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Physics
High Energy, Nuclear, Particle Physics
Transition matrix element and Isospin
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[QUOTE="Xico Sim, post: 5505114, member: 593114"] Hi, guys. A type of problem that often appears is to find the relation between cross sections of some processes. An example would be: $$\pi _{- }+ p \rightarrow K_0 + \Sigma_0$$ $$\pi _{- }+ p \rightarrow K_+ + \Sigma_-$$ $$\pi _{+}+ p \rightarrow K_+ + \Sigma_+$$ To do this, I argue that $$\sigma \, \alpha \, \Gamma \, \alpha \, M$$ with ##M## the transition matrix element. In this case, the interactions are strong. I write the initial and final states for each process in the ##{I,i}## basis and I then write ##M=\langle i | H_s | f \rangle##. I end up getting, for example for the third process: ##M=\langle 3/2,3/2 | H_s | 3/2, 3/2 \rangle##. For the first process, I get one term of the form ##\langle 3/2,-1/2 | H_s | 3/2,-1/2 \rangle##. My question: are there two expressions I just wrote equal? i.e. does ##M=\langle I,i | H_s | I,i' \rangle## depend only on the value of ##I##? Why? [/QUOTE]
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High Energy, Nuclear, Particle Physics
Transition matrix element and Isospin
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