Conclusions

In the present work, we have applied the relativistic mean field model to describe ground state and collective properties of E1 excitations in atomic nuclei. The framework of relativistic random phase approximation has been used to investigate possible soft isovector dipole modes (pygmy resonances) through the periodic table. It has been shown that the RRPA isovector dipole strength consists of two parts: the well known giant dipole resonance, and separated low energy mode. In general, low lying dipole strength increase relatively more when compared with the GDR strength, as the number of neutrons increase. RRPA approach have been applied to analyze the collectivity of dipole excitations in the region of the low-lying dipole strength. The collective nuclear properties of the low-energy states which exhausts a few percent of energy weighted sum rule, have been investigated through the periodic table. In particular we have analyzed the low-lying dipole strength by separating the contributions from RRPA amplitudes of each particle-hole configuration to the RRPA eigenvalues. The relationship between the neutron particle-hole excitations in the low-energy region and the existence of collective pygmy modes have been investigated. Calculations are performed with the standard nonlinear parameterization NL3 without additional adjustments, here resulting with the isovector giant resonances which obey the $A^{-1/3}$ law. In RRPA analysis, properties of the low-lying modes have been systematically compared with the corresponding giant resonances, to display the difference between the two modes. In the case of light neutron rich nuclei, in addition to the giant dipole resonance, we observe the onset of low-lying dipole strength corresponding mainly to the strong contribution of the single particle-hole excitations, without evidence of collectivity in these modes. As the mass number increase, more particle-hole configurations play a significant role in the low-energy states. The degree of collectivity increases with the mass number, and evidence of collective pygmy resonances is identified in the medium-heavy nuclei. Transition densities of low-energy peaks are characterized with a neutron dominated tail beyond the nuclear surface, with proton and neutron transition densities oscillating in phase in the internal region of nucleus. In comparison, the proton and neutron transition densities of the GDR mode have opposite signs, and both have similar contributions. The study of transition currents have been applied to investigate the collective low-lying dipole modes in medium nuclei. The corresponding velocity fields have disclosed the dynamical properties of soft dipole resonances. Accordingly, neutron excess oscillates against the symmetric proton-neutron core occupying the same orbitals, with main out of phase behavior in the region close to the surface region. Collective description with velocity fields makes possibillity of comparing the soft modes with simple hydrodynamical models describing similar dynamics of low-lying modes. But in these models oscillations of excess neutrons against the rest of nucleons are obtained as a result of such initial description of the system. In contrast, we describe dynamics of pygmy resonances in microscopic self-consistent approach, without special adjustments to a particular low-energy mode. Resulting properties of RRPA velocity fields nicely fits into the hydrodynamical assumption of two-fluid model. In the heavy nuclei, the existence of the collective low-energy pygmy mode is well established, characterized with many comparable neutron particle-hole contributions dominating against the response of proton p-h configurations.

Acknowledgments

This work has been supported in part by the Bundesministerium für Bildung und Forschung under contract 06 TM 979, by the Deutsche Forschungsgemeinschaft, and by the Gesellschaft für Schwerionenforschung (GSI) Darmstadt.

Nils Paar, 2001.