Dipole response in ${}^{128,130}\mathrm{Te}$ below the neutron threshold

Background: Numerous studies of the ground-state decay of the pygmy dipole resonance (PDR) have been carried out in the past. However, data on the decay of the PDR to low-lying excited states is still very scarce due to limitations of the sensitivity to weak branching transitions of experimental setups.

Purpose: We present a detailed examination of the low-energy dipole response of ${}^{128}\mathrm{Te}$ and ${}^{130}\mathrm{Te}$ below their neutron separation thresholds of 8.8 and 8.5 MeV, respectively.

Methods: Photonuclear reactions with the subsequent $\gamma$-ray spectroscopy of the decay channel with continuous-energy bremsstrahlung at varying endpoint energies and linearly polarized quasimonochromatic $\gamma$-ray beams with energies ranging from 2.7 to 8.9 MeV in steps of roughly 250 keV were used for probing the decay behavior of the low-energy dipole response in ${}^{128}\mathrm{Te}$ and ${}^{130}\mathrm{Te}$. In addition, $(\vec{\gamma },{\gamma }^{\prime }{\gamma }^{\prime \prime })$ reactions were used to study the population of low-lying states of ${}^{128}\mathrm{Te}$.

Results: Spin-parity quantum numbers and reduced transition probabilities are determined for individual photo-excited states. The analysis of average decay properties for nuclear levels in narrow excitation-energy bins enable the extraction of photoabsorption cross sections, average branching ratios to the $2_1^{+}$ state, and the distinction between $E1$ and $M1$ transitions to the ground state and to the $2_1^{+}$ state accounting for resolved and unresolved transitions.

Conclusions: Above 5 MeV, the experimental data are in reasonable agreement to calculations within the quasiparticle phonon model. The major fraction of the ground-state decay channel is due to $E1$ transitions, while less than $5–10$% stem from $M1$ transitions. Furthermore, first direct experimental evidence is provided that the population of the $2_1^{+}$ state of ${}^{128}\mathrm{Te}$ via primary $\gamma$-ray transitions from excited states in the PDR region from 5 to 9 MeV is dominated by $E1$ transitions of $1^{-}$ states.

Figure 1

Measured $\gamma$-ray spectra at an azimuthal scattering angle of $\vartheta ={130}^{\circ }$ at DHIPS for ${}^{128}\mathrm{Te}$ (upper panel) and ${}^{130}\mathrm{Te}$ (lower panel) with electron beam energies of $E_{e^{-}}=9.13$ MeV and $E_{e^{-}}=8.5$ MeV, respectively. Peaks originating from transitions of the calibration standard ${}^{11}\mathrm{B}$ and the single escape (SE) peak of the 5020-keV transition of ${}^{11}\mathrm{B}$ are indicated.

Figure 2

Spectral beam distributions exemplarily for two beam energies of $E_b=6.19$ MeV and $E_b=7.72$ MeV at $\mathrm{HI}\gamma \mathrm{S}$ (black). The absolute photon flux $N_{\gamma }$ is determined by normalization to known integrated cross sections of excited states of ${}^{128}\mathrm{Te}$ (red dots) determined in the NRF experiment with bremsstrahlung at DHIPS.

Figure 3

Illustration of the experimental approach to extract the photoabsorption cross section, ${\sigma }_{\gamma }={\sigma }_{\gamma \gamma }+{\sigma }_{\gamma {\gamma }^{\prime }}$, from NRF measurements using quasimonochromatic $\gamma$-ray beams at $\mathrm{HI}\gamma \mathrm{S}$. (a) The “elastic” part ${\sigma }_{\gamma \gamma }$ is determined by observing all ground-state transitions (green solid arrows). (b) The “inelastic” contribution ${\sigma }_{\gamma {\gamma }^{\prime }}$ is approximated by the ground-state transition intensity of the first (few) $2^{+}$ states (red solid arrow), which are populated by cascading transitions (red dashed arrows). Transitions potentially bypassing the first $2^{+}$ states are indicated (gray dotted arrows).

Figure 4

Typical spectra from single $\gamma$-ray spectroscopy (black histograms) recorded with an HPGe (upper panel) and an LaBr (lower panel) detector at a beam energy of $E_b=6.4$ MeV (dashed line). Deploying a detector-response deconvolution procedure on natural-background corrected $\gamma$-ray spectra results in the corresponding red histograms.

Figure 5

Typical low-energy part of the $\gamma$-ray spectrum recorded with an HPGe detector after photoexcitation of levels of ${}^{128}\mathrm{Te}$ with $E_b=8.56$ MeV at $\mathrm{HI}\gamma \mathrm{S}$. Decays of the first excited states of ${}^{128}\mathrm{Te}$ are observed, which are populated via cascade transitions of states excited in the energy region of 8.56 MeV.

Figure 6

Angular distribution ratio for the determination of spin-quantum numbers of excited states in ${}^{130}\mathrm{Te}$. In total 156 $J^{\pi }=1^{\pm }$ states were observed for the first time (filled blue circles), while three $J^{\pi }=1^{\pm }$ levels were already known before (open blue circles) [80].

Figure 7

Obtained $\gamma$-ray spectra at a beam energy of $E_b=6.45$ MeV with HPGe detectors placed perpendicular (upper panel) and parallel (lower panel) to the polarization plane indicated by the double-sided arrow.

