Possible Configurations for the First Excited State in 17-F-9

In summary, the conversation discusses determining the spin-parity of excited states, specifically for the ground state and first excited state of the radioisotope 17-F-9. Two possible configurations for the first excited state are suggested, and the answer in the back provides explanations for how the spin-parity is determined in both cases. The conversation also includes questions about how the spin-parity is determined in the second case, and how the parities of the protons and neutrons are multiplied to give an overall parity.
  • #1
Warr
120
0
I am confused how to determine the spin / parity of excited states.

In my textbook, one of the questions states:

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The ground state of the radioisotope 17-F-9 has spin-parity j_P = (5/2)+ and the first excited state has j_P=(1/2)-. Suggest two possible configurations for the latter state.

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Here is the answer in the back:

The configuration of the ground state is:

protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2(1d_\frac{5}{2})[/tex]
neutrons:[tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2[/tex]

To get j_P= (1/2)-, one could promote a p_1/2 proton to the d_5/2 shell giving

protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^{-1}(1d_\frac{5}{2})^2[/tex]

Then by the pairing hypothesis, the two d_5/2 protons could give j_P = 0+ so that the total spin-parity would be determined by the unpaired p_1/2 neutron (j_P=(1/2)-).

Alternatively, one of the p_3/2 protons could be promoted to the d_5/2 shell, giving

protons: protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^{-1}(1p_\frac{1}{2})^2(1d_\frac{5}{2})^2[/tex]

and the two d_5/2 protons could combine to give j_P = 2+, so that when this combines with the single unpaired j_P = 3/2- proton, the overall spin is j_P = 1/2-

-----------------------

So here are two things I am confused about:

Firstly, how can the two d_5/2 protons combine to have j_P = 0+ in the first case and j_P = 2+ in the second case?

Secondly, how is it that in the second case, the spin-parity ends up being j_P = 1/2-. Is it that the parities of the two are multiplied (ie the parity of the two d_5/2 protons is 1+ and the parity of the unpaired p_3/2 proton is 1-, giving an overall parity of 1-, and then the spin is 2 - 3/2 = 1/2? I don't really get how that works).

If I can understand this I may be able to even get started on the homework.
 
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  • #2
you have already made this thread in Nuclear- and particle physics section. Double posting is not ok!
 

What is the Shell Model Spin-parity?

The Shell Model Spin-parity is a quantum mechanical model used to describe the distribution of protons and neutrons in the atomic nucleus. It takes into account the energy levels of the nucleons and their interactions to determine the overall spin and parity of the nucleus.

How does the Shell Model Spin-parity work?

The Shell Model Spin-parity is based on the concept of energy levels, similar to the electron shell structure in atoms. Nucleons (protons and neutrons) are arranged in energy levels or shells, with different amounts of energy required to move between them. The model also takes into account the strong and weak nuclear forces between nucleons, which can affect the overall spin and parity of the nucleus.

What is the significance of Shell Model Spin-parity?

The Shell Model Spin-parity is important because it helps explain the behavior and properties of atomic nuclei. It can predict the energy levels and stability of different nuclei, as well as provide insight into nuclear reactions and decays. It also helps in understanding the structure of heavy and unstable nuclei.

What are the limitations of the Shell Model Spin-parity?

One limitation of the Shell Model Spin-parity is that it does not take into account the effects of nuclear forces beyond the nearest neighbors. It also does not consider the effects of nuclear shape or deformation. Additionally, the model becomes increasingly complex for larger nuclei, making calculations more challenging.

How is the Shell Model Spin-parity used in research?

The Shell Model Spin-parity is a widely used tool in nuclear physics research. It is used to study the properties of different nuclei and to understand the underlying structure of the nucleus. It is also used in theoretical calculations and simulations to predict the behavior of nuclei in different scenarios, such as nuclear reactions or decays.

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