Isospin Character of Low-Lying Pygmy Dipole States in ${}^{208}\mathrm{Pb}$ via Inelastic Scattering of ${}^{17}\mathrm{O}$ Ions

The properties of pygmy dipole states in ${}^{208}\mathrm{Pb}$ were investigated using the ${}^{208}\mathrm{Pb}$(${}^{17}\mathrm{O}$, ${}^{17}\mathrm{O}’\gamma$) reaction at 340 MeV and measuring the $\gamma$ decay with high resolution with the AGATA demonstrator array. Cross sections and angular distributions of the emitted $\gamma$ rays and of the scattered particles were measured. The results are compared with ($\gamma$, ${\gamma }^{\prime }$) and ($p$, $p^{\prime }$) data. The data analysis with the distorted wave Born approximation approach gives a good description of the elastic scattering and of the inelastic excitation of the $2^{+}$ and $3^{-}$ states. For the dipole transitions a form factor obtained by folding a microscopically calculated transition density was used for the first time. This has allowed us to extract the isoscalar component of the $1^{-}$ excited states from 4 to 8 MeV.

Figure 1

Left panel: $\gamma$-ray energy spectrum, measured with the AGATA array, corresponding to the ${}^{17}\mathrm{O}$ scattering channel and with the additional condition for selecting transitions to the ground state. The inset shows the details of the spectrum at high energy. Right panel: the angular distributions of the $E1$ $\gamma$-ray transition from the $1^{-}$ state at 5.512 MeV (top) and of the $E2$ transition from the $2^{+}$ state at 6.194 MeV. The red (blue) circle and line are for the $E1$ ($E2$) transition at 5.512 (6.194) MeV.

Figure 2

Cross section measurements (closed circles) and DWBA predictions (solid curves) for the ${{}^{208}\mathrm{Pb}({}^{17}\mathrm{O},{}^{17}\mathrm{O})}^{208}$ and ${}^{208}\mathrm{Pb}({}^{17}\mathrm{O},{{}^{17}\mathrm{O}}^{\prime }\gamma ){}^{208}\mathrm{Pb}$ at $E_{\text{beam}}=340\mathrm{MeV}$ in the center of mass frame. (a) Elastic-scattering cross section divided by the Rutherford cross section. (b),(c),(d) Cross sections for excited states at 2.618 MeV ($3^{-}$ state), at 4.085 MeV ($2^{+}$ state), and at 6.194 MeV ($2^{+}$ state), respectively. The error bars represent the statistical error. The green curves in panel (d) take into account the experimental error in the $B(E2{)}^{\uparrow }$ value known from ($\gamma$, ${\gamma }^{\prime }$) [23, 27].

Figure 3

Top panels: the measured differential cross section at the average angle of 15.6° for $E1$ transitions (red bars in the left panel) and $E2$ transitions (blue bars in the right panel). The inset shows the details in the higher energy region. The dashed bars give calculated DWBA excitation cross sections using the $B(E1)\uparrow$ and $B(E2)\uparrow$ values from ($\gamma$, ${\gamma }^{\prime }$) [23, 27] and standard form factors (see text). The shaded areas show the sensitivity limit of the experiment. Bottom panels: electromagnetic reduced transition strength measured with ($\gamma$, ${\gamma }^{\prime }$) experiments [23]. The statistical error of the experiment implies lower and upper values indicated with the short horizontal bars.

Figure 4

Panels (a) and (b) show the inelastic scattering cross section ${}^{208}\mathrm{Pb}({}^{17}\mathrm{O},{{}^{17}\mathrm{O}}^{\prime }){208\mathrm{Pb}}^{*}$ at 340 MeV for the $E1$ states 4.842 and 5.512 MeV, respectively. The error bars are the statistical errors. The lines show DWBA calculations. The green dotted curves are the Coulomb excitation cross sections and the blue dashed lines are calculations with the standard phenomenological form factor (tail of the GDR). The solid lines include the nuclear contribution calculated with the microscopic form factor shown in the bottom panel [panel (c), see text] and derived with the transition density shown in the inset.