Probing the structure of pygmy dipole resonance with its gamma decay

Abstract

The isospin properties and the collectivity of the pygmy dipole resonance (PDR) are long-standing open questions in nuclear structure studies. To answer these questions, the $γ$-decay of PDR states in $^{208}$Pb to the low-lying $2_{1}^{+}$ state is investigated using the Skyrme particle-vibration coupling (PVC) model. It is found that the $E1$ $γ$ decay from the PDR states to the low-lying $2_{1}^+$ state is strongly suppressed compared to that from the isovector giant dipole resonance (IVGDR), which reveals the predominantly isoscalar character of PDR. A detailed decomposition of the decay diagrams of the amplitudes of the processes contributing to the decay demonstrates the non-negligible presence of the 1 particle-1 hole configurations coupled to the $2_1^{+}$ phonon in the PDR wave function. Furthermore, we give a quantitative way to identify the components of complex-configurations in the wave function, and it is found that such component in PDR is smaller than that in IVGDR and much smaller than that in isoscalar giant quadrupole resonance (ISGQR).

Figures (4)

• Figure 1: The 12 lowest-order diagrams associated with the $\gamma$-decay between two vibrational states. The circle with lines includes the contribution to $Q_{\lambda\mu}$ from nuclear polarization Bohr1998II.
• Figure 2: Discrete isovector dipole transition strengths in $^{208}$Pb for SGII (a), SLy5 (b), and LNS (c). The black curves are the corresponding strength functions obtained by Lorentzian smoothing with $\Gamma/2=0.5$ MeV. The proton (red line) and neutron (blue line) transition densities of the dipole states around neutron emission threshold are shown in the inset graphs.
• Figure 3: The $\gamma$ transition strengths of PDR (a) and GDR (b) to $2_{1}^{+}$ in $^{208}$Pb for the 3 Skyrme interactions considered in this work. The black and blue hatched bars represent the total transition strength $B_{\gamma}$ and the average of proton and neutron contributions $\bar{B}_{\gamma}^{pn}$, respectively.
• Figure 4: Cumulative $\gamma$ transition strengths of the 12 diagrams of the selected pygmy dipole states to $2_{1}^{+}$ in $^{208}$Pb with the SLy5 interaction. The black solid and blue dashed lines represent the total transition strength $B_\gamma$ and the average of proton and neutron contributions $\bar{B}_{\gamma}^{pn}$, respectively.