Is Strangeness Conserved? A Determine whether the following reaction occurs on the basis of conservation of strangeness. π^0 + n → K^+ + ∑^-

Question

Is Strangeness Conserved?

A Determine whether the following reaction occurs on the basis of conservation of strangeness.

[latex] \pi^{0}+ n \quad \rightarrow \quad K ^{+}+\Sigma^{-} [/latex]

B Show that the following reaction does not conserve strangeness.

[latex] \pi^{-}+ p \rightarrow \pi^{-}+\Sigma^{+} [/latex]

Accepted Answer

A:

From Table 31.2, we see that the initial system has strangeness S = 0 + 0 = 0. Because the strangeness of the [latex] K ^{+} [/latex] is S = +1 and the strangeness of the [latex] \Sigma^{-} [/latex] is S = -1, the strangeness of the final sysstem is +1 - 1 = 0.
Therefore, strangeness is conserved and the reaction is allowed.

B:

The initial system has strangeness S = 0 + 0 = 0, and the final system has strangeness S = 0 + (-1) = -1. Therefore, strangeness is not conserved.

TABLE 31.2 Some Particles a+A1:L26nd Their PropertiesA1:L22
Category	Particle Name	Symbol	Anti-particle	Mass [latex]\left( MeV / c^{2} ight)[/latex]	B	[latex]L_{e}[/latex]	[latex]L _{ \mu }[/latex]	[latex]L _{ au}[/latex]	S	Lifetime(s)	Principal Decay [latex] ext { Modes }^{a} [/latex]
Leptons	Electron	[latex]e^{-}[/latex]	[latex]e^{+}[/latex]	0.511	0	+1	0	0	0	Stable
	Electron– neutrino	[latex] u_{e}[/latex]	[latex]\bar{ u}_{e}[/latex]	[latex]<7 eV / c^{2}[/latex]	0	+1	0	0	0	Stable
	Muon	[latex]\mu^{-}[/latex]	[latex]\mu^{+}[/latex]	105.7	0	0	+1	0	0	[latex]2.20 imes 10^{-6}[/latex]	[latex] e ^{-\bar{ u}_{e} u_{\mu}}[/latex]
	Muon–neutrino	[latex] u_{\mu}[/latex]	[latex] \bar{ u}_{\mu}[/latex]	[latex]<0.3[/latex]	0	0	+1	0	0	Stable
	Tau	[latex] au^{-}[/latex]	[latex] au^{+}[/latex]	1 784	0	0	0	+1	0	[latex]<4 imes 10^{-13}[/latex]	[latex]\mu^{-\bar{ u}_{\mu}} u_{ au}, e ^{-\bar{ u}_{e} u_{ au}}[/latex]
	Tau–neutrino	[latex] u_{ au}[/latex]	[latex]\bar{ u}_{ au}[/latex]	[latex]<30[/latex]	0	0	0	+1	0	Stable
Hadrons Mesons	Pion	[latex]\pi^{+}[/latex]	[latex]\pi^{-}[/latex]	139.6	0	0	0	0	0	[latex]2.60 imes 10^{-8}[/latex]	[latex]\mu^{+} u_{\mu}[/latex]
		[latex]\pi^{0}[/latex]	Self	135.0	0	0	0	0	0	[latex]0.83 imes 10^{-16}[/latex]	[latex]2 \gamma[/latex]
	Kaon	[latex]K ^{+}[/latex]	[latex]K ^{-}[/latex]	493.7	0	0	0	0	+1	[latex]1.24 imes 10^{-8}[/latex]	[latex]\mu^{+} u_{\mu}, \pi^{+} \pi^{0}[/latex]
