Abstract
The effects of ground-state correlations on the dipole and quadrupole excitations are studied for $^{40}$Ca and $^{48}$Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Large effects of the ground-state correlations are found in the fragmentation of the giant quadrupole resonance in $^{40}$Ca and in the low-lying dipole strength in $^{48}$Ca. It is discussed that the former is due to a mixing of different configurations in the ground state and the latter is from the partial occupation of the neutron single-particle states. The dipole and quadrupole strength distributions below 10 MeV calculated in ERPA are in qualitatively agreement with experiment.
Highlights
The random phase approximation (RPA) based on the Hartree-Fock (HF) ground state has extensively been used to study nuclear collective excitations
It is generally considered that the HF + RPA approach is the most appropriate for doubly-closed shell nuclei such as 16O and 40Ca for which the HF theory would give a good description of the ground states
The effects of ground-state correlations on the dipole and quadrupole excitations were studied for 40Ca and 48Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory
Summary
The random phase approximation (RPA) based on the Hartree-Fock (HF) ground state has extensively been used to study nuclear collective excitations. Recent theoretical studies for 16O show that the ground state of 16O is highly correlated and that the occupation probabilities of the single-particle states near the Fermi level deviate more than 10 % from the HF values [4, 5] This indicates that the HF + RPA approach which neglects the effects of ground-state correlations may not be so well founded even for doubly-closed shell nuclei. The self-consistent RPA (SCRPA) [8, 9] includes both the fractional occupation of the single-particle states and the correlated two-body density matrix which gives a self energy to a p-h pair and modifies p-h correlations. The procedures to determine the occupation probabilities and the correlation matrix are complicated and ambiguous [7, 9], and their applications have been limited to model Hamiltonians
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