Extrapolation of scattering data to the negative-energy region. III. Application to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">O</mml:mi><mml:mprescripts/><mml:none/><mml:mn>16</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> system

The problem of analytic continuation of the scattering data to the negative-energy region to obtain information on asymptotic normalization coefficients (ANCs) of bound states is discussed. It is shown that a recently suggested $\mathrm{\ensuremath{\Delta}}$ method [O. L. Ram\'{\i}rez Su\'arez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] is not strictly correct in the mathematical sense since it is not an analytic continuation of a partial-wave scattering amplitude to the region of negative energies. However, it can be used for practical purposes for sufficiently large charges and masses of colliding particles. Both the $\mathrm{\ensuremath{\Delta}}$ method and the standard method of continuing of the effective range function are applied to the $p\ensuremath{-}^{16}\mathrm{O}$ system, which is of interest for nuclear astrophysics. The ANCs for the ground $5/{2}^{+}$ and excited $1/{2}^{+}$ states of $^{17}\mathrm{F}$ are determined.

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