Wavelength-independent fringe spacing in rainbows from falling neutrons

For particles with speed v and mass m emitted isotropically from a point source and falling under gravity g, the quantal probability density is dominated by a paraboloidal caustic decorated with paraboloidal interference fringes. Near the caustic, the fringes have a spacing independent of v and hence of wavelength, given by Delta R=3.53897*(h(cross)²/m²g)^1/3 for the first two (brightest) fringes at the level of the source. For neutrons in the Earth's field, Delta R=0.02617 mm. The effect might be difficult to detect.