Breakup Threshold Anomaly: New Manifestation of the Dispersion Relation

It is pointed out that the usual threshold anomaly, found operative in the energy behavior of the imaginary and real parts of the optical potential representing the elastic scattering of tightly bound nuclei at near- and below-barrier energies, suffers a drastic qualitative change in the case of the elastic scattering of weakly bound nuclei. Owing to the strong coupling to the breakup channel even at sub-barrier energies, the imaginary potential strength seems to increase as the energy is lowered down to below the natural, barrier, threshold, accompanied by a decrease in the real potential strength. This feature is consistent with the dispersion relation. The system $^{6}$Li + $^{208}$Pb is analyzed to illustrate this new phenomenon.