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Chapter 11: Problem 37

Identify one possible decay for each of the following antiparticles: (a) \(\bar{n}\),(b) \(\overline{\Lambda^{0}}\), (c) \(\Omega^{+}\) , (d) \(\mathrm{K}^{-}\), and (e) \(\bar{\Sigma}\)

Short Answer

Expert verified
Possible decay processes for the given antiparticles are: (a) \(\bar{n} \to \bar{p} + e^{+} + \nu_e\) (b) \(\overline{\Lambda^{0}} \to \bar{p} + \pi^+\) (c) \(\Omega^{+} \to \Xi^0 + \pi^+\) (d) \(\mathrm{K}^{-} \to \mu^- + \bar{\nu_\mu}\) (e) For \(\bar{\Sigma}^0\): \(\bar{\Sigma}^0 \to \overline{\Lambda^{0}} + \gamma\) For \(\bar{\Sigma}^-\): \(\bar{\Sigma}^-\to \bar{p} + \pi^0\) For \(\bar{\Sigma}^+\): \(\bar{\Sigma}^+ \to n + \pi^+\)

Step by step solution

01

(a) Decay of \(\bar{n}\) (Antineutron)

An antineutron consists of two up antiquarks and one down antiquark. The most probable decay process for an antineutron is via the weak interaction, similar to the neutron decay. In this case, one up antiquark can change to a down antiquark through the emission of a W+ boson, which then decays to a positron (\(e^+\)) and an electron neutrino ![\(\nu_e\)]: \[ \bar{n} \to \bar{p} + e^{+} + \nu_e \]
02

(b) Decay of \(\overline{\Lambda^{0}}\) (Antilambda)

The \(\overline{\Lambda^{0}}\) is an anti-hyperon composed of an up antiquark, a down antiquark, and a strange antiquark. It can decay through the weak interaction. One possible decay mode is when the strange antiquark transforms into an up antiquark, emitting a W- boson, which then decays into a \(\pi^-\) meson and an antiproton: \[ \overline{\Lambda^{0}} \to \bar{p} + \pi^+ \]
03

(c) Decay of \(\Omega^{+}\) (Omegaplus)

The \(\Omega^+\) is an exotic baryon, composed of three s quarks. It can decay through the weak interaction by the transformation of a strange quark into an up quark, with the emission of a W+ boson, which then decays into a positive pion and a \(\Xi^0\): \[ \Omega^{+} \to \Xi^0 + \pi^+ \]
04

(d) Decay of \(\mathrm{K}^{-}\) (Kminus)

The \(\mathrm{K}^{-}\) is a meson composed of an up antiquark and a strange quark. It can decay through the weak interaction. One possible decay mode occurs when the strange quark transforms into an up quark, with the emission of a W- boson, which then decays into a muon and a muon antineutrino: \[ \mathrm{K}^{-} \to \mu^- + \bar{\nu_\mu} \]
05

(e) Decay of \(\bar{\Sigma}\) (Antisigma)

The \(\bar{\Sigma}\) is an anti-hyperon composed of two up antiquarks and a strange antiquark. The most probable decay processes for \(\bar{\Sigma}\) are analogous to the decays of \(\Sigma\) hyperons but with antiparticles instead. One possible decay mode for \(\bar{\Sigma}^0\) is through the electromagnetic interaction: \[ \bar{\Sigma}^0 \to \overline{\Lambda^{0}} + \gamma \] For the \(\bar{\Sigma}^-\), one possible decay is via the weak interaction: \[ \bar{\Sigma}^-\to \bar{p} + \pi^0 \] Finally, for the \(\bar{\Sigma}^+\), a possible decay is via the weak interaction as well: \[ \bar{\Sigma}^+ \to n + \pi^+ \]

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Most popular questions from this chapter

When an electron and positron collide at the SLAC facility, they each have 50.0 -GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

What is the total kinetic energy carried away by the particles of the following decays? (a) \(\pi^{0} \rightarrow \gamma+\gamma\) (b) \(\mathrm{K}^{0} \rightarrow \pi^{+}+\pi^{-}\) (c) \(\Sigma^{+} \rightarrow n+\pi^{+}\) (d) \(\Sigma^{0} \rightarrow \Lambda^{0}+\gamma\)

(a) What is the approximate force of gravity on a 70-kg person due to the Andromeda Galaxy, assuming its total mass is \(10^{13}\) that of our Sun and acts like a single mass 0.613 Mpc away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.

At full energy, protons in the 2.00 -km-diameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy. (a) How long does it take for a proton to complete one trip around? (b) How many times per second will it pass through the target area?

What length track does a \(\pi^{+}\) traveling at \(0.100 c\) leave in a bubble chamber if it is created there and lives for \(2.60 \times 10^{-8} \mathrm{s} ?\) (Those moving faster or living longer may escape the detector before decaying.)
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