Nuclear Shell Model - Spin-parity

• Warr
In summary, the question asks for two possible configurations for the first excited state of the radioisotope 17-F-9, which has a spin-parity of (1/2)-. One possible configuration is to promote a p_1/2 proton to the d_5/2 shell, giving a total spin-parity of j_P = 0+ due to the pairing hypothesis. Another possibility is to promote a p_3/2 proton to the d_5/2 shell, resulting in a total spin-parity of j_P = 2+. This combines with the unpaired p_3/2 proton to give a final spin-parity of (1/2)-. The overall parity is determined by multiplying the
Warr
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: $$(1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2(1d_\frac{5}{2})$$
neutrons:$$(1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2$$

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

protons: $$(1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^{-1}(1d_\frac{5}{2})^2$$

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: $$(1s_\frac{1}{2})^2(1p_\frac{3}{2})^{-1}(1p_\frac{1}{2})^2(1d_\frac{5}{2})^2$$

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-

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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.

This has been posted twice, not ok!

Yes parties are multiplied.

And according to angular momenta addition , you can combine two J = 5/2 to a total J by anything from 0 to 5.

Sorry about the 2x post. I posted here first, and then figured this might not be quite suitable in the homework forum.

there are people that moves threads etc. So next time, just don't do anything.

One further question for this example:

Since the resulting j_P = 2+ and j_P = 3/2- can result in (2-3/2)=(1/2)-, does that mean they can result in the range (5/2)- to (1/2)- ?

I don't understand you here. A single particle can not have an integer spin in the shell model.

What I meant is, can it have either (5/2)-, (3/2)- or (1/2)- ?

Coupling angular momenta j1 = 2 with j2 = 3/2 can give you:

7/2, 5/2, 3/2, 1/2

Parity is negative, since +*- = -

Alright, thanks again.

1. What is the Nuclear Shell Model?

The Nuclear Shell Model is a theoretical model used to explain the structure and behavior of atomic nuclei. It describes how protons and neutrons are arranged in the nucleus and how they interact with each other.

2. What is Spin-parity in the context of the Nuclear Shell Model?

Spin-parity refers to the intrinsic angular momentum (spin) and intrinsic parity (odd or even symmetry) of a nucleus. In the Nuclear Shell Model, spin-parity is used to classify and label different energy levels and states of the nucleus.

3. How is the Nuclear Shell Model used in nuclear physics?

The Nuclear Shell Model is used to predict and explain the properties and behavior of atomic nuclei, such as their stability, energy levels, and nuclear reactions. It is also used to guide and interpret experiments in nuclear physics.

4. What is the significance of the magic numbers in the Nuclear Shell Model?

The magic numbers in the Nuclear Shell Model refer to the specific numbers of protons or neutrons that result in especially stable and symmetric nuclei. These numbers (2, 8, 20, 28, 50, 82, 126) correspond to completely filled shells of protons or neutrons, leading to increased nuclear stability.

5. How has the Nuclear Shell Model evolved over time?

The Nuclear Shell Model has evolved over time as our understanding of nuclear physics has advanced. Early versions of the model were based on empirical observations, but with advancements in mathematical and computational techniques, it has become more precise and predictive. Additionally, the model has been expanded to include more complex interactions between nucleons, such as pairing and residual interactions.

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