Measuring the cross section of the $^{15}$N($\alpha$,$\gamma$)$^{19}$F reaction using a single-fluid bubble chamber

$^{15}$N($\alpha$,$\gamma$)$^{19}$F is believed to be the primary means of stellar nucleosynthesis of fluorine. Here we present the use of a single-fluid bubble chamber to measure the cross section of the time-inverse photo-dissociation reaction. The method benefits from a luminosity increase of several orders of magnitude due to the use of a thicker liquid target -- when compared to thin films or gas targets -- and from the reciprocity theorem. We discuss the results of an experiment at the Thomas Jefferson National Accelerator Facility, where the cross section of the photodisintegration process $^{19}$F($\gamma$, $\alpha$)$^{15}$N was measured by bombarding a superheated fluid of C$_3$F$_8$ with bremsstrahlung $\gamma$-rays produced by impinging a 4 - 5.5 MeV electron beam on a Cu radiator. From the photodissociation yield the cross section was extracted by performing a convolution with a Monte Carlo-generated $\gamma$-ray beam spectrum. The measurement produced a cross section that was then time inverted using the reciprocity theorem. The cross section for the $^{15}$N($\alpha$,$\gamma$)$^{19}$F reaction was determined down to a value in the range of hundreds of picobarns. With further improvements of the experimental setup the technique could potentially push cross section measurements down to the single picobarn range.