Splitting of the pygmy dipole resonance in ${}^{138}\mathrm{Ba}$ and ${}^{140}\mathrm{Ce}$ observed in the $(\alpha ,\alpha {}^{\prime }\gamma )$ reaction

The $N=82$ nuclei ${}^{140}\mathrm{Ce}$ and ${}^{138}\mathrm{Ba}$ have been investigated by means of the $(\alpha ,{\alpha }^{\prime }\gamma )$ coincidence method to study the pygmy dipole resonance (PDR). The experiments have been performed at the AGOR cyclotron at KVI, Groningen, at a primary beam energy of $E_{\alpha }=136$ MeV. The Big-Bite Spectrometer and seven large-volume high-purity germanium detectors were used in coincidence to perform a simultaneous spectroscopy of the scattered $\alpha$ particles and the $\gamma$ decay. The comparison with results of nuclear resonance fluorescence experiments reveals a splitting of the PDR into two components. Up to about 6 MeV the same states that could be observed in $(\gamma ,{\gamma }^{\prime })$ are also excited in $\alpha$-scattering experiments, whereas the higher-lying states are missing in the $(\alpha ,{\alpha }^{\prime }\gamma )$ reaction. This indicates a structural splitting of the PDR into two modes with different underlying structure.

Figure 1

This $\alpha$-$\gamma$ coincidence matrix shows the $\gamma$-ray decay energy, $E_{\gamma }$, measured with a germanium detector positioned at backward angles versus the excitation energy, $E_x$, in the experiment on ${}^{138}\mathrm{Ba}$. In this matrix, transitions between bound states occur as thin horizontal lines. The regions of ground-state decays and decays into the $2_1^{+}$ state are marked with diagonal lines.

Figure 2

Two-dimensional scattering matrix and projections for the ${}^{138}\mathrm{Ba}(\alpha ,{\alpha }^{\prime }\gamma )$ experiment. Different decay channels can be selected by applying conditions on the $\alpha$-$\gamma$ coincidence matrix. Ground-state decays can be selected to study $E1$ ground-state transitions of the PDR. The resulting $\gamma$ spectrum has a strongly reduced background and shows clearly separated peaks.

Figure 3

Illustration of the angles for the $\alpha$-$\gamma$ angular correlation.

Figure 4

$\alpha$-$\gamma$ angular correlations for transitions from states with $J^{\pi }=1^{-}$, 2${}^{+}$, and $3^{-}$ to the ground state of an even-even nucleus as a function of ${\theta }_{\gamma }$. Each plot shows the distribution of the averaged angular correlation for the full acceptance of the BBS, which was positioned at 3.5°.

Figure 5

Ground-state decay spectra obtained with HPGe detectors at different angles for ${}^{138}\mathrm{Ba}(\alpha ,{\alpha }^{\prime }\gamma )$. The value of the averaged angular correlation $W(L\pi )$ is denoted for the corresponding angles. Strong transitions are labeled with the angular momentum. Peaks marked with asterisks (*) stem from background transitions in ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$.

Figure 6

$\alpha$-$\gamma$ angular correlations for dipole and quadrupole transitions in ${}^{138}\mathrm{Ba}$. The upper plot shows the calculated $E1$ distribution (solid line) and the extracted data points for the $1^{-}$ state at 5511.3(10) keV. The lower plot shows the corresponding values for the $2_1^{+}$ state at 1435.816(10) keV. The given errors are statistical only. Due to a laboratory scattering angle of $3.5^{°}$ (corresponding to the central BBS angle) the angular correlation is not symmetric around ${180}^{°}$ and therefore it has been plotted for angles (${\theta }_{\gamma }$) from $0^{°}$ up to ${360}^{°}$ in the reaction plane.

Figure 7

(a) Final $\gamma$-ray spectrum for ground-state decay measured in ${}^{140}\mathrm{Ce}(\alpha ,{\alpha }^{\prime }\gamma )$ and summed for all the HPGe detectors. Peaks marked with an asterisk (*) stem from transitions in ${}^{16}\mathrm{O}$. (b) Single cross sections for the excitation of the $1^{-}$ states in ${}^{140}\mathrm{Ce}$ deduced from $(\alpha ,{\alpha }^{\prime }\gamma )$ measurement. The solid line shows the energy-dependent sensitivity limit. (c) $B(E1)$$\uparrow$ strength distribution measured with the $(\gamma ,{\gamma }^{\prime })$ reaction.

Figure 8

Same as in Fig. 7 but for ${}^{138}\mathrm{Ba}(\alpha ,{\alpha }^{\prime }\gamma )$ and ${}^{138}\mathrm{Ba}(\gamma ,{\gamma }^{\prime })$. Around 4439 keV the spectrum is dominated by the transition stemming from ${}^{12}\mathrm{C}$.

Figure 9

$B(E1)\uparrow$ strength distribution measured in $(\gamma ,{\gamma }^{\prime })$ convoluted with a Lorentzian function with $\Gamma =500$ keV for ${}^{140}\mathrm{Ce}$ (upper part) and ${}^{138}\mathrm{Ba}$ (lower part), respectively. All of the $1^{-}$ states are included in the gray-shaded distribution. The black-shaded distribution includes only states that could be observed in $(\gamma ,{\gamma }^{\prime })$ as well as in $(\alpha ,{\alpha }^{\prime }\gamma )$.