Proton Charge Distribution and Form Factor Problem

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SUMMARY

The discussion focuses on evaluating the charge distribution of a proton and finding the constant of proportionality required to normalize the charge density function ρ. The user successfully completed part I by integrating ρ(r)dV, resulting in a constant of proportionality of 1/(4πR²). However, they encountered difficulties in part II, which involves a complex integral with exponential and sine functions. The user seeks confirmation on whether to proceed with the cyclic integral approach for part II.

PREREQUISITES
  • Understanding of charge distribution in particle physics
  • Knowledge of integral calculus, specifically volume integrals
  • Familiarity with spherical coordinates and their applications
  • Basic concepts of normalization in mathematical functions
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  • Research methods for solving complex integrals involving exponential and trigonometric functions
  • Study the concept of cyclic integrals and their applications in physics
  • Explore normalization techniques in quantum mechanics and particle physics
  • Learn about charge density functions and their implications in field theory
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Students and researchers in physics, particularly those focusing on particle physics and mathematical modeling of charge distributions.

Borntofly123
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Homework Statement



Hi all - I have been trying to evaluate part II of this problem for a long time now... For a simplified model of a proton's charge distribution,
hw1eqn2.gif


  1. Find the constant of proportionality required to normalise ρ correctly.
  2. Show that
    hw1eqn3.gif

Homework Equations


N/A

The Attempt at a Solution


I have done part I by method of integrating rho(r)dV between 0 and infinity and setting it equal to 1. dV in this case would just be 4*pi*r^2*dr with no angular dependence.
I have got the constant of proportionality as 1/4*pi*R^2

When I attempt to do part II all I get to is a horrible integral with an exponential and a sin function in... Am I going about this correctly, should i follow through with the cyclic integral?
 
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