Pygmy dipole strength in ${}^{90}\mathrm{Zr}$

The dipole response of the $N=50$ nucleus ${}^{90}\mathrm{Zr}$ was studied in photon-scattering experiments at the electron linear accelerator ELBE with bremsstrahlung produced at kinetic electron energies of 7.9, 9.0, and 13.2 MeV. We identified 189 levels up to an excitation energy of 12.9 MeV. Statistical methods were applied to estimate intensities of inelastic transitions and to correct the intensities of the ground-state transitions for their branching ratios. In this way we derived the photoabsorption cross section up to the neutron-separation energy. This cross section matches well the photoabsorption cross section obtained from ($\gamma$, $n$) data and thus provides information about the extension of the dipole-strength distribution toward energies below the neutron-separation energy. An enhancement of $E1$ strength has been found in the range of 6 to 11 MeV. Calculations within the framework of the quasiparticle-phonon model ascribe this strength to a vibration of the excessive neutrons against the $N=Z$ neutron-proton core, giving rise to a pygmy dipole resonance.

Figure 1

Parts of a spectrum of photons scattered from ${}^{90}\mathrm{Zr}$ combined with ${}^{11}\mathrm{B}$ during the irradiation with bremsstrahlung produced by electrons of an energy of $E_e^{\mathrm{kin}}=13.2$ MeV. This spectrum is the sum of the spectra measured with the two detectors placed at ${127}^{°}$ relative to the beam. The most dominant transitions assigned to ${}^{90}\mathrm{Zr}$ are marked with their energies in keV.

Figure 2

Absolute photon flux at the target deduced from intensities of transitions in ${}^{11}\mathrm{B}$ (circles) using the calculated efficiency and the relative photon flux calculated as described in the text (solid line).

Figure 3

Ratios of integrated cross sections $I_{s+f}$ of transitions in ${}^{90}\mathrm{Zr}$ obtained at different electron energies.

Figure 4

Experimental spectrum of ${}^{90}\mathrm{Zr}$ (corrected for room background and detector response) and simulated spectrum of atomic background (multiplied with efficiency and measuring time).

Figure 5

Scattering cross sections in ${}^{90}\mathrm{Zr}$, derived as ${\sigma }_{\gamma {\gamma }^{\text{'}}}=\sum _{\Delta }{I}_s/\Delta$, not corrected for branching and averaged over energy bins of $\Delta =0.2$ MeV, as derived from the difference of the experimental spectrum and the atomic background shown in Fig. 4 (“peaks $+$ cont.,” triangles) and from the resolved peaks only (“peaks,” circles).

Figure 6

Simulated intensity distribution of transitions depopulating levels in a 100-keV bin around 9 MeV in ${}^{90}\mathrm{Zr}$. The squares depict the intensities obtained from 10 individual nuclear realizations.

Figure 7

Branching ratios of ground-state transitions as obtained from the simulations of $\gamma$-ray cascades for ${}^{90}\mathrm{Zr}$. The squares represent the values of 10 individual nuclear realizations.

Figure 8

Photoabsorption cross section deduced from the present ($\gamma$, ${\gamma }^{\text{'}}$) data for ${}^{90}\mathrm{Zr}$ after correction for branching transitions (red circles) in comparison with data obtained from an experiment with monoenergetic photons (open black circles) [2], ($\gamma$, $n$) data taken from Ref. [27] (green boxes), and ($\gamma$, $p$) cross sections calculated with the TALYS code [30] (blue triangles).

Figure 9

Photoabsorption cross sections deduced from the present ($\gamma$, ${\gamma }^{\text{'}}$) data for ${}^{90}\mathrm{Zr}$ like the red circles in Fig. 8, but with modified $E1$ strength functions. The black squares are the results for a Lorentz curve with energy-dependent width (black line) and the red circles are the results for the assumption of a PDR on top of a Lorentz curve with constant width (pink line). The Lorentz curve with a constant width and without PDR is shown as a black dashed line.

Figure 10

Total photoabsorption cross section of ${}^{90}\mathrm{Zr}$ obtained by combining the present ($\gamma$, ${\gamma }^{\text{'}}$) data, the ($\gamma$, $n$) data of Ref. [27], and the ($\gamma$, $p$) calculations of Ref. [30]. The data were averaged over 0.5-MeV bins to reduce statistical fluctuations. The black dashed line represents a Lorentz curve with the parameters taken from Ref. [27], as also shown in Fig. 9. The blue solid line is the result of QRPA calculations discussed in Sec. 4b.

Figure 11

Proton and neutron ground-state densities of the $N=50$ isotones ${}^{88}\mathrm{Sr}$ and ${}^{90}\mathrm{Zr}$.

Figure 12

Calculated dipole one-phonon transition strengths up to $E_x=22$ MeV for the isotones ${}^{88}\mathrm{Sr}$ and ${}^{90}\mathrm{Zr}$.

Figure 13

Total photoabsorption cross section of ${}^{88}\mathrm{Sr}$ as taken from Ref. [7]. The black dashed line represents a Lorentz distribution with the parameters given in Ref. [7]. The blue solid line is the result of the present QRPA calculations.

Figure 14

Proton (solid lines) and neutron (dashed lines) transition densities in the $N=50$ nuclei ${}^{88}\mathrm{Sr}$ and ${}^{90}\mathrm{Zr}$.

Figure 15

Experimental cross sections derived from resolved peaks (squares) and from the full intensity corrected for inelastic transitions and branching ratios (circles) and cross sections predicted by QPM calculations (blue triangles) for ${}^{90}\mathrm{Zr}$, averaged over energy bins of 0.5 MeV. Lines are drawn to guide the eye.