Pygmy resonance and low-energy enhancement in the $\gamma$-ray strength functions of Pd isotopes

Background: An unexpected enhancement in the $\gamma$-ray strength function, as compared to the low-energy tail of the giant dipole resonance (GDR), has been observed for Sc, Ti, V, Fe, and Mo isotopes for $E_{\gamma }<4$ MeV. This enhancement was not observed in subsequent analyses on Sn isotopes, but a pygmy dipole resonance (PDR) centered at $E_{\gamma }\approx 8$ MeV was however detected. The $\gamma$-ray strength functions measured for Cd isotopes exhibit both features over the range of isotopes, with the low-energy enhancement decreasing and PDR strength increasing as a function of neutron number. This suggests a transitional region for the onset of low-energy enhancement, and also that the PDR strength depends on the number of neutrons.

Purpose: The $\gamma$-ray strength functions of ${}^{105–108}\mathrm{Pd}$ have been measured in order to further explore the proposed transitional region.

Method: Experimental data were obtained at the Oslo Cyclotron Laboratory by using the charged particle reactions $({}^3\mathrm{He},{}^3\mathrm{He}{}^{\prime }\gamma )$ and (${}^3\mathrm{He},\alpha \gamma$) on ${}^{106,108}\mathrm{Pd}$ target foils. Particle-$\gamma$ coincidence measurements provided information on initial excitation energies and the corresponding $\gamma$-ray spectra, which were used to extract the level densities and $\gamma$-ray strength functions according to the Oslo method.

Results: The $\gamma$-ray strength functions indicate a sudden increase in magnitude for $E_{\gamma }>4$ MeV, which is interpreted as a PDR centered at $E_{\gamma }\approx 8$ MeV. An enhanced $\gamma$-ray strength at low energies is also observed for ${}^{105}\mathrm{Pd}$, which is the lightest isotope measured in this work.

Conclusions: A PDR is clearly identified in the $\gamma$-ray strength functions of ${}^{105–108}\mathrm{Pd}$, and a low-energy enhancement is observed for ${}^{105}\mathrm{Pd}$. Further, the results correspond and agree very well with the observations from the Cd isotopes, and support the suggested transitional region for the onset of low-energy enhancement with decreasing mass number. The neutron number dependency of the PDR strength is also evident.

Figure 1

Coincidence matrices for ${}^{107}\mathrm{Pd}$. Details are provided in the text.

Figure 2

Normalization of the level density of ${}^{108}\mathrm{Pd}$. Data points are fitted between the arrows, and further details are provided in the text.

Figure 3

Normalization of the transmission coefficients of ${}^{108}\mathrm{Pd}$. The arrows indicate fit limits, and further details are provided in the text.

Figure 4

Extracted level densities (a) and $\gamma$-ray strength functions (b) of ${}^{105–108}\mathrm{Pd}$.

Figure 5

The extracted $f\left(E_{\gamma }\right)$ compared to models. The shaded area indicates systematical errors in the normalization procedure due to uncertainties in $\sigma ,D_0$, and $\langle {\Gamma }_{\gamma }\rangle$. The error bars of the Oslo data contain statistical errors, as well as uncertainties in the unfolding and extraction of first-generation $\gamma$-ray spectra.

Figure 6

The integrated PDR strengths of the Cd [16] and Pd isotopes.