Chapter 32, Problem 33P

To determine

(a) To determine:

Find out whether following decay are possible.

${\Xi }^0\stackrel{}{\to }{\Sigma }^{+}+{\Pi }^{-}$

Answer to Problem 33P

Solution:

Forbidden

Explanation of Solution

${\Xi }^0\stackrel{}{\to }{\Sigma }^{+}+{\Pi }^{-}$

Charge: 0=+1-1=0

Charge on both sides of the equation are equal. Thus, charge is conserved.

Baryon: 1=1+0

Baryon on both sides of the equation are equal. Thus, baryon is conserved.

Lepton:0=0+0

Lepton on both sides of the equation are equal. Thus, lepton is conserved.

Strangeness: $-2\ne -1+0$

Strangeness on both sides of the equation are not equal. Since, Strangeness is not conserved.Thus, the above decay is forbidden.

To determine

(b) To determine:

Find out whether following decay are possible.

${\Omega }^{-}\stackrel{}{\to }{\Sigma }^0+{\Pi }^{-}+v$

Answer to Problem 33P

Solution:

Forbidden

Explanation of Solution

${\Omega }^{-}\stackrel{}{\to }{\Sigma }^0+{\Pi }^{-}+v$

Charge: -1=0-1

Charge on both sides of the equation are equal. Thus, charge is conserved.

Baryon: 1=1+0+0

Baryon on both sides of the equation are equal. Thus, baryon is conserved.

Lepton: -3=-1+0+0

Lepton on both sides of the equation are not equal. Since, lepton is not conserved. Thus, the above decay is forbidden.

To determine

(c) To determine:

Find out whether following decay are possible.

${\Sigma }^0\stackrel{}{\to }{\Lambda }^0+\gamma +\gamma$

Answer to Problem 33P

Solution:

Possible

Explanation of Solution

${\Sigma }^0\stackrel{}{\to }{\Lambda }^0+\gamma +\gamma$

Charge: 0=0+0+0

Charge on both sides of the equation are equal. Thus, charge is conserved.

Baryon: 1=1+0+0

Baryon on both sides of the equation are equal. Thus, baryon is conserved.

Lepton:0=0+0

Lepton on both sides of the equation are equal. Thus, lepton is conserved.

Strangeness: -1=-1+0+0

Strangeness on both sides of the equation are equal. Thus, Strangeness is conserved.

Isospin: 0=0+0+0

Isospin on both sides of the equation are equal. Thus, Isospin is conserved.

Thus, the above decay is possible.