A sign rule for nuclear potentials finally gets a rigorous proof

Physicists studying exotic hadrons like tetraquarks use the sign of the effective range to tell compact quark clusters apart from loosely bound molecular states, but this criterion lacked a firm theoretical basis. This work proves rigorously that any finite-range potential with a repulsive core and an attractive outer tail must have a strictly positive effective range, provided the scattering length exceeds the range of the potential. The result validates a widely used phenomenological rule and sharpens the conditions under which a negative effective range can reliably signal exotic compact states.