$1^{-}$ and $2^{+}$ discrete states in ${}^{90}\mathrm{Zr}$ populated via the $\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right)$ reaction

$2^{+}$ and $1^{-}$ states in ${}^{90}\mathrm{Zr}$ were populated via the $\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right)$ reaction at 340 MeV. The $\gamma$ decay was measured with high resolution using the AGATA (advanced $\gamma$ tracking array demonstrator array). Differential cross sections were obtained at few different angles for the scattered particle. The results of the elastic scattering and inelastic excitation of $2^{+},3^{-}$, and $1^{-}$ states are compared with distorted-wave Born approximation (DWBA) calculations, using both the standard collective form factor and a form factor obtained by folding microscopically calculated transition densities. This allowed to extract the isoscalar component of the $1^{-}$ state at 6.424 MeV. The comparison of the present $\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right)$ data with existing $\left(\gamma ,{\gamma }^{\prime }\right)$ and $\left(p,p^{\prime }\right)$ data in the corresponding region of the $\gamma$ continuum (6–11 MeV), characterized by a large $E1$ component, shows completely different behaviors of the cross section as a function of the nuclear excitation energy. The comparison of the data with DWBA calculations suggests a decrease of the isoscalar strength in the cross section with increasing excitation energy.

Figure 1

(Top) $\gamma$-ray energy spectrum in the 100–1250-keV interval, measured with the AGATA array and corresponding to the ${}^{17}\mathrm{O}$ scattering channel with the additional gating condition for selecting the kinetic energy loss of the scattered ions corresponding to $E_X>1$ MeV. (Middle) $\gamma$-ray energy spectrum in the 730–950-keV interval, measured with the AGATA array, corresponding to the ${}^{17}\mathrm{O}$ scattering channel with a gate at $E_x=4.7$ MeV ($\pm 0.5$ MeV). (Bottom) Same as above; in this case the gate is at $E_x=3.5$ MeV ($\pm 0.5$ MeV).

Figure 2

(Top) $\gamma$-ray energy spectrum in the 2–7-MeV interval, measured with the AGATA array and corresponding to the ${}^{17}\mathrm{O}$ scattering channel. (Middle) $\gamma$-ray energy spectrum in the same interval, corresponding to the ${}^{17}\mathrm{O}$ scattering channel with the additional condition of selecting the deexciting transitions to the ground state. (Bottom) $\gamma$-ray energy spectrum in the 5–12-MeV interval, measured with the AGATA array, corresponding to the ${}^{17}\mathrm{O}$ scattering channel, selecting the deexciting transitions to the ground state and with the additional condition on the angle between the emitted $\gamma$ ray and the recoil direction which enhances the $E1$ component. The peak corresponding to the single escape (s.e.) from pair production for the 6424-keV transition is indicated with an arrow.

Figure 3

The yield ratio $Y_R=Y\left({125}^{\circ }\text{–}{150}^{\circ }\right)/Y\left({100}^{\circ }\text{–}{125}^{\circ }\right)$ is shown for the known $1^{-}$ state at 6.424 MeV and for the known $2^{+}$ states at 2.186, 3.309, and 3.842 MeV together with that of continuous transitions in the energy interval 6.5–10 MeV. The error bars are statistical uncertainties. The two colored bands are one for the $E1$ transitions (the blue one) and the other for $E2$ transitions (the red one). They give the average $Y_R$ values for $E1$ and $E2$ transitions and the average uncertainty.

Figure 4

The level scheme of ${}^{90}\mathrm{Zr}$ relevant to this measurement, showing the $\gamma$ transitions observed in the present work.

Figure 5

(Top) ${}^{90}\mathrm{Zr}\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}\right){}^{90}\mathrm{Zr}$ elastic-scattering differential cross section in the center-of-mass frame measured at $E_{\text{beam}}=340$ MeV is shown in the inset of the figure. Data and calculations divided by the Rutherford cross section are displayed in the panel. (Bottom) Measured differential cross section ${}^{90}\mathrm{Zr}\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right){}^{90}\mathrm{Zr}$* at the same bombarding energy for the $3^{-}$ state at 2.748 MeV. The error bars shown with the data points represent the statistical error. The solid line curves are the predictions, described in the text, obtained within the optical model and the DWBA approach.

Figure 6

Inelastic scattering cross section ${}^{90}\mathrm{Zr}\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right){}^{90}\mathrm{Zr}$* at 340 MeV for the $2^{+}$ states 2.186 MeV (a), 3.309 MeV (b), 3.842 MeV (c) (black solid squares). The error bars are the statistical errors. The lines show DWBA calculations. The blue solid curves are the calculations with the standard phenomenological form factor [displayed in panel (d), blue line]. The red solid lines include the nuclear contribution calculated with the microscopic form factor shown in panel (d) (red line; see text) and derived with the transition density shown in the bottom panel of Fig. 7. For the case of the 3.842-MeV state [panel (c)] DWBA calculations performed with the standard phenomenological form factor but considering $M_n/M_p=0.1*N/Z$ (green line) are displayed. The gray curve represents the calculation performed considering only the Coulomb excitation.

Figure 7

(Top) Inelastic scattering cross section ${}^{90}\mathrm{Zr}\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right){}^{90}\mathrm{Zr}$* at 340 MeV for the $1^{-}$ state 6.424 MeV. The error bars are the statistical errors. The lines show DWBA calculations. The black solid curve represents the calculations with the standard phenomenological form factor. The red solid line includes the nuclear contribution calculated with the microscopic form factor shown in the bottom panel (see text) and derived with the transition density shown in the Fig. 8.

Figure 8

Transition densities for protons (red line) and neutrons (blue line) used to derive the form factors for the microscopic calculations for the $1^{-}$ pygmy states (top panel) and $2^{+}$ states (bottom panel).

Figure 9

(Top) The quantity ${\sigma }_R=\sigma \left(E_x\right)/\sigma \left(7\text{MeV}\right)$ in 0.5-MeV bins as a function of excitation energy, for the reactions $\left({}^{17}\mathrm{O},{}^{17}\mathrm{O}^{\prime }\gamma \right)$ (black solid circles), and deduced from $\left(\gamma ,{\gamma }^{\prime }\right)$ data (red triangles) [17] and from $\left(p,p^{\prime }\right) E1$ data (blue solid squares) from Ref. [18]. The lines are to guide the eyes and the error bars the statistical uncertainties. (Middle) The measured differential cross section at the average angle 10.$5^{\circ }$ for $\gamma$ transitions in 0.5-MeV bins is displayed with blue bars. The red bars give calculated DWBA cross-section predictions assuming $E1$ and using the $B\left(E1\right)\uparrow$ values from $\left(\gamma ,{\gamma }^{\prime }\right)$ [17] and standard form factors (see text). (Bottom) Electromagnetic reduced $E1$ transition strength deduced from the $\left(\gamma ,{\gamma }^{\prime }\right)$ data of Ref. [17], assuming $E1$ transitions.