solutions 03

Introductory Nuclear Physics

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PHY431 Homework Set 3 Reading: Lecture Notes Homework: See below: Due date: Wednesday Feb 9 Hints and Solutions Problem III.1 Calculate the form factor squared | F ( q ²)|² as function of q and as function of scattering angle θ for 400 MeV electron scattering off a fixed nuclear charge distribution: ρ ( r ) = ρ 0 for r <5 fm, ρ ( r ) = 0 for r >5 fm Make a plot of the form factor squared distribution. Hints: Use the Fourier transform, and properly normalize the form factor to 1 at q ²=0. Use EXCEL or some other graphing software for the plot. Solution: As given in the notes, we have the form factor: F ( q ²) = 4 π / ZEq 0 ρ ( r ) r sin( qr ) d r , with ρ ( r ) = ρ 0 for 0< r <5 fm, and 0 elsewhere. Because we will normalize the form factor to 1 at q ²=0, we only need to take care of the parameters q and r . We will make a change of variables x qr . Then: F ( q ²) = 1 / ( qR ρ 0 0 qR x sin( x ) d x = 1 / ( qR ρ 0 [- x cos x ] 0 qR + 1 / ( qR ρ 0 0 qR cos( x

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This homework help was uploaded on 02/05/2008 for the course PHY 431 taught by Professor Rijssenbeek during the Spring '01 term at SUNY Stony Brook.

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solutions 03 - phy431_s99_hw03 PHY431 Homework Set 3...

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