New method of analytic continuation of elastic-scattering data to the negative-energy region, and asymptotic normalization coefficients for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">O</mml:mi><mml:mprescripts/><mml:none/><mml:mn>17</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mn>13</mml:mn></mml:mmultiscripts></mml:math>

A new method is proposed for extrapolation of elastic-scattering data to the negative-energy region for a short-range interaction. The method is based on the analytic approximation of the modulus-squared of the partial-wave scattering amplitude and can serve as an alternative to the traditional one based on continuation of the effective-range function. The new method has been applied to determine the asymptotic normalization coefficients for the $^{17}\mathrm{O}$ and $^{13}\mathrm{C}$ nuclei in the $n+^{16}\mathrm{O}$ and $n+^{12}\mathrm{C}$ channels, respectively. The asymptotic normalization coefficients obtained by the new method are compared with the ones obtained in the effective-range function approach.

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