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Description
The pygmy dipole resonance (PDR) is commonly associated with excess $E1$ strength superimposed on the low-energy tail of the giant dipole resonance (GDR), near the neutron-separation energy in both stable and unstable heavy nuclei. Although its detailed structure, properties, and origin remain under debate, the neutron-skin oscillation picture still prevails, suggesting a dependence of the PDR strength on neutron excess. Recent experimental studies, however, have challenged this interpretation [1, 2]. To further elucidate its structure, systematic investigations across isotopic chains, both of the PDR and the low-lying $E1$ strength in general, are of highly desired.
This work presents the most recent update on a consistent systematic study of the low-lying electric dipole strength and the potential PDR in stable and unstable Pd, Cd, In, Sn, and Sb isotopes with the Oslo method [3]. This method exploits the compound-nucleus mechanism to extract dipole $\gamma$-ray strength functions and nuclear level densities below the neutron threshold from particle–$\gamma$ coincidence data obtained in light-ion–induced reactions at the Oslo Cyclotron Laboratory. The most recent ($p,p^{\prime}\gamma$) and ($\alpha,p\gamma$) experiments have been performed with a new array of 30 LaBr3(Ce) scintillator detectors (OSCAR) with an improved energy resolution and timing properties for the selection of particle-$\gamma$ events as compared to the earlier experiments done with the NaI(Tl) detector array CACTUS. All previously published GSFs of Cd [3] and Pd [4] isotopes have been re-analysed to provide a more consistent analysis of the strengths in the Sn mass region.
With a wide range of isotopes, from neutron-deficient $^{109}$In to neutron-rich $^{127}$Sb, these dipole strengths provide an excellent basis for investigating the evolution of the PDR with increasing proton–neutron asymmetry. By combining these data with available $(\gamma,n)$ cross sections and dipole strengths from (p,p$^{\prime}$) Coulomb excitation experiments, we extract the low-lying $E1$ component of the total dipole strength in each case. This component is found to exhaust approximately $1$–$3\%$ of the classical Thomas–Reiche–Kuhn (TRK) sum rule, remaining nearly constant along the Sn isotopic chain and showing only a weak increase with neutron number in Cd and Pd isotopes. This behavior contradicts most theoretical approaches, such as relativistic quasiparticle random-phase and time-blocking approximations, which predict a strong, steady increase in low-lying $E1$ strength with neutron number. Moreover, a possible isovector component of the PDR is identified for $^{118-122,124}$Sn. Particular attention in this work will be given to the most neutron-deficient case, $^{109}$In, recently studied at OCL, which exhibits little to no excess $E1$ strength below the neutron threshold and thus stands out among neighboring isotopes. An interpretation of this observation within the random-phase time-blocking approximation framework will be discussed.
References
1. P. von Neumann-Cosel \textit{et al.}, Phys. Rev. Lett. \textbf{133}, 232502 (2024).
2. M. Markova \textit{et al.}, Phys. Lett. B \textbf{860}, 139216 (2025).
3. A. C. Larsen \textit{et al.}, Phys. Rev. C \textbf{83}, 034315 (2011).