Figure 8

Experimental asymmetries determined for individual nuclear transitions (upper panel) observed in ${}^{130}\mathrm{Te}$ and averaged over the excitation-energy range defined by the spectral distribution of the monoenergetic $\gamma$-ray beam (lower panel). The dotted horizontal lines indicate the simulated expectation values taking the detector geometry into account for pure $E1$ and $M1$ or $E2$ transitions, which cannot be distinguished in the given setup geometry.

Figure 9

Experimental $\gamma$-ray spectra obtained for ${}^{128}\mathrm{Te}$ with HPGe detectors placed perpendicular (a) and parallel (b) to the beam's polarization plane. Panel (c) shows the $\gamma$-ray spectrum recorded at a backward position defined in Table 2. The spectral distribution of the incoming $\gamma$-ray beam with $E_b=4.33$ MeV (dashed line) is displayed in (a). The dashed vertical lines indicate all observed transitions in this measurement.

Figure 10

Experimental asymmetries determined for individual nuclear transitions (upper panel) observed in ${}^{128}\mathrm{Te}$ and averaged over the excitation-energy range defined by the spectral distribution of the monoenergetic $\gamma$-ray beam (lower panel). The dotted horizontal lines indicate the expectation values for pure $E1$ and $M1$ or $E2$ transitions, which cannot be distinguished in the given setup geometry.

Figure 11

Experimental asymmetries ${\epsilon }_v$ (a) and ${\epsilon }_h$ (b) obtained with the ${\gamma }^3$ setup for ${}^{128}\mathrm{Te}$ in the excitation-energy range from 2.7 to 9.0 MeV. The correlation of both asymmetries (c) enables a simultaneous assignment of spin and parity-quantum numbers.

Figure 12

Summed matrix for all combinations of $\gamma \text{−}\gamma$ coincidences between two LaBr detectors at $E_b=8.0$ MeV. Low-energy trigger thresholds are set to $\approx 600$ keV to reduce the dead time of the detection system.

Figure 13

Gated spectra of the $\gamma \text{−}\gamma$ coincidence matrix shown in Fig. 12. Insets: Low-energy region of the projection from LaBr-LaBr coincidences below 1.6 MeV. The hatched and cross-hatched areas correspond to applied gates on $\gamma$-ray transitions of ${}^{128}\mathrm{Te}$ and on random background radiation, respectively. For details see text.

Figure 14

Experimental $E1$ strength distribution for ${}^{128}\mathrm{Te}$ (a) and ${}^{130}\mathrm{Te}$ (b) with the corresponding experimental sensitivity limit displayed as red-dotted line. Values from QPM calculations are shown in (c) for ${}^{128}\mathrm{Te}$ and in (d) for ${}^{130}\mathrm{Te}$, where the marked values are scaled down by a factor of 1.5 for a better display. Predicted $M1$ excitations are shown for both nuclei in panels (e) and (f). See text for details.

Figure 15

Average cross sections for ${}^{128}\mathrm{Te}$ and ${}^{130}\mathrm{Te}$. Elastic cross sections are determined accounting for isolated transitions (open green squares) and including contributions from unresolved transitions (blue squares) shown in panels (a) and (b). A comparison of the total photoabsorption cross sections (black dots), the complete elastic cross sections (blue squares), and the inelastic cross sections (red triangles) to $(\gamma ,n)$ cross sections (green diamonds) from Ref. [94] and computed values in the QPM (dotted line) is displayed in panels (c) and (d). For a detailed discussion see text.

Figure 16

Separation of the elastic cross sections into contributions from $E1$ and $M1$ transitions for ${}^{128}\mathrm{Te}$. Above 4.5 MeV a decomposition of the complete elastic cross sections presented in Fig. 15 is performed for each beam-energy setting. The summed reduced ground-state transition widths are displayed for the $E1$ (blue circles) and the $M1$ parts (black circles). Below 4.5 MeV in light blue and light gray bars the results for individual transitions are shown.

Figure 17

Separation of the elastic cross sections into contributions from $E1$ and $M1$ transitions for ${}^{130}\mathrm{Te}$. A decomposition of the complete elastic cross sections shown in Fig. 15 is performed for each beam-energy setting. The summed reduced ground-state transition widths are displayed for the $E1$ (blue circles) and the $M1$ parts (black circles).

Figure 18

Balance of experimentally extracted primary $\gamma$-ray transitions to low-lying excited states as a function of the beam energy. (a) Complete cross sections for direct population of the $2_1^{+}$ state (black squares). Its separation into parts stemming from $1^{-}$ states (open squares) and $1^{+}$ states (blue crosses) will be discussed in more detail in Sec. 4e. (b) Comparison of the average branching ratio $\langle b_1\rangle$ between experiment (black dots) and QPM calculations for $1^{-}$ states (blue line). (c) Analysis of the different relative contributions to ${\sigma }_{\gamma {\gamma }^{\prime }}$ from direct decays to the $2_1^{+}$ state (black bar) and to other low-lying states (shaded bar) including resolved and unresolved transitions.

Figure 19

Angular correlations from $\gamma \text{−}\gamma$ measurements (black squares) with ${}^{32}\mathrm{S}$ and its well-known $1^{+}$ state at $E_b=8.125$ MeV (left-hand side) and exemplarily with ${}^{128}\mathrm{Te}$ at $E_b=6.19$ MeV (right-hand side) compared to theoretical values (triangles and circles) grouped into seven correlation groups. For details see text.