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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Phase factors under rotations of strong and weak isospin

The strong isospin raising operator changes a $d$ quark into a $u$: $$ \tau_+ \big|d\big> = \big|u\big> $$ However, for antiquarks, there is an additional phase factor: $$ \tau_+ \big|\bar u\big&...
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What's with the very slightly larger mass of the neutron compared to the proton?

Neutron mass: 1.008664 u Proton mass: 1.007276 u Why the discrepancy? On a related note, how does one go about measuring the mass of a neutron or proton, anyway?
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Is the neutral pion a singlet?

In Griffiths' Introduction to Elementary Particles, it is mentioned p. 179 that the $\pi^0$ is a singlet under $SU(2)$ isospin. But it is also part of the $\pi^-,\pi^0,\pi^+$ isospin triplet. How can ...
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Why is there no baryon isospin singlet with spin 3/2?

All of the baryons in the spin-1/2 octet except the $\Lambda$ isospin singlet have spin-3/2 excited states in the baryon decuplet. What is it that prevents the existence of a $\Lambda^{*}$ baryon with ...
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How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

Title says it all: How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content? Doesn't this make them the same baryon?
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Labelling representations using isospin and hypercharge

Can someone explain how isospin and hypercharge can be used to label representations? What is the meaning of the term singlet, doublet etc in this context? In particular how can I use it to label ...
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What is the exact relation between $\mathrm{SU(3)}$ flavour symmetry and the Gell-Mann–Nishijima relation

I'm trying to understand how the Gell-Mann–Nishijima relation has been derived: \begin{equation} Q = I_3 + \frac{Y}{2} \end{equation} where $Q$ is the electric charge of the quarks, $I_3$ is the ...
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Coulomb barrier and proton evaporation

Why is it that neutrons evaporate from nuclei more easily than protons do? Intuitively, since protons are electrostatically repelled (in addition to whatever nuclear forces they have in common with ...
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106 views

Why do excited states in $^4$He not decay by photon emission?

Here's a level scheme for the $^4$He nucleus (source; click image to see full size): Notice that all of the confirmed decay modes are by disintegration — emission of a neutron, proton, or deuteron. ...
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What is the cause of the minor mass difference between the proton and the neutron?

As known, the proton is from two up and a single down quark, while the neutron is from a single up and two down quarks. The down quark is a little bit more massive and the up, and so the neutron is ...
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If weak isospin is not conserved in time, what does the Noether theorem tell us?

As far as I understand weak isospin is only conserved in interactions but not as time evolves. Nevertheless, we get from Noethers theorem, because of global $SU(2)$ invariance a conserved quantity ...
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(Iso)spin coupling of three particles

I need Isospin calculations to predict the relative amount of strong decays, namely $D^{**0}\to D\pi\pi$, where the $D$ and $\pi$ can be charged or neutral. My problem is the order of contracting the ...
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Why do the $u$ and $d$ quark not have an associated quantum number?

All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions. This allows, among other things, flavour ...
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Quark composition of the neutral pion

I wonder why the neutral pi meson is $$ | \pi^0\rangle = \frac{1}{\sqrt{2}}\left(\vert u\overline {u}\rangle - \vert d \overline{d} \rangle \right) $$ and not $$ | \pi^0\rangle = \frac{1}{\sqrt{2}}...
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Weak isospin transformation of $\bar\psi \psi \phi$

In an old exam I found the following question regarding the Higgs potential: Write down the gauge invariant Yukawa interaction term in the Lagrangian that gives rise to the electron mass. The ...
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Selection rule of Kaon decay to pions

in Peskin QFT page 611, he said the isospin change for $${K^0} \to {\pi ^ + }{\pi ^ - }$$ is 1/2, while isospin change for $${K^ + } \to {\pi ^ + }{\pi ^0}$$ is 3/2. Why? If ${I_3}({K^ + }) = 1/2$,$...
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Why are the neutron and proton masses nearly equal? [duplicate]

