First application of the Trojan horse method with a radioactive ion beam: Study of the ${}^{18}\mathrm{F}{(p,\alpha )}^{15}\mathrm{O}$ reaction at astrophysical energies

Measurement of nuclear cross sections at astrophysical energies involving unstable species is one of the most challenging tasks in experimental nuclear physics. The use of indirect methods is often unavoidable in this scenario. In this paper the Trojan horse method is applied for the first time to a radioactive ion beam-induced reaction studying the ${}^{18}\mathrm{F}(p,\alpha$)${}^{15}\mathrm{O}$ process at low energies relevant to astrophysics via the three-body reaction ${}^2\mathrm{H}{(}^{18}\mathrm{F},{\alpha }^{15}\mathrm{O})n$. The knowledge of the ${}^{18}\mathrm{F}{(p,\alpha )}^{15}\mathrm{O}$ reaction rate is crucial to understand the nova explosion phenomena. The cross section of this reaction is characterized by the presence of several resonances in ${}^{19}\mathrm{Ne}$ and possibly interference effects among them. The results reported in literature are not satisfactory and new investigations of the ${}^{18}\mathrm{F}{(p,\alpha )}^{15}\mathrm{O}$ reaction cross section will be useful. In the present work the spin-parity assignments of relevant levels have been discussed and the astrophysical $S$ factor has been extracted considering also interference effects.

Figure 1

$Q$-value spectra. The $Q$-value spectrum for the ${}^2{\mathrm{H}(}^{18}\mathrm{F},{\alpha }^{15}\mathrm{O}$)$n$ reaction (black solid histogram) is overlaid to the total $Q$-value spectrum (dashed line). The arrow represents the theoretical $Q$ value (0.658 MeV) for the reaction at hand. The red line is a Gaussian fit with $\mu =0.668\mathrm{MeV}$ and $\sigma =0.322\mathrm{MeV}$, in agreement with the expected theoretical value and the experimental resolution.

Figure 2

Momentum distribution for the $p-n$ intercluster motion in deuteron. The solid line is the Hulthén function in momentum space.

Figure 3

The nuclear cross section spectrum in function of the $p{-}^{18}\mathrm{F}$ cm energy for the events that pass the conditions described in the text. The blue vertical line shows the position of the threshold for the ${}^{18}\mathrm{F}+p$ reaction ($E_{\mathrm{th}}=6.41\mathrm{MeV})$. The red dashed lines represent the Gaussians used for fitting the data as explained in the text. The red solid line is the total fit. The numbers above the arrows represents the peak positions in ${}^{19}\mathrm{Ne}$ excitation energy obtained from the fitting procedure.

Figure 4

The ${}^{18}\mathrm{F}(p,\alpha$)${}^{15}\mathrm{O}$ astrophysical $S$ factor from the present experiment. The full dots are THM experimental data with the assumption of $J^{\pi }=3/2^{+}$ for the resonance at $E=6460\mathrm{keV}$, the open ones correspond to the assumption of $J^{\pi }=5/2^{-}$ (the difference from this last assumption to the other possible value $1/2^{-}$ and $3/2^{-}$ being negligible within the errors). The blue solid and red dashed lines shown in figure are calculations reported and discussed in Ref. [30] smeared to the present experimental resolution. Each pair represents the upper and lower limit for each calculation in Ref. [30].