Isoscalar response of ${}^{68}\mathrm{Ni}$ to $\alpha$-particle and deuteron probes

Isoscalar giant resonances have been measured in the unstable ${}^{68}\mathrm{Ni}$ nucleus using inelastic alpha and deuteron scattering at $50A$ MeV in inverse kinematics with the active target MAYA at GANIL. Using alpha scattering, the extracted isoscalar giant monopole resonance (ISGMR) centroid was determined to be $21.1\pm 1.9$ MeV and the isoscalar giant quadrupole resonance (ISGQR) to be $15.9\pm 1.3$ MeV. Indications for soft isoscalar monopole and dipole modes are provided. Results obtained with both $\left(\alpha ,{\alpha }^{\prime }\right)$ and $\left(d,d^{\prime }\right)$ probes are compatible. The evolution of isoscalar giant resonances along the Ni isotopic chain from ${}^{56}\mathrm{Ni}$ to ${}^{68}\mathrm{Ni}$ is discussed.

Figure 1

Angular distribution predictions calculated in the DWBA approximation for the monopole excitation at 21 MeV, the dipole at 15 MeV, and the quadrupole at 17 MeV: (a) for the ${}^{68}\mathrm{Ni}\left(\alpha ,{\alpha }^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction; (b) for the ${}^{68}\mathrm{Ni}\left(d,d^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction. Both reactions have been performed at $50A$ MeV. For all these predictions, microscopic RPA transition densities are used to calculate the angular distribution.

Figure 2

Experimental setup: the active target MAYA used to study both ${}^{68}\mathrm{Ni}\left(\alpha ,{\alpha }^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ and ${}^{68}\mathrm{Ni}\left(d,d^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reactions.

Figure 3

(a) Scatter plot of recoiling alpha energy versus scattering angle in the laboratory frame for the ${}^{68}\mathrm{Ni}\left(\alpha ,{\alpha }^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction. (b) Same for recoiling deuterons for the ${}^{68}\mathrm{Ni}\left(d,d^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction.

Figure 4

(a) Reconstructed events transformed in the c.m. frame and corrected for geometrical and reconstruction efficiency for the ${}^{68}\mathrm{Ni}\left(\alpha ,{\alpha }^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction. (b) The same for the ${}^{68}\mathrm{Ni}\left(d,d^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction.

Figure 5

(a) Excitation-energy spectrum of ${}^{68}\mathrm{Ni}$ obtained for the ${}^{68}\mathrm{Ni}\left(\alpha ,{\alpha }^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction, for all angles deduced from the alpha kinematics and corrected for efficiency. (b) The same with a zoom on the ISGR region. The background is represented with a green dot-dot–short-dashed line. The fitted resonances which are expected to be of monopole character are represented with a red solid line, and the one that is expected to be of quadrupole character is represented with a blue long-dashed line. The resonance at higher energy, composed of several multipolarities $L=0,1,3$, is represented with a black dot–long-dashed line. The solid black line corresponds to the sum of all contributions. From (c) to (g) the same at ${\theta }_{\mathrm{c}.\mathrm{m}.}=3.5$°, 4.5°, 5.5°, 6.5°, 7.5°. In (c) and (d) there is no data at low energy due to geometrical acceptance as shown in Fig. 4.

Figure 6

(a) Experimental angular distribution extracted for the resonance at 12.9 MeV and fitted assuming an $L=0$ multipolarity (a1), $L=1$ multipolarity (a2), or $L=2$ multipolarity (a3). (b) The same for the resonance at 15.9 MeV assuming an $L=2$ multipolarity. (c) The same for the resonance at 21.1 MeV assuming an $L=0$ multipolarity.

Figure 7

(a) Experimental ${}^{68}\mathrm{Ni}$ angular distribution extracted in 2 MeV broad bins of excitation energy and fitted with a linear combination of $L=0,1,2$ theoretical angular distributions and a background. The solid black line corresponds to the sum of all contributions.

Figure 8

(a) Monopole strength distribution in ${}^{68}\mathrm{Ni}$ resulting from MDA. (b) The same for dipole strength. (c) The same for quadrupole strength.

Figure 9

Proton distribution coming from the deuteron breakup on ${}^{68}\mathrm{Ni}$, corrected for efficiency.

Figure 10

(a) Excitation-energy spectrum of ${}^{68}\mathrm{Ni}$ obtained in the ${}^{68}\mathrm{Ni}\left(d,d^{\prime }\right){}^{68}{\mathrm{Ni}}^{*}$ reaction, for all angles deduced from the deuteron kinematics and corrected for efficiency. The subtracted background is represented with a green dot-dot–short-dashed line. The resonances resulting from the fits are represented with a red solid line $\left(L=0\right)$, and with a blue long-dashed line $\left(L=2\right)$. The solid black line corresponds to the sum of all contributions. Panels (b) to (e) show the same fit at different angles in the c.m. frame, from 2.5° to 5.5°.

Figure 11

(a) Experimental angular distribution extracted for the resonance at 12.6 MeV and fitted assuming an $L=0$ multipolarity. (b) The same for the resonance at 20.8 MeV.

Figure 12

Experimental ${}^{68}\mathrm{Ni}$ angular distribution extracted for 2 MeV bins of excitation energy and fitted with a linear combination of $L=0$ and $L=2$ theoretical angular distributions and the simulated deuteron breakup induced background. The solid black line corresponds to the sum of all contributions.

Figure 13

Monopole strength distribution resulting from MDA.