The neutron to proton mass ratio is nearly one. Is there some fundamental reason from this or this simply a coincidence?
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306 views

Isospin of the neutral sigma baryon

I was typing up another answer on P.S.E. and I wanted to use the fact that the decay $$\Sigma^0\longrightarrow\Lambda^0+\gamma$$ does not occur strongly as an example of isospin conservation. But then ...
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Eigenstates of total isospin, I

In the book from which I'm studying particle physics (by Mark Thompson) it is stated that states of two quarks of third component of isospin = 0 (like ud or du) are not eigenstates of the total ...
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Ambiguity in ordering of isospin states for Clebsch-Gordan coefficients

In studying isospin for nuclear physics, I am confused a bit by an ambiguity I found. If a process that goes from $K^- + p \rightarrow \Sigma^0+ \pi^0$, I can write the isospin for the left hand side ...
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101 views

Why is $\vert I=1,I_3=1\rangle = -p\bar n$

My book doesn't explain well how to build a doublet of antiparticles that transforms the same way the particle doublet $(p,n)^T$ (proton neutron) does. They claim $$\tag 1 \vert I=1,I_3=1\rangle = -...
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Elastic vs Inelastic vs isospin violating scattering particle physics models

I'm looking for a nice paper that explains the difference between three particle physics models for spin-independent dark matter interaction with nuclei: elastic, inelastic and isospin violating ...
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Isospin In Kaon Decay

The decay $ K \to \pi \pi $ at zero-strong interaction level is calculated by considering the matrix element of the operator $ Q_2 = (\bar{s}u)_{V-A} (\bar{u}d)_{V-A} $ for two kinds of processes: ...
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Anti-neutrons, anti-quarks, isospin: What is observed and what is derived?

I would be a little more restrained with the existence of antineutrons. First at all - if I understood right - the existence of antiquarks is hypothetical. If one not agree with this please refer to ...
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Motivation for isospin

I am having trouble understanding the point of isospin. Why do we need isospin? The rationalization that protons and neutrons are similar doesn't make sense to me.
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Why are the antimatter compositions of neutrons and protons different? Why by about 1%? References?

In his blog at http://motls.blogspot.com/2010/09/can-antimatters-gravity-be-repulsive.html Lubos Motl writes "...neutrons contain a slightly different mass contribution from the antiquarks (...
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How do protons and neutrons interchange?

I recently read in a book that a nucleon with +1/2 isospin is a proton and if the isospin is changed to -1/2, it is a neutron, so it is the same particle in different states. If a proton has a ...
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Nucleon-meson interaction

Suppose interaction lagrangian between neutron-proton doublet and $\pi$-mesons: $$ \tag 1 L_{\pi pn} = \bar{\Psi}\pi_{a}\tau_{a}(A\gamma_{5} + B)\Psi , \quad \Psi = \begin{pmatrix} p \\ n\end{pmatrix} ...
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Why is isospin so useful?

I'm currently reading about isospin in nuclear physics, and I know how to calculate it, and all the math, but I'm actually not sure WHY it is so useful? Can anyone come with some examples where not ...
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Why $U(1)_Y$ hypercharge rather than $U(1)_\text{em}$ electromagnetism?

In the Standard Model we have $SU(2)_I\times U(1)_Y$, where $U(1)_Y$ is weak hypercharge and $SU(2)_I$ is the symmetry group of weak isospin. Why do we introduce $U(1)_Y$ of weak hypercharge rather ...
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If isospin is conserved under strong interactions why it is represented by SU(2)?

As far as I know from my readings SU(2) is a representation group of isospin symmetry which shows deep symmetry of the strong force which conserves flavor. Isospin symmetry is broken under weak ...
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287 views

Why is neutral sigma baryon more massive than lambda baryon?

