The assumed depth is the diameter of Earth. That's where the 10^-7 figure comes in. Look at eq. (1). It's dividing the initial energy (1,000 TeV, or 10^15) by t

The assumed depth is the diameter of Earth. That's where the 10^-7 figure comes in. Look at eq. (1). It's dividing the initial energy (1,000 TeV, or 10^15) by the diameter of Earth (10^-7) The beam energy of 1000TeV is chosen to "have approximately single interaction before the neutrino beam hits the bomb". The mechanism is for a neutrino to interact with the Earth a few meters before the bomb, creating a hadron shower that does the real work. If you look at the equations, they're sub-scripting "E" with "dep", meaning deposited. The figure is arrived at after accounting for the 1/10^7 probability that a given neutrino in the beam actually interacts in the right zone of soil. > The range of the neutrino is 10^7 meters and the effective neutrino interaction is restricted within a few meters away from the bomb because of the interaction range of the hadrons. Which I'm reading as: "we're going to lose the vast majority of this energy in the Earth itself, so we need to choose an initial power level so that, by the time the beam is interacting with the dirt just under the bomb, it's delivering ≈ 1kW of power."