Chapter 17: Problem 21
Exactly what does the strangeness quantum number \(S\) specify?
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Chapter 17: Problem 21
Exactly what does the strangeness quantum number \(S\) specify?
These are the key concepts you need to understand to accurately answer the question.
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Why can we say that the \(\pi^{0}\) meson is its own antiparticle? Do all particles have antiparticles? What about the photon?
In the laboratory (LAB) frame of reference, particle 1 is at rest with total relativistic energy \(E_{1}\), and particle 2 is moving to the right with total relativistic energy \(E_{2}\) and momentum \(p_{2}\). (a) Use the relativistic momentum-energy transformation equations $$ \begin{aligned} &p_{x}^{\prime}=\frac{1}{\sqrt{1-v^{2} / c^{2}}}\left(p_{x}-v E / c^{2}\right) \\\ &p_{y}^{\prime}=p_{y} \\ &p_{z}^{\prime}=p_{z} \\ &E^{\prime}=\frac{1}{\sqrt{1-v^{2} / c^{2}}}\left(E-v p_{x}\right) \end{aligned} $$ to show that the frame in which the center of the relativistic masses of the system is at rest is moving to the right with velocity $$ v=c \frac{c p_{2}}{E_{1}+E_{2}} $$ relative to the laboratory frame, and show that the total momentum of the system is zero in this center-of-mass (CM) frame. (b) Now let the two particles have the same rest mass \(m_{0}\), and let the total relativistic energy of the system in the laboratory frame be \(E_{\mathrm{LAB}}\). Evaluate \(E_{\mathrm{CM}}\), the total relativistic energy of the system in the center- of-mass frame, and show that $$ E_{\mathrm{CM}}=\sqrt{2 m_{0} c^{2} E_{\mathrm{LAB}}} $$
A nucleon is incident on a nucleon which is initially stationary. Its kinetic energy, which is also the total kinetic energy of the system in that frame of reference, is \(K\). Show that the total kinetic energy of the system, in a frame of reference in which the center of mass of the system is stationary, is \(K / 2\).
For each of the following reactions state the fastest interaction through which the conservation laws allow it to proceed. If the reaction is forbidden by all interactions, state why. (a) \(p \rightarrow \pi^{+}+e^{+}+e^{-}\) (b) \(\Lambda^{0} \rightarrow p+e^{-}\) (c) \(\mu^{-} \rightarrow e^{-}+v_{e}+v_{\mu}\) (d) \(n+p \rightarrow \Sigma^{+}+\Lambda^{0^{\mu}}\) (e) \(p+\bar{p} \rightarrow \gamma+\gamma\) (f) \(p+\bar{p} \rightarrow n+\overline{\Sigma^{0}}+K^{0}\) (g) \(K^{0} \rightarrow \pi^{+}+\pi^{-}+\pi^{0}+\pi^{0}\)
Why is \({ }^{3} P_{1}\) not a component of the ground state of the deuteron? What about \({ }^{1} S_{0}\) ?
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