Nuclear Spin of Sodium 23 Explained

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    Sodium Spin
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Discussion Overview

The discussion centers on the nuclear spin of Sodium-23, exploring the calculations and theoretical models used to determine its spin value. Participants examine the shell model of nucleons and consider factors such as nuclear deformation and pairing effects.

Discussion Character

  • Technical explanation, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant calculates the nuclear spin of Sodium-23 using the shell model, arriving at a predicted spin of 1/2, while the literature states it is 3/2, prompting a request for clarification.
  • Another participant suggests that the shell model might predict a spin of 5/2 and mentions that nuclear deformation could explain discrepancies between theoretical predictions and experimental results.
  • A different participant expresses difficulty in finding references on nuclear deformation and shares a similar experience with Titanium-47, where their calculation also differed from established values.
  • A quote from Burcham is presented, indicating that the observed spin of Sodium-23 can be explained by the coupling of equivalent nucleons or by nuclear deformation.
  • One participant critiques the shell model's predictive limitations, arguing that it oversimplifies the situation by only allowing for specific unpaired nucleons and does not account for the interactions between nucleons that can alter energy levels.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the shell model and its predictions for nuclear spin, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Limitations include the dependence on the shell model's assumptions and the potential influence of nuclear deformation, which are not fully explored in the discussion.

bluesquare
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i am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and neutrons separately, I found 3 protons in the 1d5/2 sub-shell and 4 neutrons in the same 1d5/2 sub-shell. So because of two pairings, neutrons give spin as 0 and because of a pairing in protons, one proton is left out which should give spin as 1/2. But in the book its, I=3/2. Please can anyone explain the fact how the spin of Na nucleus is 3/2. Thank you in advance.
 
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Hi bluesquare,

Looking at wikipedia (http://en.wikipedia.org/wiki/File:Shells.png), would the shell model not lead to a spin of 5/2?
However, I remember that deformation of the nuclei can re-order the level.
Could that not be an explanation why the sheel model does not lead to the experimental spin?

m
 
Yeah I know that we have deformities but I am unable to find it anywhere. Can you site any reference. Meanwhile i tried to calculate the spin of Ti -47 and from the shell model i got the spin as 1f7/2.. But when i checked in it is actually 5/2..So i am like ...

thank you for the reply though.
 
"For 23Na, the observed spin must be explained by coupling of equivalent nucleons or by deformation." -- Burcham
 
The approach you are using predicts that the only allowed nuclear spins are 0, 1/2 and 1 - you allow exactly one unpaired nucleon per shell. This is not borne out by data, so the shell model must be oversimplified. The oversimplification is that the shells in fact do depend on the other nuclei, and that moves the energy levels around, so you have the shell order change slightly.
 

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