# Questions tagged [isospin-symmetry]

Isospin is a symmetry in nuclear physics under the interchange of neutrons and protons. The strong nuclear force conserves isospin, but the symmetry is broken by the electromagnetic force, which only operates between protons.

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### Relation between isospin invariance and charge independence

I don't know if this question is better suited for this forum or math.stackexchange.com. I come from a mathematical background and I'm struggling to understand a passage in Lipkin's book "Lie groups ...
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### Highest and Lowest $SU(3)_F$ states

For the finite dimensional $(p,q)$-irreducible representation of $SU(3)_F$, we can label the states as $\mid T_3,Y\rangle$. Where $T_3$ is the third component of isospin and $Y$ is the hypercharge. ...
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### Isovector Representation of $SU(2)$

In Electroweak Interactions by Renton (page 407) there is the calculation of matrix elements for electromagnetic interactions/weak interactions involving nuclei: A point of confusion for me is the ...
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### Isospin and $\Delta$ Production

Edited to add new information I have seen the relation between cross sections postulated: \begin{align} \sigma(\nu+p\to\mu^- + \Delta^{++})=9\sigma(\nu+n\to\mu^- + \Delta^{+}) \end{align} Motivated ...
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### Explaining branching ratio of $J/\!\psi \!\to \Lambda \bar\Lambda$ and $J/\!\psi \!\to \Sigma^0 \bar\Sigma^0$

I am quite puzzled by the branching ratio of $J/\!\psi \!\to \Lambda \bar\Lambda$ and $J/\!\psi \!\to \Sigma^0 \bar\Sigma^0$. The ratio is measured as ~60%, whereas I expect a ratio of $1/3$. Maybe ...
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### Why does the upper component of a $SU(2)$ doublet has $T^3=1/2$ and lower component $T^3=-1/2$ and not the opposite?

For a $SU(2)$ doublet, why does the upper component have $T^3=1/2$ and lower component $T^3=-1/2$? I know that this can be answered in the Standard Model by using $Q=T^3+Y/2$. But that is because we ...
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### How to determine isospin $T$ (not just $T_z$) of a nuclear ground state

I’m trying to work out the total isospin and the $z$-component of the isospin for specific elements like $^{20}O$ and $^{20}F$ in the ground state. I’ve worked out the $z$-component, as I concluded ...
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### What is meant by “the symmetry of an interaction”?

My understanding of a symmetry is this: apply an operation (e. g. parity inversion) to a system. If it behaves the same afterwards, it is symmetric under that operation. Now, quite often I see ...
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### Two-nucleon coupling: symmetrization postulate

I have some trouble understanding isospin symmetry. If we consider a system of a proton and a neutron as two different iso-states of a nucleon and we wish to write the wave function, do we have to ...
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### What are the other components of the weak isospin?

Sorry for a lazy question, I was just looking this up on the internet for a basic grasp of Standard Model. However, I couldn’t find anything on Wikipedia or just somehow managed to miss it on my ...
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### Are both Gell-Mann Nishijima formulas true for the same reason?

The Gell-Mann Nishijima formula states that $$Q = I_3 + \frac{Y}{2}$$ where $Q$ is the electric charge, $I_3$ is the third component of isospin, and $Y$ is the hypercharge. This was an empirical fact ...
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### What is the isospin of the photon?

As already mentioned in this Phys.SE post, the PDG booklet says that the isospin of a photon is $0,1$. Is it referring to the strong or to the weak isospin of the photon? What would be the 3rd ...
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