Nuclear-matter radius studies from ${}^{58}\mathrm{Ni}(\alpha ,\alpha )$ experiments at the GSI Experimental Storage Ring with the EXL facility

A novel method for measuring nuclear reactions in inverse kinematics with stored ion beams was successfully used to extract the nuclear-matter radius of ${}^{58}\mathrm{Ni}$. The experiment was performed at the experimental heavy-ion storage ring at the GSI facility using a stored ${}^{58}\mathrm{Ni}$ beam at energies of 100 and 150 MeV/u and an internal helium gas-jet target. Elastically scattered $\alpha$-recoils at low momentum transfers were measured with an in-ring detector system compatible with ultrahigh vacuum. Experimental angular distributions were fitted using density-dependent optical model potentials within the eikonal approximation. This permitted the extraction of the point-matter root-mean-square radius of ${}^{58}\mathrm{Ni}$ with an average value of 3.70(7) fm. Results from this work are in good agreement with several experiments performed in the past in normal kinematics. This pioneering experiment demonstrates a major breakthrough towards future investigations with far-from-stability stored beams using the present technique.

Figure 1

Schematic illustration of the vacuum chamber installed in the ESR for the present experiment [19]. The stored beam interacts with the gas-jet target oriented perpendicular to the beam. The detectors were assembled at two internal pockets centered at 81° and 32°, with respect to the beam direction. A slit plate was installed in front of the pocket centered at 81° (pocket 1) in order to reduce the angular spread caused by the extension of the target.

Figure 2

Energy deposited by recoils in the vertical strips of DSSD1 (pocket 1) vs. laboratory polar angle corresponding to each strip. Elastic scattering can be observed at angles from 86° to 89°. Inelastic scattering reaction channels can also be observed and their kinematics are highlighted with the dashed lines.

Figure 3

Elastic scattering cross section of ${}^{58}\mathrm{Ni}+\alpha$ at 100 and 150 MeV/u. The differential cross section is presented as ratio to the Rutherford elastic scattering cross section. The experimental data was fitted using different optical model potentials (for details see text).

Figure 4

(a) Probability density distribution obtained from a fit to the elastic scattering cross section using Eq. (4). At the bottom, one-dimensional PDFs $\left[p\right(x)=\int p(x,y\left)dy\right]$ are shown for the half-density radius (b) and the diffuseness (c). The best fit values are obtained from each function assuming a 68% confidence interval.

Figure 5

Point-density distributions of ${}^{58}\mathrm{Ni}$ deduced from the results of this work. The solid line is the result from the present experiment and the color band is its respective uncertainty. The point-matter density is compared with a Skyrme-Hartree-Fock calculation (SHF).