Reaction dynamics for the system ${}^{17}\mathrm{F}+{}^{58}\mathrm{Ni}$ at near-barrier energies

Charged reaction products originated from the interaction of the loosely bound radioactive ion beam ${}^{17}\mathrm{F}$ ($S_p=600$ keV) with the proton-shell closed ${}^{58}\mathrm{Ni}$ target were measured at two colliding energies slightly above the Coulomb barrier. The collected data were analyzed within the framework of the optical model to deduce the reaction cross section and to investigate the role played by inelastic excitations, transfer channels, and the breakup process ${}^{17}\mathrm{F}\to {}^{16}\mathrm{O}+p$ at near-barrier energies. The reaction cross section at the lower ${}^{17}\mathrm{F}$ energy showed a moderate enhancement ($~$$20\%$) with respect to that of the system ${}^{16}\mathrm{O}+{}^{58}\mathrm{Ni}$. At this energy direct reaction channels were also found to be more relevant than those for the reaction induced from the tightly bound projectile ${}^{16}\mathrm{O}$ on the same target. Both features could be strongly related to the very low binding energy of the ${}^{17}\mathrm{F}$ valence proton.

Figure 1

Layout of the secondary beam tracking system and the beam diagnostic detectors of the facility EXOTIC. All dimensions are in millimeters.

Figure 2

Energy spectra collected with a silicon detector placed along the beam axis 700 mm upstream the secondary target. The production reaction is ${}^1\mathrm{H}$(${}^{17}\mathrm{O}$,${}^{17}\mathrm{F}$)$n$ at a primary beam energy of 100 MeV and for a target gas pressure of 750 mbar at liquid-nitrogen temperature. The upper spectrum was obtained with the WF off, while the lower one was collected with a voltage difference $\pm$40 kV (corresponding to 80% of the maximum applicable voltage) across the WF electrodes.

Figure 3

Energy spectrum measured with the end-channel detector located along the beam axis 250 mm downstream of the secondary target. The production reaction is ${}^1\mathrm{H}$(${}^{17}\mathrm{O}$,${}^{17}\mathrm{F}$) $n$ at a primary beam energy of 100 MeV and for a gas pressure of 950 mbar at room temperature. The voltage applied across the electrodes of the WF was $\pm$40 kV.

Figure 4

${}^{17}\mathrm{F}$ horizontal (left column) and vertical (right column) secondary beam profiles. The top and middle rows were measured with the $x-y$-position-sensitive PPAC_A and PPAC_B, respectively. The bottom row corresponds to the event-by-event reconstruction of the secondary beam profile at the target position. The target profiles appear smoother because they were plotted with a 1-mm binning, whereas the original signals collected by the PPACs were used in the top and middle rows. See text for additional details.

Figure 5

Charged reaction products energy spectra collected at forward angles for the interaction of ${}^{17}\mathrm{F}$ ions with a ${}^{58}\mathrm{Ni}$ target at two beam energies: 54.1 MeV (left column) and 58.5 MeV (right column). Experimental data are drawn with histograms, while continuous lines are the results of Monte Carlo calculations assuming a pure Rutherford scattering process. See text for additional details.

Figure 6

JT spectrum collected from the EXODET modules located in the forward hemisphere for the reaction ${}^{17}\mathrm{F}+{}^{58}\mathrm{Ni}$ at 54.1 MeV. Each channel corresponds to a time interval of about 67 ns.

Figure 7

Quasielastic differential cross sections for the system ${}^{17}\mathrm{F}+{}^{58}\mathrm{Ni}$ at 54.1 and 58.5 MeV. Plotted errors include both statistical and systematical uncertainties. The solid and the dashed lines are the results of the optical model analysis performed according to the procedure described in detail in Sec. 4.

Figure 8

Calculated ${}^{17}\mathrm{F}$ and ${}^{16}\mathrm{O}$ energy spectra for inelastic scattering processes leading to the excitation of first excited state of ${}^{17}\mathrm{F}$ and ${}^{58}\mathrm{Ni}$ (a), for $p$ stripping reactions leading to the ${}^{59}\mathrm{Cu}$ ground state, second excited state (0.914 MeV), and a (possible) state with excitation energy around the $Q_{\mathrm{opt}}$ window (b), and for a breakup process occurring at excitation energies of 0.5 and 1.0 MeV above the breakup threshold (c). The calculated energy spectrum (multiplied by a factor of 0.01) for the ${}^{17}\mathrm{F}$ elastic scattering process was added to each panel for comparison. The calculations were performed for a secondary beam energy of 54.1 MeV and for a multistrip around ${\theta }_{\mathrm{c}.\mathrm{m}.}={76}^{°}$. For all processes but the elastic scattering, constant differential cross sections in the center-of-mass frame were employed for simplicity. More realistic angular distributions, for instance, peaked around the reaction grazing angle, would only slightly modify the shape of the spectra. The curves were normalized to the differential cross sections calculated at ${\theta }_{\mathrm{c}.\mathrm{m}.}={76}^{°}$. For the transfer process to a ${}^{59}\mathrm{Cu}$ excited state at 6.2 MeV, a differential cross section of 1.0 mb/sr was assumed.

Figure 9

Differential transition rates to the continuum for dipole (left) and quadrupole (right) electric operators. The initial state is the $d_{5/2}$ ground state of ${}^{17}\mathrm{F}$, and the final states are continuum states of the ${}^{16}\text{O}+p$ system with quantum numbers indicated in the legend. The quadrupole response shows the combined effect of resonant and nonresonant behavior for some multipolarities, while this is absent in the dipole response.

Figure 10

Optical model analysis of the experimental quasielastic angular distributions for the system ${}^{17}\mathrm{F}+{}^{58}\mathrm{Ni}$ at 54.1 (a) and 58.5 (b) MeV secondary beam energy. Dashed, dot-dashed, and solid lines show the contribution of the elastic scattering process (“Elastic”), the sum of the elastic and inelastic scattering angular distributions (“$\mathrm{Elastic}+\mathrm{Inelastic}$”), and the sum of differential cross sections for the elastic, inelastic, $p$ stripping, and breakup processes (“Quasi-Elastic”), respectively.

Figure 11

“Reduced” reaction cross sections for systems consisting of light projectiles interacting with a ${}^{58}\mathrm{Ni}$ or ${}^{64}\mathrm{Zn}$ target. The reduction is done according to the procedure described in Ref. [46].