Constraining the destruction rate of $^{40}$K in stellar nucleosynthesis through the study of the $^{40}$Ar(p,n)$^{40}$K reaction

40K plays a significant role in the radiogenic heating of earth-like exoplanets, which can affect the development of a habitable environment on their surfaces. The initial amount of 40K in the interior of these planets depends on the composition of the interstellar clouds from which they formed. Within this context, nuclear reactions that regulate the production of 40K during stellar evolution can play a critical role. In this study, we constrain for the first time the astrophysical reaction rate of 40K(n,p)40Ar, which is responsible for the destruction of 40K during stellar nucleosynthesis. We performed differential cross-section measurements on the 40Ar(p,n)40K reaction, for six energies in the center-of-mass between 3.2 and 4.0 MeV and various angles between 0-deg and 135-deg. The experiment took place at the Edwards Accelerator Laboratory at Ohio University using the beam swinger target location and a standard neutron time-of-flight technique. The total and partial cross-sections varied with energy due to the contribution from isobaric analog states and Ericson type fluctuations. The energy-averaged neutron angular distributions were symmetrical relative to 90-deg and consistent with the theoretical predictions of the statistical model. Based on the experimental data, local transmission coefficients were extracted and were used to calculate the astrophysical reaction rates of 40Ar(p,n)40K and 40K(n,p)40Ar reactions. Our results support that the destruction rate of 40K in massive stars via the 40K(n,p)40Ar reaction is larger compared to previous estimates. This result directly affects the predicted stellar yields of 40K from nucleosynthesis, which is a critical input parameter for the galactic chemical evolution models that are currently employed for the study of significant properties of exoplanets.