Damping of multiphonon giant resonances

Abstract

The phonon damping model (PDM) is applied to derive the equations that describe the damping of three-, and n -phonon giant resonances. As examples of the application of this approach, the results of numerical calculations for the double giant resonance (DGDR) ( n=2) and triple giant dipole resonance (TGDR) ( n=3) in 90 Zr, 120 Sn and 208 Pb are discussed and compared with those obtained by folding independent giant dipole resonances (GDRs) (the folding results). For the DGDR in the double magic nucleus 208 Pb, we found that these results are very close to the folding results. In the open-shell nuclei 90 Zr and 120 Sn, a clear deviation from the folding results is observed in calculations in agreement with the experimental trend. The results for the integrated strength and energy of TGDR are found to be much closer to the folding results in all three nuclei. The TGDR widths in the open shell nuclei are found to be larger than the folding results. We also show that the relationship S 1 (2)=4 S 1 (1) S 0 (1) , which connects the energy-weighted sum (EWS) S 1 (2) of the DGDR strengths to the EWS S 1 (1) and the non-energy-weighted sum of strengths (NEWS) S 1 (1) of GDR, does not hold in any approximation in which the energy of the two-phonon state is deviated from the sum of energies of the two one-phonon states due to anharmonicity. A small deviation of the two-phonon energy is enough to cause a noticeable change in the DGDR strength compared to the independent-phonon picture. A new sum rule relationship is derived within the PDM.