Collectivity of double giant resonances in extended RPA theories

A comparison among extended random phase approximation (RPA) theories is made by calculating the strength functions of double phonon states of isovector dipole and isoscalar quadrupole giant resonances in ⁴⁰Ca using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM includes all the elements of one-body and two-body amplitudes and provides us with a quite general framework of extended RPA theories which consider the coupling of one-body amplitudes to two-body amplitudes. The results are compared with those obtained by using time-dependent versions of the second RPA (SRPA) and other extended RPA theories. It is found that SRPA overestimates collectivity of the isovector mode and underestimates that of the isoscalar mode. From a comparison between STDDM and other extended RPA theories, it is concluded that the inclusion of particle-hole--particle-hole amplitudes is necessary to obtain appropriate collectivity of double phonon states of giant resonances.