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Recently, a new $\Delta$ method for the calculation of asymptoticnormalization coefficients (ANC) from phase-shift data has been formulated,proved and used for bound states. This method differs from the conventional oneby fitting only the nuclear part of the effective-range function which includesa partial phase shift. It should be applied to large-charge nuclei when theconventional effective-range expansion or the Pad\'e-approximations using theeffective-range function $K_l(k^2)$ fitting do not work. A typical example isthe nucleus vertex $\alpha+^{12}$C $\longleftrightarrow ^{16}$O. Here we applythe $\Delta$ method, which totally excludes the effective-range function, toisolated resonance states. In fact, we return to the initial renormalizedscattering amplitude with a denominator which defines the well-known polecondition. Concrete calculations are made for the resonances observed in the$^3$He-$^4$He, $\alpha$-$\alpha$, and $\alpha$-$^{12}$C collisions. We use theexperimental phase-shift and resonant energy data including their uncertaintiesand find the ANC variations for the states considered. The correspondingresults are in a good agreement with those for the $S$-matrix pole method whichuses the differing formalism. The simple formula for narrow resonances given inthe literature is used to check the deduced results. The related ANC functionclearly depends on the resonance energy ($E_0$) and width ($\Gamma$), which isused to find the ANC uncertainty ($\Delta$ANC) through the energy ($\DeltaE_0$) and the width ($\Delta\Gamma$) uncertainties.We also discuss the $\Delta$method differences between bound and resonance states pole conditions.

Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function