		[latex]K _{ s }^{0}[/latex]	[latex]\overline{ K }_{ S } 0[/latex]	497.7	0	0	0	0	+1	[latex]0.89 imes 10^{-10}[/latex]	[latex]\pi^{+} \pi^{-}, 2 \pi^{0}[/latex]
		[latex]K _{ L }^{0}[/latex]	[latex]\overline{ K }_{ L }^{0}[/latex]	497.7	0	0	0	0	+1	[latex]5.2 imes 10^{-8}[/latex]	[latex]\begin{aligned}&\pi^{\pm} e ^{\mp} \bar{ u}_{e}, 3 \pi^{0} \&\pi^{\pm} \mu^{\mp} bar{ u}_{\mu}\end{aligned}[/latex]
	Eta	[latex]\eta[/latex]	Self	548.8	0	0	0	0	0	[latex]<10^{-18}[/latex]	[latex]2 \gamma, 3 \pi^{0}[/latex]
		[latex]\eta^{\prime}[/latex]	Self	958	0	0	0	0	0	[latex]2.2 imes 10^{-21}[/latex]	[latex]\eta \pi^{+} \pi^{-}[/latex]
Baryons	Proton	p	[latex]\overline{ p }[/latex]	938.3	+1	0	0	0	0	Stable
	Neutron	n	[latex]\bar{n}[/latex]	939.6	+1	0	0	0	0	614	[latex]pe ^{-\bar{ u}_{e}}[/latex]
	Lambda	[latex]\Lambda^{0}[/latex]	[latex]\bar{\Lambda}^{0}[/latex]	1 115.6	+1	0	0	0	-1	[latex]2.6 imes 10^{-10}[/latex]	[latex]p \pi^{-}, n \pi^{0}[/latex]
	Sigma	[latex]\Sigma^{+}[/latex]	[latex]\bar{\Sigma}^{-}[/latex]	1 189.4	+1	0	0	0	-1	[latex]0.80 imes 10^{-10}[/latex]	[latex]p \pi^{0}, n \pi^{+}[/latex]
		[latex]\Sigma^{0}[/latex]	[latex]\bar{\Sigma}^{0}[/latex]	192.5	+1	0	0	0	-1	[latex]6 imes 10^{-20}[/latex]	[latex]\Lambda^{0} \gamma[/latex]
		[latex]\Sigma^{-}[/latex]	[latex]\bar{\Sigma}^{+}[/latex]	1 197.3	+1	0	0	0	-1	[latex]1.5 imes 10^{-10}[/latex]	[latex]n \pi^{-}[/latex]
	Delta	[latex]\Delta^{++}[/latex]	[latex]\bar{\Delta}^{--}[/latex]	1 230	+1	0	0	0	0	[latex]6 imes 10^{-24}[/latex]	[latex]p \pi^{+}[/latex]
		[latex]\Delta^{+}[/latex]	[latex]\bar{\Delta}^{-}[/latex]	1 231	+1	0	0	0	0	[latex]6 imes 10^{-24}[/latex]	[latex]p \pi^{0}, n \pi^{+}[/latex]
		[latex]\Delta^{0}[/latex]	[latex]\bar{\Delta}^{0}[/latex]	1 232	+1	0	0	0	0	[latex]6 imes 10^{-24}[/latex]	[latex]n \pi^{0}, p \pi^{-}[/latex]
		[latex]\Delta^{-}[/latex]	[latex]\bar{\Delta}^{+}[/latex]	1 234	+1	0	0	0	0	[latex]6 imes 10^{-24}[/latex]	[latex]n \pi^{-}[/latex]
	Xi	[latex]\Xi^{0}[/latex]	[latex]\bar{\Xi}^{0}[/latex]	1 315	+1	0	0	0	-2	[latex]2.9 imes 10^{-10}[/latex]	[latex]\Lambda^{0} \pi^{0}[/latex]
		[latex]\Xi^{-}[/latex]	[latex]\bar{\Xi}^{+}[/latex]	1 321	+1	0	0	0	-2	[latex]1.64 imes 10^{-10}[/latex]	[latex]\Lambda^{0} \pi^{-}[/latex]
	Omega	[latex]\Omega^{-}[/latex]	[latex]\Omega^{+}[/latex]	1 672	+1	0	0	0	-3	[latex]0.82 imes 10^{-10}[/latex]	[latex]\Xi^{-} \pi^{0}, \Xi^{0} \pi^{-}, \Lambda^{0} K ^{-}[/latex]

