Why protons and neutrons have spins?

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Discussion Overview

The discussion revolves around the spins of protons and neutrons, specifically how these spins can be explained in terms of their quark composition. Participants explore the quantum mechanical principles underlying spin addition and the complexities involved in understanding nucleon spin structure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants state that protons and neutrons are baryons composed of quarks, with each quark having a spin of 1/2.
  • One participant mentions that combining three spins of 1/2 does not simply yield a spin-1/2 state, suggesting a need for a more complex explanation.
  • Another participant explains that angular momentum does not add linearly, highlighting that the spin of a proton is 1/2 despite containing three quarks.
  • There is a discussion about the contributions to the nucleon spin structure, with references to quantum field theory and ongoing experimental investigations.
  • Some participants express that without a background in quantum mechanics, understanding the spin of nucleons in terms of quarks is challenging.
  • One participant suggests that a simple explanation with some background information could be beneficial for those unfamiliar with quantum mechanics.
  • Another participant emphasizes that the addition of spins in quantum mechanics involves complex mathematics, specifically mentioning Clebsch-Gordan coefficients.
  • A participant provides specific details about the neutron's transformation to a proton and their respective spins and magnetic dipole moments.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the quantum mechanical principles involved in nucleon spin. There is no consensus on a simple explanation, and multiple competing views on how to approach the topic remain evident.

Contextual Notes

Participants note the complexity of quantum mechanics and the necessity of a foundational understanding to grasp the discussions about nucleon spin. There are references to specific mathematical frameworks and ongoing research that may not be fully accessible without prior knowledge of quantum mechanics.

Winga
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Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?
 
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Because they are made of two up quarks and one down quark (uud), protons are baryons. So are neutrons (udd). The magnitude of the spin-value of each quark is 1/2

marlon
 
Composing 3 spins of 1/2,according to Clebsch-Gordan's theorem,doesn't necessarily yield a spin 1/2 state...In fact,it yields a linear combination of 1/2 & 3/2 states.Something more is needed to explain the spin of those 2 barions.

Daniel.
 
Angular momentum doesn't add linearly. That is, a proton contains three quarks, but its spin is not 3/2, but 1/2. When you add angular momentum, you have a range of possible results, which goes from the maximum (the arithmetic sum) down to the minimum (the larger minus the smaller) with possible values at unit steps in between. If you add two spin-1/2 fermions, you get either spin 0 or spin 1 (a boson). If you add 5 units of angular momentum to 2 units, you get 3, 4, 5, 6, or 7 units of angular momentum. If you add 3/2 units and 2 units, you get 1/2, 3/2, 5/2, or 7/2 units. A proton has spin 1/2. As you should expect, there's another particle with the same quark content as the proton, but spin 3/2, the Δ+.

marlon
 
Are quarks also have spins, +1/2 & -1/2?
 
Eigenvalues of \hat{S}_{z}...?Of course.

Daniel.
 
Let me just say that the truth is far more complex than the simple constituent quark model could let one think

see for instance : Present understanding of the nucleon spin structure

there are several contribution to the spin of the nucleon, and it is a superbe illustration of the strength of QFT that they precisely add up to exactly one-half. The experimetal resolution of this puzzle is currently being performed.
 
Is there any easier way to explain this phenomenon?
 
Winga said:
Is there any easier way to explain this phenomenon?

No, sorry, this is QM. Though the explanation by Humanino is entirely correct, i suggest you make sure you understand how addition of the J-operator and the associated Clebsch-Gordan coefficients work. This is basic QM-stuff.

Question is : did you study any QM yet ?

regards
marlon
 
  • #10
Mmmm...not yet!
 
  • #11
Winga said:
Mmmm...not yet!

In that case, Houston we have a problem...


Within what context do you need to answer this question of proton-spin ?


regards
marlon
 
  • #12
No offense,but "Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?" and "Not yet" when asked about studying QM,do not really match.There's an order to everything...You can ask about everything,it's a forum,but the explanations you asked for "...in terms of quarks" are not simple to understand,if you have no theoretical preparation...

Daniel.
 
  • #14
The first site given by astronuc indeed gives a splendid explanation as to why there are six quarks. However, it does not explain the problem at hand here. one cannot bypass the QM-nature of it's solution.

regards
marlon
 
  • #15
marlon said:
Because they are made of two up quarks and one down quark (uud), protons are baryons. So are neutrons (udd). The magnitude of the spin-value of each quark is 1/2

marlon
For protons, the spin of one up quark cancels out the spin of one down quark, and one up quark left with spin value 1/2?
 
  • #16
Unfortunately its not that simple. Spins don't add like regular numbers in quantum mechanics much less field theory. You have to play an intricate game with things called Clebsch Gordon Coefficients and the like. A first course in QM should suffice to explain the correct algebra.
 
  • #17
Would the correct algebra be able to be taught here? If not, where can I find an easy explanation of what to do?
 
  • #18
The CRC Handbook for 2002 says:

Winga said:
Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?
Hi Winga,
The free neutron undergoes, with half-life of 614 seconds, a convulsive transformation to a proton + a 782 KeV beta- and its spin is +1/2 and its magnetic dipole moment is -1.913 nuclear magneton units.
The residual Proton's spin is also +1/2 but its magnetic dipole moment is
+2.793 nuclear magniton units. Cheers, Jim
 

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