A significant fraction of stars between 7-11 solar masses are thought to become supernovae, but the explosion mechanism is unclear. The answer depends critically on the rate of electron capture on 20 Ne in the degenerate oxygen-neon stellar core. However, due to the unknown strength of the transition between the ground states of 20 Ne and 20 F, it has not previously been possible to fully constrain the rate. By measuring the transition, we have established that its strength is exceptionally large and enhances the capture rate by several orders of magnitude. This has a decisive impact on the evolution of the core, increasing the likelihood that the star is (partially) disrupted by a thermonuclear explosion rather than collapsing to form a neutron star. Importantly, our measurement resolves the last remaining nuclear physics uncertainty in the final evolution of degenerate oxygen-neon stellar cores, allowing future studies to address the critical role of convection, which at present is poorly understood. Stars of 7-11 solar masses (M ) are prevalent in the Galaxy, their birth and death rate comparable to that of all heavier stars combined [1]. Yet, the ultimate fate of such "intermediate-mass stars" remains uncertain. According to current models [2-4], a significant fraction explode, but the mechanism is a matter of ongoing debate [5][6][7][8]. The answer-gravitational collapse or thermonuclear explosion-depends critically on the rate of electron capture on 20 Ne in the stellar core. However, due to the unknown strength of the transition between the ground states of 20 Ne and 20 F, it has not previously been possible to constrain this rate in the relevant temperature-density regime [9]. Here, we report the first measurement of this transition, provide the first accurate determination of the capture rate and explore the astrophysical implications.Intermediate-mass stars that undergo central carbon burning become super-AGB stars [1] with a degenerate oxygen-neon (ONe) core consisting mainly of 16 O and 20 Ne and smaller amounts of 23 Na and 24,25 Mg. We are interested in the scenario where the ONe core is able to increase its mass gradually and approach the Chandrasekhar limit, M Ch ∼ 1.37 M . This can occur if nuclear burning continues long enough outside the core or if the core, having lost its outer layers, becoming a white dwarf (WD), is able to accrete material from a binary companion star. As the core approaches M Ch , it contracts and warms up, but only gradually as the heating from compression is balanced by cooling via the emission of thermal neutrinos. The density, on the other hand, rises rapidly eventually triggering a number of electroncapture processes that greatly influence the temperature evolution of the core. First, the core is cooled by cycles of electron capture followed by β decay on the odd-mass nuclei 25 Mg and 23 Na [10]. At higher densities, the core is cooled by another such cycle on 25 Na, and heated by double electron captures on the even-mass nuclei 24 Mg and 20 Ne, which produce substant...