Relation between scattering amplitude and isospin

[Barny]

Hi,

I'm an undergrad physicist in a bit of a pickle over how isospin relates to scattering amplitude.

It's been quoted to me that the scattering amplitude is given by the matrix element of the initial and final isospin states. I'd ideally like to show you this in latex, however I can't seem to work the latex thing that well so at a rough stab it would be <Ii,Ii3!H!If,If3>

here the lower case i and f represent initial and final states and H is the appropriate operator for this matrix element. I is total isospin andI3 represents the 3rd component of isospin.

Can anyone shed some light on this or point me to an appropriate text. The course text and documents are unsatisfactory as is Hughes and Giffiths (although in general i like these books alot)

 

[LightHero]

Thanks a lotThe scattering amplitude can be written as a matrix element of the initial and final isospin states:$\langle I_i,I_{i3} | H | I_f,I_{f3}\rangle$, where $H$ is the Hamiltonian that is responsible for the interaction and $I_i$ and $I_f$ are the total isospins of the initial and final states, respectively. The third component of the isospin is denoted by $I_{i3}$ and $I_{f3}$. To learn more about isospin and its relation to scattering amplitude, you may want to look into textbooks such as Introduction to Elementary Particles by D. Griffiths or Quantum Mechanics: Non-Relativistic Theory by L. Landau and E. Lifshitz. You may also find the following article helpful: "Isospin in Nuclear Physics" by T.T.S. Kuo and G.E. Brown.

 

[sir-pinski]

Hi there,

This is a great question and one that is often confusing for students studying nuclear and particle physics. Let me try to explain the relationship between scattering amplitude and isospin.

First, let's define what we mean by isospin. Isospin is a concept in particle physics that describes the symmetry between certain particles. This symmetry arises from the fact that some particles (such as protons and neutrons) have the same properties except for their charge. Isospin is a quantum number that is conserved in strong interactions, meaning that the total isospin of a system before and after a strong interaction remains the same.

Now, let's talk about scattering amplitude. Scattering amplitude is a mathematical quantity that describes the probability amplitude for a particle to scatter off another particle. In other words, it tells us how likely it is for a particle to interact with another particle.

So, how are these two related? The scattering amplitude is given by the matrix element of the initial and final isospin states, as you mentioned. This means that the isospin states of the particles involved in the scattering process play a role in determining the scattering amplitude. In other words, the isospin of the particles affects how likely they are to interact with each other.

To put it in simpler terms, the isospin of a particle is like its "flavor" and the scattering amplitude is affected by the "flavors" of the particles involved. Just like how different flavors of ice cream can interact with each other differently, particles with different isospins can interact with each other differently.

I hope this explanation helps clarify the relationship between scattering amplitude and isospin. If you want to learn more, I would recommend looking into books or resources specifically on nuclear and particle physics. Best of luck with your studies!