Proton Electric Pygmy Dipole Resonance

The evolution of the low-lying $E1$ strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of $N=20$ isotones and $Z=18$ isotopes. For nuclei close to the proton drip line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

Figure 1

The $\mathrm{RHB}+\mathrm{RQRPA}$ isovector dipole strength distributions in the $N=20$ isotones, calculated with the DD-ME1 effective interaction (upper panels). For ${}^{44}\mathrm{Cr}$ and ${}^{46}\mathrm{Fe}$ the proton and neutron transition densities for the main peak in the low-energy region are displayed in the lower panels and, for ${}^{46}\mathrm{Fe}$, the transition densities for the main GDR peak.

Figure 2

The discrete Hartree-Bogoliubov and full RQRPA $E1$ spectra in ${}^{46}\mathrm{Fe}$ (left panel). For the main peaks in the low-energy region and in the region of the isovector GDR, the distributions of the RQRPA amplitudes are shown as functions of the unperturbed energy of the respective $2qp$ configurations (right panel).

Figure 3

The $\mathrm{RHB}+\mathrm{RQRPA}$ isovector dipole strength distribution in ${}^{32}\mathrm{Ar}$ (left panel). For the argon isotopes, the mass dependence of the centroid energy of the pygmy peak and the corresponding values of the integrated $B(E1)$ strength below 10 MeV excitation energy are shown in the right panel.

Figure 4

Transition densities and RQRPA amplitudes for selected $1^{-}$ states in ${}^{32}\mathrm{Ar}$. For the main peaks in the low-energy region and in the region of the isovector GDR, the proton and neutron transition densities are shown in the left panel. The corresponding distributions of the RQRPA amplitudes are displayed as functions of the unperturbed energy of the respective $2qp$ configurations (right panel).