Constraints on the low-energy<i>E</i>1 cross section of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>(α,γ<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>16</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>O from the β-delayed α spectrum of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>16</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The shape of the low-energy part of the \ensuremath{\beta}-delayed \ensuremath{\alpha}-particle spectrum of $^{16}\mathrm{N}$ is very sensitive to the \ensuremath{\alpha}${+}^{12}$C reduced width of the 7.117 MeV subthreshold state of $^{16}\mathrm{O}$. This state, in turn, dominates the low-energy p-wave capture amplitude of the astrophysically important $^{12}\mathrm{C}$(\ensuremath{\alpha},\ensuremath{\gamma}${)}^{16}$O reaction. The \ensuremath{\alpha} spectrum following the decay of $^{16}\mathrm{N}$ has been measured by producing a low-energy $^{16}\mathrm{N}^{14}$${\mathrm{N}}^{+}$ beam with the TRIUMF isotope separator TISOL, stopping the molecular ions in a foil, and counting the \ensuremath{\alpha} particles and $^{12}\mathrm{C}$ recoil nuclei in coincidence, in thin surface-barrier detectors. In addition to obtaining the \ensuremath{\alpha} spectrum, this procedure determines the complete detector response including the low-energy tail. The spectrum, which contains more than ${10}^{6}$ events, has been fitted by R- and K-matrix parametrizations which include the measured $^{12}\mathrm{C}$(\ensuremath{\alpha},\ensuremath{\gamma}${)}^{16}$O cross section and the measured \ensuremath{\alpha}${+}^{12}$C elastic scattering phase shifts. The model space appropriate for these parametrizations has been investigated. For ${\mathit{S}}_{\mathit{E}1}$(300), the E1 part of the astrophysical S factor for the $^{12}\mathrm{C}$(\ensuremath{\alpha},\ensuremath{\gamma}${)}^{16}$O reaction at ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=300 keV, values of 79\ifmmode\pm\else\textpm\fi{}21 and 82\ifmmode\pm\else\textpm\fi{}26 keV b have been derived from the R- and K-matrix fits, respectively.