Electromagnetic dipole strength of ${}^{136}$Ba below the neutron separation energy

The electromagnetic dipole strength of the nucleus ${}^{136}$Ba has been investigated. Two measurements were performed with electron energies of 7.0 and 11.4 MeV at the bremsstrahlung facility at the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. Photon scattering experiments on the same nucleus have been performed at the high-intensity gamma-ray source (HI$\gamma$S) facility of the Triangle Universities Nuclear Laboratory between 4.7 and 9.3 MeV. The geant4 code has been used to determine detector response and non-nuclear scattered events. Thus it is possible to account for the dipole strength in the quasicontinuum of unresolvable transitions. A statistical code was used to simulate inelastic transitions and to determine the branching ratios of transitions to the ground state. The resulting photoabsorption cross section is compared to quasiparticle random-phase approximation and relativistic quasiparticle time blocking approximation calculations.

Figure 1

Photon flux determined from the known integrated scattering cross sections of states in ${}^{11}$B (circles) in comparison with the flux distribution explained in Sec. 3e (black curve) and its uncertainties (dashed curves).

Figure 2

The measured spectra of ${}^{136}$Ba after six days of beam time with $p_e·c$ $=$ 11.4 MeV summed over the detector pair at 127${}^{\circ }$ (black curve) and 90${}^{\circ }$ (red curve). The arrows indicate the known transitions of ${}^{11}$B.

Figure 3

Ratio of the integrated scattering cross sections of resolved states plotted for the two experiments at ELBE with different end points in photon energy.

Figure 4

Ratios of the intensities of transitions observed in the spectrum in the measurement with $p_e·c$ $=$ 11.4 MeV at ELBE. Ratios around the expected value of 0.74 (dashed line) are assumed to have dipole character; those close to 2.28 to have quadrupole character.

Figure 5

Comparison of the simulated and experimental detector response. Shown in the figure is the measured spectrum of a ${}^{60}$Co source (black curve) and the simulation (red curve) under the same geometrical conditions. The simulation is normalized to the experimental counts in the full energy peak at 1332 keV.

Figure 6

(a) Spectrum of photons scattered from ${}^{\mathrm{nat}}$C (black curve) in comparison with the simulations with geant3 (green curve) and geant4 (red curve). The simulations reproduce the single escape peak (SE) as well as the double escape peak (DE), when fitting the simulated area of the full energy peak (FE) to the experimental one. (b) A closer look at the energy region below the 15.1-MeV peak.

Figure 7

Spectrum summed for detectors at 127${}^{\circ }$ in the different steps of data analysis. The original spectrum, natural background removed (black curve), is corrected for detector response (red curve). The simulated non-nuclear scattered events (blue dashed curve) simulated with geant4 have to be subtracted from this. The final spectrum (green) includes only $\gamma$ rays from nuclear transitions. The abbreviations FE and SE denote the full energy peak and the single escape peak of the ${}^{11}$B transition at 8.9 MeV, as described in Sec. 3b.

Figure 8

Absolute detector efficiency obtained from calibration standards (data points) and from simulations with geant3 (black curve) and geant4 (red dashed curve) for one detector at 127${}^{\circ }$.

Figure 9

Comparison of detector resolution and level spacing. The dots show the full width at half maximum (FWHM) of the observed transitions. The solid curve shows the average level spacing, predicted by the back-shifted Fermi-gas model (BSFG) as mentioned in Sec. 3d just for $J^{\pi }=1^{-}$ states. The dashed curve is the average level spacing in the BSFG model including all spins and parities.

Figure 10

Integrated level density in experiment and model. The stairs show the experimental number of levels up to a certain energy bin. BSFG model (dashed line) and constant-temperature model (dotted curve) describe the low-energy part and the region around $S_n$ [33], but no assertion can be made about which model should be preferred, due to the finite detector resolution.

Figure 11

Simulated ratio of the intensity of ground-state transitions to the intensity for all transitions of levels in a given bin for ten realizations (black squares) in comparison to experimental values obtained from the experiment at HI$\gamma$S (red circles).

Figure 12

Spectra from the experiment at HI$\gamma$S. The plots show the response-corrected spectra (black) for two different beam energies. After removing the simulated non-nuclear scattered events (red), the resulting spectra (green) show the groups of transitions to the ground state (g.s.) and to excited states ($2_1^{+},2_2^{+},...$). The blue lines below the energy axis show the energy spread of the incident photon beam.

Figure 13

Photoabsorption cross section in ${}^{136}$Ba as a function of excitation energy. Open circles show the cross section without the correction for feeding and branching. The filled circles show the corrected absorption cross section. The solid curve represents a single Lorentz curve with the parameters given in the text, and the dashed curve shows the prediction of the TLO model.

Figure 14

Comparison between different isotopes in the same mass region. The measurement of this work on the nucleus ${}^{136}$Ba is represented by the black points. The strength function (black dashed curve) is given as a theoretical prediction. The green dots represent the measured photoabsorption cross section on ${}^{139}$La [13] whereas the green dashed curve shows an SLO as fitted in the RIPL3 database to ($\gamma ,n$) data on the same nucleus [38] corrected with a factor 0.85 [39]. The red circles [14] and the dashed curve [6] show the same information for the nucleus ${}^{138}$Ba, respectively.

Figure 15

Experimental data (black circles) in comparison to an SLO curve (black curve), the results of the RQTBA calculation (red curve), and the QRPA calculation (green curve). All data sets are given in 100-keV bins, QRPA strength is smeared out with Lorentzian functions of 250-keV width, and RQTBA results are obtained with the imaginary part of the energy variable equal to 250 keV.