Experimental study of the ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ fusion reaction and its implications for fusion of proton-halo systems

The total fusion cross section for the ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ system at incident energies near the top of the Coulomb barrier was studied using the newly developed Encore active-target detector at Florida State University. The ${}^{17}\mathrm{F}$ nucleus exhibits interesting nuclear structure properties in that although it has a low threshold against ${}^{17}\mathrm{F}\to {}^{16}\mathrm{O}+p$ breakup $(S_p=600\mathrm{keV})$, the valence proton is in the $1d_{5/2}$ shell in the ground state so that the nuclear matter radius is predicted to be similar to that of the ${}^{16}\mathrm{O}$ core. By contrast, the low-lying $1/2^{+}$ first excited state (bounded by 105 keV) with the valence proton in the $2s_{1/2}$ shell is considered to be a proton halo. In this paper possible influences of both the weak binding and the halo nature of the excited state on the total fusion cross section were investigated. The new data reported here complement existing measurements for the total fusion of ${}^{17}\mathrm{F}$ with heavy $\left({}^{208}\mathrm{Pb}\right)$ and medium mass (${}^{58}\mathrm{Ni}$) targets by extending the range of systems studied to one where Coulomb effects should be minimal. Total fusion cross sections for the stable counterpart systems ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ and ${}^{19}\mathrm{F}+{}^{12}\mathrm{C}$ were also measured to enable a systematic comparison. No significant influence of either the weak binding or the halo nature of the ${}^{17}\mathrm{F}1/2^{+}$ first excited state on the above barrier total fusion excitation function was observed when compared with the stable counterpart systems.

Figure 1

Upper panel: Three-dimensional schematic of the Encore detector, a multisampling ionization chamber where the field cage produces a perpendicular electric field. The field cage consists of a negatively biased cathode, voltage divider wired planes, a Frisch grid, and a segmented anode. The beam passes through the center of the active region. Lower panel: Schematic of the segmented anode. The first and last strips are used as veto and control, respectively. The 16 strips subdivided into left and right halves are also shown. The black arrow indicates a beam particle entering the active region of the detector. A fusion reaction occurs in strip 7 creating an evaporation residue (red arrow) which is identified by its larger energy loss signal.

Figure 2

Experimental traces measured in Encore. The beam traces inside the detector (black) have been normalized to a fixed value for the analysis. The normalization allows a consistent threshold to be set when searching for energy jumps within the segmented anode strips of the detector. Experimental ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ fusion events occurring in strip 7 are shown by the red traces. A jump in energy loss is seen as a result of the creation of an evaporation residue which will stop in the detector prior to the beam. The inset in the top-left corner shows the separation of the ${}^{17}\mathrm{F}$ and ${}^{16}\mathrm{O}$ beams in Encore due to their different time of flight.

Figure 3

Total fusion cross sections for ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ (black diamonds) measured in the present experiment compared with previously published data [36, 37, 38, 39, 40, 41, 42, 43, 44].

Figure 4

Total fusion cross sections for ${}^{19}\mathrm{F}+{}^{12}\mathrm{C}$ (black diamonds) measured in the present experiment compared with previously published data [36, 45, 46].

Figure 5

Reduced total fusion cross sections for the ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ (black circles) and ${}^{19}\mathrm{F}+{}^{12}\mathrm{C}$ (red triangles) systems measured in this paper. The corresponding no-coupling barrier penetration calculations using double-folded real potentials are denoted by the solid and dotted lines, respectively. The fusion barrier heights extracted from the potentials are indicated by the vertical arrows.

Figure 6

Reduced total fusion cross sections for the ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ (black circles) and ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ (blue diamonds) systems measured in this paper. The corresponding no-coupling barrier penetration calculations using double-folded real potentials are denoted by the solid and dotted lines, respectively. The fusion barrier heights extracted from the potentials are indicated by the vertical arrows.

Figure 7

Fusion excitation functions for ${}^{17}\mathrm{F}+{}^{12}\mathrm{C}$ calculated using the code fresco. The solid curve denotes the total fusion cross section, the dashed curve fusion for the entrance channel (projectile and target in their respective ground states), the dot-dashed curve fusion for the channel with the ${}^{17}\mathrm{F}$ in its 0.495-MeV $1/2^{+}$ excited state, the ${}^{12}\mathrm{C}$ in its ground state, and the dotted curve fusion for the channel with ${}^{17}\mathrm{F}$ in its ground state and ${}^{12}\mathrm{C}$ in its 4.44-MeV $2^{+}$ excited state.