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 ($N=50$) ${}^{88}\mathrm{Sr}$, ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Mo}$ is performed within this framework. The RQRPA extended by the coupling to collective vibrations generates spectra with a multitude of $2q\otimes \mathrm{phonon}$ (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.

Figure 1

The calculated dipole spectra for the light tin isotopes ${}^{100}\mathrm{Sn}$, ${}^{106}\mathrm{Sn}$, ${}^{114}\mathrm{Sn}$. Photo absorption cross sections computed with the artificial width 200 keV (b, d, f). The low-lying portions of the corresponding spectra in terms of the strength function, calculated with 20-keV smearing (a, c, e). Calculations within the RQRPA are shown by the dashed curves, and the RQTBA by the solid curves.

Figure 2

The same as in Fig. 1, but for heavier tin isotopes ${}^{116}\mathrm{Sn}$, ${}^{120}\mathrm{Sn}$, ${}^{130}\mathrm{Sn}$, compared to data of Ref. 53 for ${}^{116,120}\mathrm{Sn}$ shown by black circles with bars.

Figure 3

The calculated dipole spectra for the $N=50$ isotones ${}^{88}\mathrm{Sr}$, ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Mo}$. Photo absorption cross sections computed with the artificial width 400 keV (b, d, f). The low-lying portions of the corresponding spectra in terms of the strength function, calculated with 10-keV smearing (a, c, e). Calculations within the RQRPA are shown by the dashed curves, and the RQTBA by the solid curves. Experimental data are taken from Ref. 53 and are shown by black circles with bars.