Configuration Mixing Effects in Isoscalar Giant Dipole Resonance

Based on an explicit verification of the coupling matrix elements between the 1p1h and 2p2h states we propose a new method of selecting the most important 2p2h states responsible for fragmentation effects. In this way the dimensionality of the problem is reduced, such that the computation becomes feasible and the spreading of the strength is realistic, as verified by some tests of convergence. Calculations in $^{208}$Pb show that due to sizable mixing effects only about 50% of the total isoscalar giant dipole resonance (ISGDR) $3\hbar\omega$ strength is located in the energy region between 20 and 25 MeV. This is the energy region which currently is available in experiment. Even above 30 MeV we find about 10% of the total strength. This indicates that the current experimantal evaluations of the ISGDR centroid energy may significantly underestimate its value.