{"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 rates affect their detection in a spherical detector.", "specific_scope": "The focus is on calculating the necessary Lorentz factor that would allow a specific proportion of fast-decaying particles to reach the inner walls of a spherical detector with a given radius.", "goal": "Determine the Lorentz factor required for approximately two thirds of the 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 fast-decaying particles to reach the inner walls of a spherical detector. The task involves understanding how the Lorentz factor influences the decay and travel of particles, ultimately leading to the conclusion that a Lorentz factor of 54 is needed for about two thirds of the particles to reach the detector."}