Is the Dispersion Relation Applicable for Exotic Nuclear Systems? The Abnormal Threshold Anomaly in the

The threshold anomaly of the phenomenological potential has been known for a long time in nuclear reactions at energies around the Coulomb barrier, where the connection between the real and imaginary potentials is well described by the dispersion relation. However, this connection is not clear yet for some weakly bound nuclear systems, especially for reactions induced by exotic radioactive nuclei. In this study, precise optical potentials of the halo nuclear system ^{6}He+^{209}Bi were extracted via ^{208}Pb(^{7}Li,^{6}He) transfer reactions with energies measured downward to the extremely sub-barrier region. The real potential presents a bell-like shape around the barrier as a normal threshold anomaly in tightly bound nuclear systems. However, the imaginary potential shows an abnormal behavior: it increases first with energy decreasing below the barrier and then falls quickly down to 0. It is the first time the threshold of the imaginary potential has been determined in an exotic nuclear system. Moreover, experimental results show the dispersion relation is not applicable for this system, which may be a common phenomenon for exotic nuclear systems. We discuss possible explanations for such a peculiar behavior, but further study is still desired for the underlying physics.