2 quick questions about the baryon octet and decuplet?

[jeebs]

Hi,
I have been looking at the baryon decuplet for spin 3/2 baryons, and the octet for spin 1/2 baryons. Here is a picture of the baryon decuplet:
http://schools-wikipedia.org/images/392/39222.png
Here is a picture of the baryon octet:
http://upload.wikimedia.org/wikiped...et-small.svg/480px-Baryon-octet-small.svg.png

As I understand it, the spin of the baryon is determined by the spins of its constituent quarks, ie. you can either have all 3 quark spins aligned, giving spin 1/2 + 1/2 + 1/2 = 3/2,
or you can have 2 of the spins in one direction and the other in the opposite direction, giving spin 1/2 + 1/2 - 1/2 = 1/2.

The differences between the decuplet and the octet appear to be that the quarks [tex]\Delta^-, \Delta^+^+ and \Omega^-[/tex] are on the decuplet but not the octet, and the octet has the quark [tex]\Lambda[/tex] but the decuplet does not.

Also, the proton and neutron on the octet are the same quark combination as the [tex]\Delta^0 and \Delta^+[/tex] do on the decuplet, but for some reason they are called different names depending on which diagram you look at.

Why do we have different names for particles with exactly the same quark content?
I thought the answer to this might be to do with the spin of the baryon, but the octet and the decuplet both include the [tex]\Sigma[/tex] quarks, with the same name and quark content. What's going on here?

My other question is why should there be ten particles in the decuplet but only eight in the octet? By that I mean, take the [tex]\Delta^-[/tex] quark that appears on the decuplet only. It has quark content ddd. Clearly if it only appears in the decuplet diagram, the ddd combination cannot form a spin 1/2 baryon.
What is the reason why these quarks ARE able align so that the baryon they form has a spin 3/2, but are NOT able to align so that they form a baryon with spin 1/2?

Or, to put it more simply, why are there 10 quarks in the one diagram but not the other?

Thanks.

 

[Jhero]

Thank you for your post and for your interest in the baryon decuplet and octet. I would like to provide some clarification on the questions you have raised.

Firstly, you are correct in stating that the spin of a baryon is determined by the spin of its constituent quarks. In the case of the baryon decuplet, all three quarks have their spins aligned, resulting in a spin of 3/2. This is known as a "triplet" state. On the other hand, in the baryon octet, two of the quarks have their spins aligned while the third has its spin in the opposite direction, resulting in a spin of 1/2. This is known as a "singlet" state. This difference in spin configurations is what distinguishes the two diagrams.

Regarding the differences in quark content between the decuplet and octet, it is important to note that these diagrams represent different combinations of quarks that form baryons. The \Delta^- quark, for example, can only exist in the decuplet because its quark content (ddd) does not allow it to form a baryon with a spin of 1/2. This is due to the Pauli exclusion principle, which states that no two fermions (such as quarks) can occupy the same quantum state. Therefore, the decuplet and octet diagrams show different combinations of quarks that are able to form baryons with different spins.

As for your question about the naming of particles with the same quark content, this is due to the historical development of particle physics. The naming convention for particles was established before the understanding of quarks and their spin configurations. Therefore, particles with the same quark content were given different names based on their observed properties. This convention has been maintained for consistency and ease of reference.

I hope this helps to clarify some of your questions. The study of baryons and their properties is a complex and ongoing area of research, and there is still much to be discovered. I encourage you to continue learning and exploring this fascinating field of physics. If you have any further questions, please do not hesitate to ask.


A scientist