{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Particle Physics", "refinement": "This problem involves understanding the behavior of particles traveling at relativistic speeds and how their decay affects their ability to reach a detector.", "specific_scope": "The focus is on calculating the required Lorentz factor for particles to reach a spherical detector's inner walls, given their decay characteristics and the geometry of the detector.", "goal": "Determine the Lorentz factor needed for approximately two thirds of the fast-decaying particles to reach the detector's inner walls."}, "summary": "This problem is rooted in the principles of relativistic physics, specifically concerning the behavior of particles at high velocities. It requires calculating the Lorentz factor necessary for a certain proportion of particles to reach a detector's inner walls, given their decay rates and the geometry of the detector. The goal is to find the appropriate Lorentz factor from the provided options that would allow about two thirds of the particles to reach the detector."}