Systematics of the double giant dipole resonances in nuclei

A generalization of the continuum open-shell r-space linear response random-phase approximation method to finite temperatures (i.e., TDRPA method) is applied in a study of the systematics of the electric double giant dipole resonance (DGDR) in magic and open-shell nuclei covering a wide range of nuclear masses. Viewing the DGDR as a single-phonon vibration in a hot nucleus, whose temperature corresponds to the centroid energy of the ground-state (zero-temperature) GDR, the TDRPA equation has been solved for the eleven nuclei whose DGDR state has recently been investigated in pion double-charge-exchange (DCX) experiments. The expected general features of a collective vibration in hot nuclei, particularly the broadening and the downshift of the GDR excitation energy due to increase in temperature, were found to be small, yet quite distinguishable. Except for the lighter nuclei, a reliable estimate for the DGDR energy would be EDGDR 2EGDR and the estimate for its width would be DGDR 2 GDR. However, the changes in the integrated cross sections of the DGDR due to finite temperature are found to be much more significant. An exact A-1/6 power law for the DGDR energy is suggested by the TDRPA solutions. A gratifying agreement between the TDRPA predictions and experiment has been established for the Q values of the relevant pion DCX reactions after taking into account the proper Coulomb and symmetry energy corrections.