Particle Interaction Homework: Solve & Improve Reasoning

[neelakash]

Homework Statement

I have already solved almost all of the following questions.Just want to check them and improve reasoning.So, please do not blame me for asking you to do it for me.

Check if the following interactions are possible or forbidden and indicate the interactions when applicable.

Homework Equations

$$\ Q$$---charge conservation test
$$\ L$$---Lecton number test
$$\ B$$---Baryon number test
$$\ I_3$$---Isospin test
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Isospin $$\ I_3$$ is violated in EM and Weak interaction
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Strangeness $$\ S$$ is violated $$\Delta$$$$\ S=1$$ in weak interaction
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The Attempt at a Solution

(i) $$\pi^-\ + \ p \rightarrow\ k^0 \ + \Lambda^0$$---Allowed [Q,B,S,I_3---all satisfied---Strong interaction]

(ii) $$\pi^-\ + \ p \rightarrow\ k^0 \ + \Sigma^0$$---Allowed [Q,B,S,I_3---all satisfied---Strong interaction]

[(I am doubtful if I have correctly said that they are strong interaction.Are they?]

(iii) $$\Sigma^0\rightarrow\Lambda^0\ + \gamma$$

---Allowed [Q,B,S,I_3---all satisfied---strong interaction]

(iv) $$\Sigma^+\rightarrow\ p \ + \gamma$$

---Not Allowed [I_3 non-conservation and ∆S=1---it looks that this might be allowed via weak interaction.But I found in book that it is not allowed. Is it bacause there is no Leptons?]

(v) $$\pi^0\rightarrow\gamma\ + \gamma$$

---Allowed.[I suspect it is EM interaction.But any strong evidence?]

(vi) $$\ K^+ \rightarrow\pi^0\ + \mu^+\ + \nu_\mu$$


---Allowed[Q,L,B satisfied---∆S=1--weak interaction because nutrino is involved only in weak interaction].

(vii) $$\Xi^-\rightarrow\Lambda^0\ + \pi^-$$

---Allowed[Q,B satisfied.∆S=1 as in weak interaction]

(viii) $$\Xi^-\rightarrow\ n \ + \pi^-$$

---Not allowed [∆S=2---never allowed in any interaction]

(ix) $$\Lambda^0\rightarrow\pi^+\ + \pi^-$$

---Not Allowed.[B,S non-conservation]

(x) $$\ n \rightarrow\ e^+ \ + \ e^-$$

---Not allowed.B non-conservation and mass non-conservation (n,e are stable particles).

 

[Jhero]

Hello,

it is important to understand and apply the principles of charge conservation, lecton number, baryon number, and isospin in order to determine the possibility or forbidden nature of interactions. It is commendable that you have attempted to solve these questions on your own and are seeking feedback to improve your reasoning. I will go through each of the given interactions and provide my analysis.

(i) \pi^-\ + \ p \rightarrow\ k^0 \ + \Lambda^0---Allowed [Q,B,S,I_3---all satisfied---Strong interaction]

Your reasoning is correct. This interaction is allowed as all the conservation laws are satisfied and it is a strong interaction.

(ii) \pi^-\ + \ p \rightarrow\ k^0 \ + \Sigma^0---Allowed [Q,B,S,I_3---all satisfied---Strong interaction]

Your reasoning is again correct. This interaction is also allowed as all the conservation laws are satisfied and it is a strong interaction.

(iii) \Sigma^0\rightarrow\Lambda^0\ + \gamma

---Allowed [Q,B,S,I_3---all satisfied---strong interaction]

Your reasoning is correct. This interaction is allowed as all the conservation laws are satisfied and it is a strong interaction.

(iv) \Sigma^+\rightarrow\ p \ + \gamma

---Not Allowed [I_3 non-conservation and ∆S=1---it looks that this might be allowed via weak interaction.But I found in book that it is not allowed. Is it bacause there is no Leptons?]

Your reasoning is also correct. This interaction is not allowed as it violates the isospin conservation law and also has a strangeness change of 1, which is only allowed in weak interactions. The reason why it is not allowed even though it involves a lepton (gamma) is because the gamma particle is not involved in the interaction itself. It is only produced as a result of the decay of the Sigma particle.

(v) \pi^0\rightarrow\gamma\ + \gamma

---Allowed.[I suspect it is EM interaction.But any strong evidence?]

Your suspicion is correct. This interaction is allowed and it is an electromagnetic (EM) interaction. This is because the pion (pi) particle is a meson, which has a non-zero charge, and it decays into two photons (gamma) particles, which are also charged. This is