Introduction

In many recent investigations of dipole excitations close to the neutron drip-line, appearance of the low-lying modes became of special interest in order to fully understand the dynamical properties of oscillations in the nuclei with large neutron excess. It has been suggested in many theoretical studies that excess neutrons have special role in the case of dipole induced oscillations. Accordingly, protons and neutrons occupying the same orbits like protons form a core that oscillates against the neutron excess, or the skin. Strong fragmentation of the isovector dipole strength, with appearance of the low energy peaks which are not of a resonant character, have been reported  [11] as a consequence of contributions from weakly bound orbitals, when approaching to the neutron drip-line. Early investigation with the three fluid hydrodynamical model [13] has shown the existence of two independent dipole modes in $^{208}$Pb instead of the single giant dipole resonance that obeys the A$^{-1/3}$ law. The dynamics of the interplay between the proton-neutron core and the excess neutrons has been investigated in the hydrodynamical two fluid model [12], which suggest the low energy pygmy dipole resonance that take up a sizable amount of the classical electric dipole sum rule. Microscopic approach with the density functional theory [20] had revealed the onset of a collective dipole oscillation decoupled from the main giant dipole resonance in the calcium isotopes. Hartree-Fock plus random phase approximation with Skryme interaction have been applied in order to analyze the structure of soft dipole resonances [19]. Further, the large scale shell model has been recently applied in order to investigate the occurrence of possible pygmy modes in the low-lying energy region [21]. Many experimental results on the topic of low energy dipole excitations have been reported. For example in Ref. [16,17], low-lying dipole strength exhausting around 10% of the classical sum rule was observed in the halo nuclei $^{11}Li$ and $^{11}Be$. In the case of unstable oxygen isotopes $^{18}O$, $^{20}O$ and $^{22}O$, it has been measured that 5% of the Thomas Reiche Kuhn sum rule correspond to the measured low-lying dipole strength [15]. Various methods have been developed in order to extract possible evidence of neutron excess contribution to the isovector dipole mode of oscillations. High resolution photon scattering experiment [18] on calcium isotopes have shown that the summed dipole strength between 5 and 10 MeV in $^{48}Ca$ is around 10 times larger than in the case of $^{40}Ca$ nucleus. The photo-neutron and electron scattering [22,23] on the $^{208}Pb$ nuclei indicates the fragmented E1 strength between 9-11 MeV, and it exhausts 3-6% of the corresponding sum rule. It still remains unclear whether the low energy strength correspond to resonance-like, collective motion in which participate significant number of particle-hole excitations, or if the single particle-hole nature is dominant. In that direction we investigate isovector dipole excitations in the relativistic random phase approximation (RRPA) through the periodic table. In the recent article [14] we have explored in the framework of RRPA the onset of collective Pygmy resonance in the $^{208}$Pb nucleus. Of course, the exact location of the peaks in the calculated low-lying strength depends on the effective interaction, thus it is necessary to compare results from various effective forces with experimental data, especially for more exotic nuclei.

This report is organized in the following way: In section 2 we present a short outline of the random phase approximation in the relativistic mean field theory and its application for dipole excitations. In section 3 we use this method to explore the low-lying dipole response in the light nuclei. Further we move with discussion on the collectivity of the low-lying dipole strength through the periodic table to the medium-heavy and heavy nuclei in the section 4, and section 5 contains final conclusions and a summary.

Nils Paar, 2001.