Quantum reflection times and space shifts for Casimir-van der Waals potential tails

The phase of the reflection amplitude for Casimir-van der Waals potential tails, depending on the criticl parameter ρ=ρ(C₃, C ₄) was studied. Three different models for the shape of the potential between the asyptotic limits was also studied. The phases were found to be more sensitive to the potential shape than the quantum reflection probabilities. It was also observed that above the threshold, the quantum reflected atom experienced a time gain relative to free motion, the time gain being smaller than that of the classical particle.