First experimental constraints on the interference of ${\frac{3}{2}}^{+}$ resonances in the ${}^{18}\mathrm{F}$($p,\alpha$)${}^{15}\mathrm{O}$ reaction

The interference effects among $J^{\pi }=3/2^{+}$ resonances in the ${}^{18}\mathrm{F}+p$ system have not been previously measured. $R$-matrix calculations show that the cross sections above the $E_{c.m.}=665$ keV resonance are sensitive to the interference between the $E_{c.m.}=8$, 38, and 665 keV resonances. An excitation function for the ${}^1\mathrm{H}$(${}^{18}\mathrm{F}$,α)${}^{15}\mathrm{O}$ reaction has been measured in the energy range of $E_{c.m.}=663\text{−}877$ keV using radioactive ${}^{18}\mathrm{F}$ beams at the Holifield Radioactive Ion Beam Facility (HRIBF). By comparing the observed cross sections with the $R$-matrix calculations, we provide the first experimental constraints on the interference. Upper limits on proton widths (${\Gamma }_p$) of the $E_{c.m.}=827$ and 842 keV resonances have been set as well.

Figure 1

A schematic diagram of the experimental setup is shown. A ${}^{18}\mathrm{F}$ beam was used to bombard a 70 μg/cm${}^2$ CH${}_2$ target. The α particles and ${}^{15}\mathrm{O}$ ions were detected in two silicon detector arrays, while scattered ${}^{18}\mathrm{F}$ were detected in a gas-filled ionization counter.

Figure 2

α energy vs heavy recoil energy plot. Events from ${}^1\mathrm{H}$(${}^{18}\mathrm{F}$,α)${}^{15}\mathrm{O}$ and ${}^1\mathrm{H}$(${}^{18}\mathrm{O}$,α)${}^{15}\mathrm{N}$ are shown in the gate. In this gate, the intense line is from ${}^1\mathrm{H}$(${}^{18}\mathrm{O}$,α)${}^{15}\mathrm{N}$ and the fainter line from ${}^1\mathrm{H}$(${}^{18}\mathrm{F}$,α)${}^{15}\mathrm{O}$. Strong elastic scattering groups lie along the x and y axes. ${}^1\mathrm{H}$(${}^{18}\mathrm{F}$,α)${}^{15}\mathrm{O}$ events could be identified by their different Q values. Two dashed lines show the regions where the events from two reactions are expected from kinematics.

Figure 3

SIDAR strip number vs energy plot for events with the correct total energy is shown. The ${}^{18}\mathrm{F}$($p,\alpha$)${}^{15}\mathrm{O}$ and ${}^{18}\mathrm{O}$($p,\alpha$)${}^{15}\mathrm{N}$ events are clearly visible. Here SIDAR strips 1–16 cover laboratory angles 29${}^{°}$–73${}^{°}$, respectively.

Figure 4

The ${}^{18}\mathrm{F}$($p,\alpha$)${}^{15}\mathrm{O}$ excitation function is shown in the figure together with calculations from the $R$-matrix code MULTI. The theoretical cross section was calculated over the complete range of energies and then averaged over the energy loss in the target as well as over the angles covered by SIDAR (${56}^{°}\le {\theta }_{c.m.}\le {138}^{°}$) for direct comparison with the data. Two cases of the relative interference signs are shown for illustration (see text). Most effective energy range for novae is indicated by the shaded box.

Figure 5

Astrophysical S-factor vs center of mass energy plots for four allowed possibilities. The signs of reduced widths for the $E_{c.m.}=8$, 38, and 665 keV resonances are shown in the legend. The most effective energy range for novae is also indicated.