Multitude of $2^{+}$ discrete states in ${}^{124}\text{Sn}$ observed via the $({}^{17}\text{O}$, ${}^{17}\text{O}^{\prime }\gamma )$ reaction: Evidence for pygmy quadrupole states

A multitude of discrete $2^{+}$ states in ${}^{124}\text{Sn}$ with energy up to 5 MeV were populated and identified with the $({}^{17}\text{O}$, ${}^{17}\mathrm{O}^{\prime }\gamma )$ reaction at 340 MeV. Cross sections were compared with distorted wave Born approximation predictions and in general a good agreement was found. The measured energy and intensity distributions of the $2^{+}$ states are very similar to the predictions based on self-consistent density functional theory and extended QRPA approach accounting for multiphonon degrees of freedom. This provides evidence of the excitation of the pygmy quadrupole resonance in skin nuclei.

Figure 1

QRPA calculations for the isoscalar and the isovector partial contributions as well as the total electric quadrupole strength in ${}^{124}\text{Sn}$.

Figure 2

Top panel: $\gamma \text{-ray}$ energy spectrum in the 2–5 MeV interval, measured with the AGATA array and corresponding to the ${}^{17}\text{O}$ inelastic scattering channel. Central panel: $\gamma \text{-ray}$ energy spectrum in the 2–5 MeV interval, measured with the AGATA array and corresponding to the ${}^{17}\text{O}$ inelastic scattering channel with the additional condition of selecting the kinetic energy loss of the scattered ions with a gate at $E_x=E_{\gamma }$. Lower panel: $\gamma \text{-ray}$ energy spectrum in the 3.5–4.8 MeV energy interval with the same conditions of the central panel. The horizontal arrows in the middle and bottom panels are indicating the region of interest for the present work.

Figure 3

The part of the level scheme of ${}^{124}\text{Sn}$ relevant to this measurement showing the $\gamma$ transitions observed in the present work. The black solid arrows correspond to the known $E2$ ground-state transitions while the red arrows correspond to the unknown $E2$ ground-state transitions observed in this work. The black dashed arrows show the $\gamma$ decay of the populated $2^{+}$ states to other excited states.

Figure 4

Angular distribution of the measured $\gamma$ rays in the angular interval $0^{\circ }$–${90}^{\circ }$ obtained for the observed transitions. The red dots indicate the results for the transitions for which the multipolarity was not yet known.

Figure 5

The ratio between the counts in the angular interval ${60}^{\circ }$–${90}^{\circ }$ over the ones in ${30}^{\circ }$–${60}^{\circ }$ was deduced for all the observed transitions. The blue and the red regions highlight the ratio predicted for pure $E2$ and $E1$ transitions, respectively.

Figure 6

Inelastic scattering cross section ${}^{124}\text{Sn}$(${}^{17}\text{O}$, ${}^{17}\mathrm{O}^{\prime }$)${}^{124}\text{Sn}$* at 340 MeV for several $2^{+}$ states. The black dots represent the results of excited states with known multipolarity while the red dots are related to states for which the multipolarity was previously unknown. The error bars are the statistical errors. The lines show DWBA calculations. The black solid curves are the calculations with the standard phenomenological form factor and assuming $M_n/M_p=N/Z$. The red solid line, instead, represents the calculations for which $M_n/M_p=2.3\times N/Z$ was assumed.

Figure 7

Inelastic scattering cross section ${}^{124}\text{Sn}$(${}^{17}\text{O}$, ${}^{17}\mathrm{O}^{\prime }$)${}^{124}\mathrm{Sn}^{*}$ at 340 MeV for several $2^{+}$ states. The red dots represent the results related to states for which the multipolarity was previously unknown. The error bars are the statistical errors. The lines show DWBA calculations. The black solid curves are the calculations with the standard phenomenological form factor and assuming $M_n/M_p=N/Z$.

Figure 8

Comparison between the transition probabilities known from previous experiments [12, 13] (top panel), the one theoretically calculated [9] (bottom panel), and the cross sections measured in our experiment (middle panel).