The time-dependent relativistic mean-field theory and the random phase approximation

Abstract

The Relativistic Random Phase Approximation (RRPA) is derived from the Time-dependent Relativistic Mean Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the ususal particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector meson fields which couple the αh-configurations with the phconfigurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the non-relativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained.

Particle-vibration coupling within covariant density functional theory

“…(57) increases considerably with the nuclear mass number because of the high level density. As it was investigated in a series of RRPA calculations [16,58], the completeness of the ph (αh) basis is very important for calculations of giant resonance characteristics as well as for current conservation and a proper treatment of symmetries, in particular, the dipole spurious state originating from the violation of translation symmetry on the mean field level. On the other side, the use of a large basis requires a considerable numerical effort and, therefore it is reasonable to solve the Eq.…”

“…A large variety of nuclear phenomena have been described over the years within this kind of model: ground state properties of finite spherical and deformed nuclei all over the periodic table [7] from light nuclei [8] to super-heavy elements [9,10], from the neutron drip line, where halo phenomena are observed [11], to the proton drip line [12] with nuclei unstable against the emission of protons [13]. Rotational bands are treated within the relativistic cranking approximation [14,15] and the Relativistic Random Phase Approximation (RRPA) [16] and quasi-particle RRPA [17] have been formulated as the small amplitude limit of time-dependent Relativistic Mean-Field (RMF) models for a description of collective and non-collective excitations. This method is successful, in particular, for the description of the positions of giant resonances and spin/isospin-excitations as the Isobaric Analog Resonance (IAR) or the Gamow-Teller Resonance (GTR) [18].…”

“…Relativistic RPA is obtained as the small amplitude limit of time-dependent Hartree theory [16]. In this case the relativistic single-particle density matrix ρ kk ′ is expanded around the static solution ρ 0 .…”

Large-scale continuum random-phase approximation predictions of dipole strength for astrophysical applications

“…In particular, the random-phase approximation (RPA), based on the relativistic mean field (RMF) theory, has proven to be a robust theory [1][2][3]. Pairing correlations for the study of open-shell nuclei as well as the self-consistent description of the residual interaction [4] have also been included over the years.…”

Continuum random-phase approximation for relativistic point coupling models

“…In order to investigate the dynamic behavior of the nuclear system, one considers oscillations around the self-consistent static solution. This can be done by solving the time dependent relativistic mean field equations (TDRMF) [7] or, in the limit of small amplitudes, by using the relativistic random phase approximation (RRPA) [8]. The corresponding eigen modes can be determined either by diagonalizing the RRPA equation in an appropriate basis or by solving the linear response equations in a time-dependent external field.…”