Nuclear Deformation and Neutron Excess as Competing Effects for Dipole Strength in the Pygmy Region

The electromagnetic dipole strength below the neutron-separation energy has been studied for the xenon isotopes with mass numbers $A=124$, 128, 132, and 134 in nuclear resonance fluorescence experiments using the $\gamma \mathrm{ELBE}$ bremsstrahlung facility at Helmholtz-Zentrum Dresden-Rossendorf and the $\mathrm{HI}\gamma \mathrm{S}$ facility at Triangle Universities Nuclear Laboratory Durham. The systematic study gained new information about the influence of the neutron excess as well as of nuclear deformation on the strength in the region of the pygmy dipole resonance. The results are compared with those obtained for the chain of molybdenum isotopes and with predictions of a random-phase approximation in a deformed basis. It turned out that the effect of nuclear deformation plays a minor role compared with the one caused by neutron excess. A global parametrization of the strength in terms of neutron and proton numbers allowed us to derive a formula capable of predicting the summed $E1$ strengths in the pygmy region for a wide mass range of nuclides.

Figure 1

Measured spectra for filled (black) and empty steel containers (red). The spectra of ${}^{134}\mathrm{Xe}$, ${}^{132}\mathrm{Xe}$, and ${}^{128}\mathrm{Xe}$ are scaled up for a better view. The neutron ($S_n$) and proton ($S_p$) separation energies are marked with arrows.

Figure 2

Resulting photo-absorption cross sections for ${}^{124}\mathrm{Xe}$ (black circles), ${}^{128}\mathrm{Xe}$ (red squares) ${}^{132}\mathrm{Xe}$ (blue triangles down), and ${}^{134}\mathrm{Xe}$ (green triangles up). For comparison, predictions of RIPL3 (solid lines) and the TLO (dashed lines) are shown in the corresponding colors. The data for ${}^{128}\mathrm{Xe}$, ${}^{132}\mathrm{Xe}$, and ${}^{134}\mathrm{Xe}$ are multiplied by the factors 3, 10, and 30, respectively.

Figure 3

Summed $B(E1)\uparrow$ values versus neutron-to-proton number. The $\gamma \mathrm{ELBE}$ data for the four xenon isotopes (black squares) and for ${}^{136}\mathrm{Ba}$ (black asterisk) are shown in comparison with the $\gamma \mathrm{ELBE}$ data for the molybdenum isotopes [14] (red triangles) and with results for ${}^{136}\mathrm{Xe}$ and further $N=82$ isotones from other experiments [13] (open green circles). Further, the results of the QRPA calculations for all stable even-mass xenon (black solid line) and molybdenum isotopes (red solid line) as well as the TLO predictions (dashed lines) are shown.

Figure 4

Summed $B(E1)\uparrow$ values for different isotopes in the $N=50$ and $N=82$ region over the nuclear quadrupole deformation parameter ${\beta }_2$. The definition of the symbols corresponds to the one in Fig. 3.

Figure 5

Comparison of experimental data (red circles) and the prediction by Eq. (3) (black diamonds). The bottom subfigure shows the divergence of the two.