Mode-coupling and the pygmy dipole resonance in a relativistic two-phonon model

A two-phonon version of the relativistic quasiparticle time blocking approximation (RQTBA-2) represents a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation (RQRPA), the two-phonon RQTBA implies a fragmentation of nuclear states over two-quasiparticle and two-phonon configurations. This leads, in particular, to a splitting-out of the lowest 1$^-$ state as a member of the two-phonon $[2^+\otimes3^-]$ quintuplet from the RQRPA pygmy dipole mode, thus establishing a physical mixing between these three modes. The inclusion of the two-phonon configurations in the model space allows to describe the positions and the reduced transition probabilities of the lowest 1$^-$ states in isotopes $^{116,120}$Sn as well as the low-energy fraction of the dipole strength without any adjustment procedures. The model is also applied to the low-lying dipole strength in neutron-rich $^{68,70,72}$Ni isotopes. Recent experimental data for $^{68}$Ni are reproduced fairly well

Elimination of 0+0^+ spurious states in the quasiparticle time blocking approximation

The quasiparticle time blocking approximation (QTBA) is considered as a model for the description of excitations in open-shell nuclei. The QTBA is an extension of the quasiparticle random phase approximation that includes quasiparticle-phonon coupling. In the present version of the QTBA, the pairing correlations are included within the framework of the BCS approximation. Thus, in this model, the $0^+$ spurious states appear, which are caused by the breaking of the symmetry related to the particle-number conservation. In this work, the method is described which solves the problem of the $0^+$ spurious states in the QTBA with the help of the projection technique. The method is illustrated by calculations of $0^+$ excitations in $^{120}$Sn nucleus.Comment: 12 pages, 3 figures - To appear in the proceedings of the 59-th International Meeting on Nuclear Spectroscopy and Nuclear Structure, June 15-19, 2009, Cheboksary, Russi

Self-consistent calculations of the electric giant dipole resonances in light and heavy mass nuclei

While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.Comment: 4 pages, 4 figure

Relativistic quasiparticle time blocking approximation. Dipole response of open-shell nuclei

The self-consistent Relativistic Quasiparticle Random Phase Approximation (RQRPA) is extended by the quasiparticle-phonon coupling (QPC) model using the Quasiparticle Time Blocking Approximation (QTBA). The method is formulated in terms of the Bethe-Salpeter equation (BSE) in the two-quasiparticle space with an energy-dependent two-quasiparticle residual interaction. This equation is solved either in the basis of Dirac states forming the self-consistent solution of the ground state or in the momentum representation. Pairing correlations are treated within the Bardeen-Cooper-Schrieffer (BCS) model with a monopole-monopole interaction. The same NL3 set of the coupling constants generates the Dirac-Hartree-BCS single-quasiparticle spectrum, the static part of the residual two-quasiparticle interaction and the quasiparticle-phonon coupling amplitudes. A quantitative description of electric dipole excitations in the chain of tin isotopes (Z=50) with the mass numbers A = 100, 106, 114, 116, 120, and 130 and in the chain of isotones with (N=50) 88-Sr, 90-Zr, 92-Mo is performed within this framework. The RQRPA extended by the coupling to collective vibrations generates spectra with a multitude of '2q+phonon' (two quasiparticles plus phonon) states providing a noticeable fragmentation of the giant dipole resonance as well as of the soft dipole mode (pygmy resonance) in the nuclei under investigation. The results obtained for the photo absorption cross sections and for the integrated contributions of the low-lying strength to the calculated dipole spectra agree very well with the available experimental data.Comment: 43 pages, 3 figure

Description of the Giant Monopole Resonance in the Even-A 112−124^{112-124}Sn Isotopes within the Microscopic Model Including Quasiparticle-Phonon Coupling

We have calculated the strength distributions of the giant monopole resonance in the even-A tin isotopes (A = 112-124) which were recently measured in inelastic $\alpha$-scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the HF+BCS approximation. The single-particle continuum was exactly included on the RPA level. The self-consistent mean field and the effective interaction were derived from the Skyrme energy functional. In the calculations, two Skyrme force parametrizations were used. The T5 parametrization with comparatively low value of the incompressibility of infinite nuclear matter ($K_{\infty}$ = 202 MeV) gives theoretical results in good agreement with the experimental data including the resonance widths.Comment: 21 pages, 2 figures; the figures have been modified: experimental data are shown in Fig.

Excitations of the unstable nuclei ^{48}Ni and ^{49}Ni

The isoscalar E1 and E2 resonances in the proton-rich nuclei ^{48,49}Ni and the {f_{7/2}3^-} multiplet in ^{49}Ni have been calculated taking into account the single-particle continuum exactly. The analogous calculations for the mirror nuclei ^{48}Ca and ^{49}Sc are presented. The models used are the continuum RPA for ^{48}Ni, ^{48}Ca and the Odd RPA for ^{49}Ni, ^{49}Sc, the latter has been developed recently and describes both single-particle and collective excitations of an odd nucleus on a common basis. In all four nuclei we obtained a distinct splitting of the isoscalar E1 resonance into 1 h-bar omega and 3 h-bar omega peaks at about 11 MeV and 30 MeV, respectively. The main part of the isoscalar E1 EWSR is exhausted by the 3 h-bar omega resonances. The 1 h-bar omega resonances exhaust about 35% of this EWSR in ^{48,49}Ni and about 22% in ^{48}Ca and ^{49}Sc. All seven {f_{7/2}3^-} multiplet members in ^{49}Ni are calculated to be in the (6-8) MeV energy region and have noticeable escape widths.Comment: 11 pages, 3 Postscript figure

Extended Theory of Finite Fermi Systems: Application to the collective and non-collective E1 strength in 208^{208}Pb

The Extended Theory of Finite Fermi Systems is based on the conventional Landau-Migdal theory and includes the coupling to the low-lying phonons in a consistent way. The phonons give rise to a fragmentation of the single-particle strength and to a compression of the single-particle spectrum. Both effects are crucial for a quantitative understanding of nuclear structure properties. We demonstrate the effects on the electric dipole states in $^{208}$Pb (which possesses 50% more neutrons then protons) where we calculated the low-lying non-collective spectrum as well as the high-lying collective resonances. Below 8 MeV, where one expects the so called isovector pygmy resonances, we also find a strong admixture of isoscalar strength that comes from the coupling to the high-lying isoscalar electric dipole resonance, which we obtain at about 22 MeV. The transition density of this resonance is very similar to the breathing mode, which we also calculated. We shall show that the extended theory is the correct approach for self-consistent calculations, where one starts with effective Lagrangians and effective Hamiltonians, respectively, if one wishes to describe simultaneously collective and non-collective properties of the nuclear spectrum. In all cases for which experimental data exist the agreement with the present theory results is good.Comment: 21 figures corrected typos in author fiel