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Chapter 39: Problem 27

Is the interaction \(p+p \rightarrow p+\pi^{+}\) allowed? If not, what conservation law does it violate?

Short Answer

Expert verified
The interaction \(p+p \rightarrow p+\pi^{+}\) is not allowed because it violates the conservation law of baryon number.

Step by step solution

01

Analyze the Interaction

Identify the properties of the participating particles. A proton (p) has charge +1, baryon number +1, and lepton number 0. A positive pion (\(\pi^{+}\)) has charge +1, baryon number 0, and lepton number 0.
02

Verify Conservation Laws

Check if every conservation law holds in this interaction: Charge Conservation: the total charge before the interaction is \(1+1=2\), and after the interaction is \(1+1=2\). The total charge is conserved.Baryon Number Conservation: the total baryon number before the interaction is \(1+1=2\), and after the interaction is \(1+0=1\). Therefore, the baryon number is not conserved. The conservation of energy and momentum are not calculable from the information given, but as the baryon number is not conserved, it can be concluded that the interaction is not possible.
03

Conclusion

Sum up the findings. In this case, although charge conservation holds, baryon number conservation is violated. Therefore, the given interaction \(p+p \rightarrow p+\pi^{+}\) is not allowed, as it violates the conservation law of baryon number.

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