TABLE 31.2 Some Particles a+A1:L26nd Their PropertiesA1:L22
Category	Particle Name	Symbol	Anti-particle	Mass $\left( MeV / c^{2}\right)$	B	$L_{e}$	$L _{ \mu }$	$L _{\tau}$	S	Lifetime(s)	Principal Decay $\text { Modes }^{a}$
Leptons	Electron	$e^{-}$	$e^{+}$	0.511	0	+1	0	0	0	Stable
	Electron– neutrino	$\nu_{e}$	$\bar{\nu}_{e}$	$<7 eV / c^{2}$	0	+1	0	0	0	Stable
	Muon	$\mu^{-}$	$\mu^{+}$	105.7	0	0	+1	0	0	$2.20 \times 10^{-6}$	$e ^{-\bar{\nu}_{e} \nu_{\mu}}$
	Muon–neutrino	$\nu_{\mu}$	$\bar{\nu}_{\mu}$	$<0.3$	0	0	+1	0	0	Stable
	Tau	$\tau^{-}$	$\tau^{+}$	1 784	0	0	0	+1	0	$<4 \times 10^{-13}$	$\mu^{-\bar{\nu}_{\mu}} \nu_{\tau}, e ^{-\bar{\nu}_{e} \nu_{\tau}}$
	Tau–neutrino	$\nu_{\tau}$	$\bar{\nu}_{\tau}$	$<30$	0	0	0	+1	0	Stable
Hadrons Mesons	Pion	$\pi^{+}$	$\pi^{-}$	139.6	0	0	0	0	0	$2.60 \times 10^{-8}$	$\mu^{+} \nu_{\mu}$
		$\pi^{0}$	Self	135.0	0	0	0	0	0	$0.83 \times 10^{-16}$	$2 \gamma$
	Kaon	$K ^{+}$	$K ^{-}$	493.7	0	0	0	0	+1	$1.24 \times 10^{-8}$	$\mu^{+} \nu_{\mu}, \pi^{+} \pi^{0}$
		$K _{ s }^{0}$	$\overline{ K }_{ S } 0$	497.7	0	0	0	0	+1	$0.89 \times 10^{-10}$	$\pi^{+} \pi^{-}, 2 \pi^{0}$
		$K _{ L }^{0}$	$\overline{ K }_{ L }^{0}$	497.7	0	0	0	0	+1	$5.2 \times 10^{-8}$	$\begin{aligned}&\pi^{\pm} e ^{\mp} \bar{\nu}_{e}, 3 \pi^{0} \\&\pi^{\pm} \mu^{\mp} bar{\nu}_{\mu}\end{aligned}$
	Eta	$\eta$	Self	548.8	0	0	0	0	0	$<10^{-18}$	$2 \gamma, 3 \pi^{0}$
		$\eta^{\prime}$	Self	958	0	0	0	0	0	$2.2 \times 10^{-21}$	$\eta \pi^{+} \pi^{-}$
Baryons	Proton	p	$\overline{ p }$	938.3	+1	0	0	0	0	Stable
	Neutron	n	$\bar{n}$	939.6	+1	0	0	0	0	614	$pe ^{-\bar{\nu}_{e}}$
	Lambda	$\Lambda^{0}$	$\bar{\Lambda}^{0}$	1 115.6	+1	0	0	0	-1	$2.6 \times 10^{-10}$	$p \pi^{-}, n \pi^{0}$
	Sigma	$\Sigma^{+}$	$\bar{\Sigma}^{-}$	1 189.4	+1	0	0	0	-1	$0.80 \times 10^{-10}$	$p \pi^{0}, n \pi^{+}$
		$\Sigma^{0}$	$\bar{\Sigma}^{0}$	192.5	+1	0	0	0	-1	$6 \times 10^{-20}$	$\Lambda^{0} \gamma$
		$\Sigma^{-}$	$\bar{\Sigma}^{+}$	1 197.3	+1	0	0	0	-1	$1.5 \times 10^{-10}$	$n \pi^{-}$
	Delta	$\Delta^{++}$	$\bar{\Delta}^{–}$	1 230	+1	0	0	0	0	$6 \times 10^{-24}$	$p \pi^{+}$
		$\Delta^{+}$	$\bar{\Delta}^{-}$	1 231	+1	0	0	0	0	$6 \times 10^{-24}$	$p \pi^{0}, n \pi^{+}$
		$\Delta^{0}$	$\bar{\Delta}^{0}$	1 232	+1	0	0	0	0	$6 \times 10^{-24}$	$n \pi^{0}, p \pi^{-}$
		$\Delta^{-}$	$\bar{\Delta}^{+}$	1 234	+1	0	0	0	0	$6 \times 10^{-24}$	$n \pi^{-}$
	Xi	$\Xi^{0}$	$\bar{\Xi}^{0}$	1 315	+1	0	0	0	-2	$2.9 \times 10^{-10}$	$\Lambda^{0} \pi^{0}$
		$\Xi^{-}$	$\bar{\Xi}^{+}$	1 321	+1	0	0	0	-2	$1.64 \times 10^{-10}$	$\Lambda^{0} \pi^{-}$
	Omega	$\Omega^{-}$	$\Omega^{+}$	1 672	+1	0	0	0	-3	$0.82 \times 10^{-10}$	$\Xi^{-} \pi^{0}, \Xi^{0} \pi^{-}, \Lambda^{0} K ^{-}$

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