PHY557_hw01_solutions

PHY557_hw01_solutions - Homework 1 1 11/1/2005 Homework I...

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Homework 1 1 11/1/2005 Homework I and Solutions Problems: I.1 Show that 1. e 2 /(4 πε 0 ) = 1.44 MeV fm. 2. α = 1/137 Solution: 1. e 2 /(4 πε 0 ) = (1.602E–19 C)/(4*3.142*8.85E–12 F/m) e = 1.440E–9 eV m = 1.44 MeV fm 2. α≡ e 2 /(4 πε 0 ) / ( ħ c ) = 1.440 MeV fm / 197.3 MeV fm = 1/137.0 I.2 Show that the process e e + γ is forbidden (in free space) by energy and momentum conser- vation. Similarly, show that the process γ e + e + is forbidden in free space. Solution: Energy-momentum conservation would be violated in the first process for a photon with non-zero energy E and momentum E/c . This is immediately obvious when one considers the process in the rest frame of the initial electron; any non-zero energy photon would involve a non-zero momen- tum, which would lead to a net energy-momentum increase in the final state. The process only occurs for energetic electrons in the Coulomb field of an nucleus, which takes up some recoil momentum in the process. The second process is forbidden because of energy-momentum conservation as well. Assume the
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PHY557_hw01_solutions - Homework 1 1 11/1/2005 Homework I...

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