Microscopic Nature of the Pygmy Dipole Resonance: The Stable Ca Isotopes

The electric dipole strength distribution in ${}^{44}\mathrm{C}\mathrm{a}$ has been measured up to 10 MeV in high resolution photon scattering experiments for the first time. The data obtained have been compared to earlier measurements on ${}^{40,48}\mathrm{C}\mathrm{a}$ in order to view the evolution of the electric pygmy dipole resonance (PDR). Calculations that were performed within the framework of the microscopic extended theory of finite Fermi systems, which adds contributions of the quasiparticle-phonon coupling to random phase approximation calculations, give a qualitative agreement with the experimental data for all three isotopes. We have shown that it is necessary to include this coupling to describe the PDR.

Figure 1

NRF spectrum of ${}^{44}\mathrm{C}\mathrm{a}$ taken at an end point energy of 9.9 MeV at a scattering angle of $130°$. Lines marked with an asterisk stem from the calibration standard ${}^{11}\mathrm{B}$ and from background lines.

Figure 2

Comparison of the experimental $B(E1)$-strength distribution in ${}^{40}\mathrm{C}\mathrm{a}$, ${}^{44}\mathrm{C}\mathrm{a}$, and ${}^{48}\mathrm{C}\mathrm{a}$ (upper panel) with calculations in the (Q)RPA (middle panel) and ETFFS (lower panel). The neutron (proton) separation energies for ${}^{40}\mathrm{C}\mathrm{a}$, ${}^{44}\mathrm{C}\mathrm{a}$, and ${}^{48}\mathrm{C}\mathrm{a}$ are 15.6 (8.3), 11.1 (12.2), and 9.9 (15.8) MeV, respectively.

Figure 3

Exhaustion of the isovector $E1$-EWSR. Experimental data points (squares) are compared to calculations in the C(Q)RPA (circles) and ETFFS (diamonds). The experimental errors are based on a linear addition of errors from each state, because the strength calculation uses the same photon flux calibration; i.e., the errors are not independent. The lines are drawn to guide the eye. One can see that the C(Q)RPA calculations give an approximately linear dependence on the neutron number, while those in the ETFFS scheme lead to an enhancement of the summed strength for ${}^{44}\mathrm{C}\mathrm{a}$ in comparison to ${}^{48}\mathrm{C}\mathrm{a}$.