Neutral sigma-star baryon, neutral sigma baryon and lambda baryon have masses 1387 MeV, 1192 MeV, 1116 MeV respectively, whereas each of these 3 particles are composed of 1 up, 1 down and 1 strange ...
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Pions as a superposition of quark states

in Isospin space there are two fundamental states called up and down quarks, which satisfy the following eigenvalue equations: $I u = (1/2) u$, $I d = (1/2) d$ and $I_3 u = (1/2) u, I_3 d = (-1/2) d$....
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Why does the alpha particle not excite the isovector transitions in nuclei?

The $\alpha$ particle is a very commonly used projectile for studying inelastic scattering. It has T=0 ans S=0. But it only excites the isoscalar vibration modes in target nuclei, and not isovector ...
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88 views

What makes neutron heavier than a proton? [duplicate]

The mass of proton is 1.672*10¯²7 kg while it is 1.675*10¯²7 kg. Both are made up of 3 quarks each. Then what makes proton lighter than a neutron?
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Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
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Why is quark flavor just a SU(N) group?

In the standard model one has U(1) for electromagnetism, SU(2) for the weak sector and SU(3) for the color sector. One could say that in the quark part of the fermions, there are $$ \underbrace{6}_\...
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Difference between $|0\rangle$ and $0$ in the context of isospin

I know this has been asked before, but I am confused having read it in the context of isospin, where the creation operators act on the "vacuum" state (representing no particles) $$a^\dagger_m|0\rangle ...
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Isoscalar and isovector terms in optical model potential

How does one obtain the isoscalar and isovector terms of the nucleus-nucleus interaction potential and what do they signify?
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Raising and lowering operators for a composite isospin $SU(2)$ system

Consider pion states composed of $q \bar q$ pairs where $q \in \left\{u,d \right\}$ transforms under an $SU(2)$ isospin flavour symmetry. These bound states transform in the tensor product $R_1 \...
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How do we determine total isospin when only third component of isospin is known?

Both $ \frac{1}{\sqrt{2}} (np - pn)$ and $\frac{1}{\sqrt{2}} (np + pn)$ has third component of isospin equal to 0. But the first combination has total isospin equal to 0 while the second combination ...
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64 views

Role of SU(2) group in isospin and in the weak interaction

I know that the SU(2) group describes internal symmetries such as isospin and the weak interaction. But isospin and weak interactions are quite different, so more precise what is the role of SU(2) in ...
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Relation between gauge symmetry and mass difference

Usually (like in Georgi's Lie Algebra book) people argue the reason why Gellmann $SU(3)$ flavor symmetry (u,d,s) can't extend to $SU(4)$ (u,d,c,s) or higher flavour symmetry is the their mass ...
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Does strong interaction care about mass? (+ Isospin question)

So in the journey of trying to understand more about the strong interaction I have encountered some passages linking mass with strong interaction. Like from Greiner and Müller Quantum Mechanics - ...
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Up/Down Quark Color and Isospin

I'm reading some notes that say the reason that the strong interaction conserve isospin is because the up and down quarks have the same color... but I'm not very convinced. Is this a universal truth? ...
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Does change in temperature affect the proton spin of molecular hydrogen?

How come the amount of parahydrogen present increases as the temperature lowers? Does change in temperature play a role in changing its proton spin? Also it lists that "At 0°K, hydrogen contains ...
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Global and local symmetry for Isospin/Strangeness etc

Why some symmetries $ \big[SU(3),SU(2)$ and $U(1)\big]$ of the Standard Model are local, and some others remain global, like Isospin and Strangeness. Is there a fundumental reason for that? Doesn't it ...
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Isospin states of deuteron

I have a stupid question to ask being the newbie amateur that I am to physics. Deuteron in the ground state normally exists in the isospin singlet state at least according the wiki site: https://en....
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Isospin and Energy

I would to know if there is a correlation between isospin and energy. Consider for example the $\eta$ meson ($I =0$) and the pions($I=1$). The $\eta$ turns out to be much heavier then the pions ($m_\...