. While it can accurately predict the spin and parity of many excited states, there are some cases where it may fall short. These may be due to complex interactions between nucleons or the presence of other factors that the shell model does not account for. In these cases, other theoretical models or experimental data may be needed to accurately predict the spin and parity of excited states.

4. How does predicting spin and parity of excited states from shell model impact our understanding of nuclear structure?

Predicting the spin and parity of excited states from the shell model helps us gain a deeper understanding of the structure of atomic nuclei. By studying the behavior and properties of excited states, we can learn about the forces that hold the nucleus together and the arrangement of nucleons within it. This information can also be used to study other nuclear phenomena, such as nuclear reactions and decays.

5. Are there any limitations or challenges in using the shell model to predict spin and parity of excited states?

While the shell model is a valuable tool, there are some limitations and challenges in its use. One limitation is that it becomes increasingly complex and difficult to apply when dealing with larger nuclei or those with more complex structures. Additionally, the shell model may not accurately predict the spin and parity of excited states in certain cases, as mentioned earlier. However, ongoing research and advancements in theoretical models and experimental techniques are helping to address these challenges and improve our understanding of nuclear structure.

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