(Solution) - Some particle detectors measure the total number of particles integrated -(2025 Original AI-Free Solution)

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Some particle detectors measure the total number of particles integrated over part of a sphere of radius R, where the target is at the center of the sphere. Assuming symmetry about the axis of the incoming particle beam, use the Rutherford scattering formula to obtain the total number of particles detected in an an interval of width d?) as a function of the scattering angle, ?.