We consider the constraints of causality and unitarity for the low-energy
interactions of protons and neutrons. We derive a general theorem that
non-vanishing partial-wave mixing cannot be reproduced with zero-range
interactions without violating causality or unitarity. We define and calculate
interaction length scales which we call the causal range and the Cauchy-Schwarz
range for all spin channels up to J = 3. For some channels we find that these
length scales are as large as 5 fm. We investigate the origin of these large
lengths and discuss their significance for the choice of momentum cutoff scales
in effective field theory and universality in many-body Fermi systems.Comment: 36 pages, 10 figures, 7 tables, version to appear in Eur. Phys. J.
