Microscopic calculation of double-dipole excitations

Abstract

In the last decade experimental and theoretical research has led to the discovery of double giant resonances—a giant resonance built on top of another giant resonance. The double-dipole resonance was first identified in a pion charge exchange reaction @1# and was predicted earlier @2#. Later the double dipole was detected in Coulomb excitation in heavyion reactions @3–5#. Properties of double dipole modes and other types of double resonances were studied and are reviewed in several review articles @2–4,6#. Theoretical studies have been mostly of the ‘‘macroscopic’’ type, introducing collective coordinates in the description of double giant resonances @2–4,6#. Some papers used semimicroscopic models in which the random phase approximation ~RPA! was employed to define the collective phonon states. Some extensions of the RPA have also been suggested @7,8#. Truly microscopic calculations are very difficult. A shell-model calculation requires very large spaces involving configurations made up of particles excited to several major shells. One must therefore truncate the space and limit the calculation to one-particle–one-hole (1p-1h) and two-particle– two-hole (2p-2h) configurations involving particles and holes in several major shells. Studies of this type were performed for some nuclei a few years ago @9#. In this work we present shell-model calculations of the double giant dipole state in O and Ca. By choosing light nuclei we are able to include a relatively large space of 1p-1h and 2p-2h configurations and therefore are able to study in detail the distribution of strength and the splitting of strength into the various allowed spin and isospin components. In the case of O we are able to account for the coupling of J50 and 2, 1p-1h states to the corresponding 2p-2h configurations. We also discuss energy weighted sum rules ~EWSR! and the relationship between these sum rules for the single and double giant resonances ~see also Ref. @10#!. The sum rules are evaluated in the shell model basis ~numerically! and in a boson model.