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ph135_hw5 - Physics 135c Homework 5 1 Determine the...

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Physics 135c Homework 5 1.) Determine the non-relativistic elastic scattering form factor F ( | q | ) = integraldisplay d 3 ( r ) e i q · r for the following two densities: a) ρ ( r ) = ρ 0 =constant for r R and ρ = 0 for r > R , b) ρ ( r ) = ρ 0 e - r/R 2.) Beginning with the non-relativistic elastic scattering form factor F ( | q | ) = integraldisplay d 3 ( r ) e i q · r show that the mean square radius of the charge distribution is related to the derivative of the form factor, i.e.: < r 2 > = lim q 0 6 vextendsingle vextendsingle vextendsingle dF ( | q | ) d | q | 2 vextendsingle vextendsingle vextendsingle 3.) What are the nuclei, spins, parities, isospins, and “3”- component of isospin for the diagrams [a) - h)], shown on the next page, representing states of the three nucleon system. Note that these diagrams are short-hand for the full states but are sufficient to identify the nuclei. Use the shell model as a guide, and assume the state of lowest excitation energy in each case. If some of the total spins are not unique, list the range of possible values.
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