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We develop a fully self-consistent subtracted second random-phaseapproximation for charge-exchange processes with Skyrme energy-densityfunctionals. As a first application, we study Gamow-Teller excitations in thedoubly-magic nucleus $^{48}$Ca, the lightest double-$\beta$ emitter that couldbe used in an experiment, and in $^{78}$Ni, the single-beta-decay rate of whichis known. The amount of Gamow-Teller strength below 20 or 30 MeV isconsiderably smaller than in other energy-density-functional calculations andagrees better with experiment in $^{48}$Ca, as does the beta-decay rate in$^{78}$Ni. These important results, obtained without \textit{ad hoc} quenchingfactors, are due to the presence of two-particle -- two-hole configurations.Their density progressively increases with excitation energy, leading to a longhigh-energy tail in the spectrum, a fact that may have implications for thecomputation of nuclear matrix elements for neutrinoless double-$\beta$ decay inthe same framework.

Gamow-Teller strength in $^{48}$Ca and $^{78}$Ni with the charge-exchange subtracted second random-phase approximation