Cluster-transfer reactions with radioactive beams: A spectroscopic tool for neutron-rich nuclei

An exploratory experiment performed at REX-ISOLDE to investigate cluster-transfer reactions with radioactive beams in inverse kinematics is presented. The aim of the experiment was to test the potential of cluster-transfer reactions at the Coulomb barrier as a mechanism to explore the structure of exotic neutron-rich nuclei. The reactions ${}^7\mathrm{Li}({}^{98}\mathrm{Rb},\alpha \mathrm{xn})$ and ${}^7\mathrm{Li}({}^{98}\mathrm{Rb},\mathrm{t}\mathrm{xn})$ were studied through particle-$\gamma$ coincidence measurements, and the results are presented in terms of the observed excitation energies and spins. Moreover, the reaction mechanism is qualitatively discussed as a transfer of a clusterlike particle within a distorted-wave Born approximation framework. The results indicate that cluster-transfer reactions can be described well as a direct process and that they can be an efficient method to investigate the structure of neutron-rich nuclei at medium-high excitation energies and spins.

Figure 1

$\mathrm{\Delta }E\text{−}{E}_{\mathrm{T}}$ spectrum from the CD detector enabling the identification of the following charged particles: ${}^7\mathrm{Li}$ from elastic and inelastic scatterings, ${}^6\mathrm{He}$ from one-proton stripping, $\alpha$ particles from t transfer as well as ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ breakup, tritons from $\alpha$ transfer and ${}^7\mathrm{Li}$ breakup, deuterons (d) from ${}^6\mathrm{Li}$ breakup, and protons (p) from elastic scattering on target contaminants. The diagonal corresponds to particles which did not punch through the $\mathrm{\Delta }E$ detector, such as elastically and inelastically scattered ${}^{19}\mathrm{F}$ nuclei.

Figure 2

Doppler-corrected $\gamma$-ray spectra measured in coincidence with identified ${}^7\mathrm{Li}$ ions showing inelastic excitations of both ${}^{98}\mathrm{Rb}$ and ${}^{98}\mathrm{Sr}$ beam components. While the 144-keV line is the $2^{+}\to 0^{+}$ transition of ${}^{98}\mathrm{Sr}$, the 51-, 95-, and 115-keV $\gamma$ rays probably belong to ${}^{98}\mathrm{Rb}$ (see discussion in the text). Inset: $\gamma$ rays in coincidence with all detected particles with mass 7 or higher, showing the background which arises mostly from the inclusion of scattered ${}^{19}\mathrm{F}$ products which did not punch through the $\mathrm{\Delta }E$ detector.

Figure 3

Projection of the prompt $\left(\approx 200\mathrm{ns}\right) \gamma \text{−}\gamma$ coincidence matrix with and without Doppler correction (black and red lines, respectively). In the Doppler-corrected spectrum, the 212-keV $2^{+}\to 0^{+}$ transition of ${}^{100}\mathrm{Zr}$ can be seen, corresponding to $5n$ evaporation. Inset: projection of the $\gamma \text{−}\gamma$ coincidence matrix gated on the 212-keV line showing the relevant coincidence relationships between yrast transitions of ${}^{100}\mathrm{Zr}$ (labeled by stars). The last observed $\gamma$ ray at 625 keV corresponds to the $8^{+}\to 6^{+}$ transition. All other strong transitions in the spectra were identified but are not labeled for clarity.

Figure 4

Particle-gated $\gamma$-ray spectra for cluster-transfer channels followed by neutron evaporation for reactions on both ${}^{98}\mathrm{Rb}$ and ${}^{98}\mathrm{Sr}$. (a) $\alpha \text{−}\gamma$ coincidence data corresponding to the t-transfer channel. For reactions on ${}^{98}\mathrm{Rb}$, the $3n$ channel $\left({}^{98}\mathrm{Sr}\right)$ is indicated by circles (red), whereas the $2n$ one $\left({}^{99}\mathrm{Sr}\right)$ is identified by squares (blue). Transitions corresponding to reactions on ${}^{98}\mathrm{Sr}$ are labeled with a star with the $2n$ channel $\left({}^{99}\mathrm{Y}\right)$ marked by triangles (green). (b) $\mathrm{t}\text{−}\gamma$ coincidence spectra corresponding to the $\alpha$-transfer channel. For reactions on ${}^{98}\mathrm{Rb}$, the $3n$ channel $\left({}^{99}\mathrm{Y}\right)$ is indicated by circles (red) whereas the $2n$ one $\left({}^{100}\mathrm{Y}\right)$ is identified by squares (blue). Transitions corresponding to reactions on ${}^{98}\mathrm{Sr}$ are labeled with a star with the $2n$ channel $\left({}^{100}\mathrm{Zr}\right)$ marked by triangles (green).

Figure 5

Experimental yield of neutron evaporation for both t and $\alpha$ transfers on the ${}^{98}\mathrm{Rb}$ and ${}^{98}\mathrm{Sr}$ beam components compared with cascade predictions for different spin distributions. Panels (a) and (b) show the experimental data corresponding to t transfer whereas panels (c) and (d) correspond to $\alpha$-transfer channels (see text for details). Squares (blue) and triangle (green) symbols correspond to $2n$ evaporation whereas dots (red) refer to $3n$ channels.

Figure 6

Angular distribution for t [dots (red)] and $\alpha$ [diamonds (blue)] transfers on ${}^{98}\mathrm{Rb}$ compared with theoretical calculations (solid lines) as explained in the text. Data were rescaled with the same normalization factor. Inset: ratio between the elastic and the Rutherford cross sections as a function of the ${}^7\mathrm{Li}$ scattering angle. Data were fitted in order to obtain the optical parameters for elastic scattering.

Figure 7

Top panel: differential cross section as a function of excitation energy for the t-transfer channel on ${}^{98}\mathrm{Rb}$. The colored area corresponds to the experimental distribution whereas theoretical calculations are shown as a solid line (see text for details). The t separation energy is also indicated $\left(S_{\mathrm{t}}=16\mathrm{MeV}\right)$ as well as the expected maximum excitation energy $\left(E_{\mathrm{opt}}^{*}=18.7\mathrm{MeV}\right)$ deduced from the optimum $Q$ value. Bottom panel: differential cross section as a function of excitation energy for the $\alpha$-transfer channel on ${}^{98}\mathrm{Rb}$. The colored area corresponds to the experimental distribution whereas theoretical calculations are shown as a solid line (see text for details). The $\alpha$ separation energy is also indicated $\left(S_{\alpha }=10\mathrm{MeV}\right)$ as well as the expected maximum excitation energy $\left(E_{\mathrm{opt}}^{*}=18\mathrm{MeV}\right)$ deduced from the optimum $Q$ value.