HW 5 problems/solutions

HW 5 problems/solutions - Homework 5 1 Homework V and...

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Homework 5 1 11/1/2005 Homework V and Solutions V.1. The π 0 γγ decay: a. Deduce an expression for the energy of a γ from the decay 0 in terms of the mass m , the laboratory energy E , and the speed β of the 0 , and of the emission angle θ * of the in the 0 CMS. Solution: 1 2 ** 0* * * * 11 /2 /2 sin cos sin cos in CMS: , sin sin sin sin 22 cos cos a Lorentz transformation of // gives: zz mm pp θφ θθ ⊥⊥ ⎛⎞ ⎜⎟ == = = ⎝⎠ z 1,2 1,2 * * , , * 0/ 2 c o s 00 ( 1 c o s ) 0 Lab Lab z m mE Em pE p γβ βγ = = ± →= −± 1p p " b. Show that in the case J ( 0 )= 0, the * distribution will be isotropic (i.e. flat in cos *), and the energy distribution of the s will be uniform (i.e. flat), extending from E (1 )/2 to E (1 + )/2. Solution: In the CMS we have that pion is spinless and that the angular distribution thus can only contain the spherical harmonic with l = m =0: Y 0 0 = (1/4 ). Thus for the number of photons emitted
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This note was uploaded on 02/22/2009 for the course PHYSICS 557 taught by Professor Michaelrijssenbeek during the Fall '05 term at SUNY Stony Brook.

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HW 5 problems/solutions - Homework 5 1 Homework V and...

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