Electric dipole response of neutron-rich calcium isotopes in relativistic quasiparticle time blocking approximation

New results for electric dipole strength in the chain of even-even calcium isotopes with the mass numbers $A=40–54$ are presented. Starting from the covariant Lagrangian of quantum hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for $J\le 6$ and natural parity were computed in a self-consistent relativistic quasiparticle random-phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations $\left(2\mathrm{q}\otimes \mathrm{phonon}\right)$ formed the model space for the calculations of the dipole response function in the relativistic quasiparticle time blocking approximation. The calculations in the latter approach were performed for the giant dipole resonance (GDR) and compared to those obtained with the RQRPA and to available data. The evolution of the dipole strength with the neutron number is investigated for both high-frequency GDRs and low-lying strengths. The development of a pygmy resonant structure on the low-energy shoulder of the GDR is traced and analyzed in terms of transition densities. A dependence of the pygmy dipole strength on the isospin asymmetry parameter is extracted.

Figure 1

Excitation spectra for the calcium isotopic chain obtained within the RQTBA (thick black curves) in comparison to the RQRPA (thin black curves). Evaluated experimental data [81] are given by green solid curves and the original data [29] are displayed by the error bars.

Figure 2

Electric dipole strength distribution in Ca isotopes at low energies, calculated in the R(Q)RPA and R(Q)TBA models. The vertical blue lines indicate the experimental particle emission thresholds (proton for ${}^{40,42}\mathrm{Ca}$ and neutron for the rest of the isotopes). See text for further details.

Figure 3

RQTBA transition densities for the most prominent peaks in ${}^{48}\mathrm{Ca}$.

Figure 4

(a) Integrated dipole strength below 10 MeV calculated within the RQTBA for calcium isotopes. (b) RQTBA pygmy dipole strength in Ca isotopes, compared to that in Pb, Sn, and Ni isotopes [69], versus the squared isospin asymmetry parameter. Energy intervals are shown in square brackets.

Figure 5

Fraction of the energy-weighted sum rule (EWSR) in Ca isotopes below 10 MeV, relative to the Thomas-Reiche-Kuhn sum rule. Inset: EWSR for ${}^{40-48}\mathrm{Ca}$ on a smaller scale, compared to data of Ref. [15]. For the cases where there are strong peaks around 10 MeV, the EWSR in reduced energy intervals excluding these peaks are presented.