Abstract
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 5fm. 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.
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Elhatisari, S., Lee, D. Causality bounds for neutron-proton scattering. Eur. Phys. J. A 48, 110 (2012). https://doi.org/10.1140/epja/i2012-12110-x
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DOI: https://doi.org/10.1140/epja/i2012-12110-x