${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ scattering and reaction dynamics around the Coulomb barrier

This work aims at investigating the projectile binding energy influence on the reaction dynamics, introducing new results and new data analysis methods in order to overcome some typically encountered problems, such as the identification of reaction products differing by few mass units and the discrimination of direct reaction processes. The ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ collision was studied at five near-barrier energies employing a compact experimental setup consisting of four double-sided silicon strip detectors (DSSSDs). Different reaction processes, namely the elastic and inelastic scattering and the $1n$ stripping, were discriminated by means of a detailed analysis of the experimental energy spectra based on Monte Carlo simulations. The elastic scattering angular distributions were investigated within the framework of the optical model using Woods-Saxon and double-folding potentials. The total reaction cross sections were extracted and the reduced cross sections compared with those obtained for ${}^{17}\mathrm{F}$ ($S_p=0.600$ MeV), the mirror nucleus of ${}^{17}\mathrm{O}$ ($S_n=4.143$ MeV), and for the tightly bound ${}^{16}\mathrm{O}$ projectile. The ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ total reaction cross sections were larger than those for ${}^{16}\mathrm{O}$ on the same target at the lowest energies studied, becoming identical, within errors, as the incident energy increased above the Coulomb barrier. This behavior was related to a strong contribution from the $1n$-stripping channel at the lowest energies.

Figure 1

(a) Photograph of the experimental setup. (b) Schematic view of the experimental setup. A, B, and D are 300 $\mu \mathrm{m}$ thick DSSSDs; C is a 43 $\mu \mathrm{m}$ thick DSSSD. An additional telescope IC/E consisting of an ionization chamber (IC) followed by a 100 $\mu \mathrm{m}$ thick surface barrier detector (E) was located at a backward angle.

Figure 2

Energy spectra collected by the back side (vertical strips) of detector A at a beam energy of $E_{\mathrm{lab}}=50$ MeV. In this three-dimensional plot the energy spectra of individual strips are plotted sequentially along the “strip number” axis from the most forward polar angle (strip 0) to the most backward polar angle (strip 31). The peak at higher (lower) energy corresponds to the ${}^{17}\mathrm{O}$ scattering from the ${}^{208}\mathrm{Pb}\left({}^{58}\mathrm{Ni}\right)$ target. The kinematics of the ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ collision is visible as the strip number (i.e., polar angle) increases.

Figure 3

Detail of the energy spectrum collected by a vertical strip at ${\theta }_{\mathrm{lab}}={119}^{\circ }$ and $E_{\mathrm{lab}}=42.5$ MeV and related to the ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ interaction. The experimental distribution (gray filled) shows binning-independent structures which indicate the contribution of more than one process. An example of the fitting procedure used for the discrimination of processes is also shown. The solid (black) line corresponds to the fitting function [Eq. (3.1)] which is the sum of four processes. The dotted line (blue), the dash-dotted line (purple), and the dashed line (red) represent the elastic scattering, the target excitation and the $1n$ stripping renormalized MC-simulated distributions, respectively. The contribution of the projectile excitation was found to be negligible at all energies.

Figure 4

Fractions of the contribution from elastic scattering (process a, blue circles), $1n$ stripping (process b, red squares), and target excitation (process d, purple diamonds) to the peak corresponding to the ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ collision at $E_{\mathrm{lab}}=42.5$ MeV for the backward detector C. The contribution of the projectile excitation was negligible. Each contribution was fitted with a second-order polynomial (solid, dashed, and dotted lines for the elastic scattering, $1n$ stripping, and target excitation, respectively).

Figure 5

Pixel correlation plot of vertical strip number 8 versus horizontal strip number 8 for detector A at $E_{\mathrm{lab}}=50$ MeV. The two spots (indicated by the arrows) at $\sim 43$ MeV and $\sim 48$ MeV correspond to the full energy peaks of ${}^{17}\mathrm{O}$ particles scattered from the ${}^{208}\mathrm{Pb}$ backing and ${}^{17}\mathrm{O}\left({}^{16}\mathrm{O}\right)$ originating from the interaction with the ${}^{58}\mathrm{Ni}$ target. Events distributed along the horizontal and vertical lines (at strip energies of $\sim 43$ and $\sim 48$ MeV) correspond to interstrip events on either side of the detector.

Figure 6

Distribution of ${}^{17}\mathrm{O}$ particles elastically scattered from the ${}^{208}\mathrm{Pb}$ target at $E_{\mathrm{lab}}=50$ MeV and detected by detector A. Pixels corresponding to ${\theta }_{\mathrm{c}.\mathrm{m}.}\simeq {55}^{\circ }$ were grouped together and highlighted.

Figure 7

Elastic scattering angular distributions for ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ at $E_{\mathrm{lab}}=50$ MeV. In the forward angular range, data from detector A (black squares) flawlessly overlap with those from detector B (red circles). Data from detector C, at backward angles, are plotted as green triangles.

Figure 8

Angular distributions for target excitation to its first excited state ($E^{*}=1.454$ MeV, $J^{\pi }=2^{+}$). These angular distributions are compared with CC calculations for the four highest beam energies: 42.5 MeV (green circles), 45 MeV (blue diamonds), 47.5 MeV (red triangles), and 50 MeV (hollow purple triangles). At $E_{\mathrm{lab}}=40$ MeV, the contribution to the integrated peak was not discriminated; see text for details.

Figure 9

Angular distributions for the $1n$ stripping process at five beam energies: 40 MeV (black squares), 42.5 MeV (green circles), 45 MeV (blue diamonds), 47.5 MeV (red triangles), and 50 MeV (hollow purple triangles). These angular distributions are compared with CCBA calculations; see text for details.

Figure 10

Elastic scattering angular distributions for ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ at five energies in the explored range. At forward angles the angular distributions extracted from detector A are plotted, whereas at backward angles the plotted angular distributions are extracted from detector C. Solid lines (WS-WS) correspond to fits using the first approach (Woods-Saxon potentials for both real and imaginary parts). Dashed lines (DF1-WS) correspond to the fits for the second approach (double folding potential for the real part and a Woods-Saxon potential for the imaginary part). Dotted lines (DF2-WS) correspond to the fits for the third approach (double folding potential with different densities for the real part and a Woods-Saxon potential for the imaginary part). The inset shows a detail of the forward angle range where the Coulomb-nuclear interference pattern is evident.

Figure 11

Trends of (a) the real part and (b) the imaginary part of the OMP as a function of the ratio to the Coulomb barrier of the incident energy ($V_b^{\mathrm{c}.\mathrm{m}.}=30.32$ MeV, $V_b^{\mathrm{lab}}=39.21$ MeV). Blue squares, red diamonds, and green triangles represent the first (WS-WS), second (DF1-WS), and third (DF2-WS) analyses, respectively; see text for additional details. Orange circles represent the scaled results for the ${}^{16}\mathrm{O}+{}^{58}\mathrm{Ni}$ system from Ref. [39]. The solid line is intended to guide the eye.

Figure 12

Total reaction cross sections for the ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}, {}^{17}\mathrm{F}+{}^{58}\mathrm{Ni}$ [48], and ${}^{16}\mathrm{O}+{}^{58}\mathrm{Ni}$ [39, 49, 50] systems compared. The energy in the center of mass system was scaled to the Coulomb barrier, whereas the reaction cross sections were scaled to the system mass according to the procedure described in Ref. [51]. Where not visible, error bars are beneath the symbol.