LAUSR

Recently a new $\Delta$-method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Pad\'e-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $\alpha+^{12}$C $\longleftrightarrow ^{16}$O. Here we extend the $\Delta$-method, which totally excludes the effective-range function, to resonance states. In fact, we return to the initial re-normalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $\alpha$-$\alpha$ and $\alpha$-$^{12}$C collisions. The corresponding results are in a good agreement with those for the $S$-matrix pole (SMP) method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results.