  $^{15}$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.
