Asymptotic normalization coefficients of alpha-particle removal from $^{16}$O($3^-,2^+,1^-$)

Abstract: Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a paper [Blokhintsev et al., Eur. Phys. J. A 58, 257 (2022)], we considered the ANC $C_0$ for the virtual decay $^{{16}$O$(0^+;} 6.05$ MeV)$\to \alpha+<sup>{12}$C(g.s.). In the present paper, which can be regarded as a continuation of the previous, we treat the ANCs $C_l$ for the vertices $^{{16}$O$(J^\pi)\to} \alpha+<sup>{12}$C(g.s.) corresponding to the other three bound excited states of $<sup>{16}$O ($J<sup>\pi=3<sup>-$, $2^+$, $1^-$, $l=J$). ANCs $C_l$ ($l=3,\,2,\,1$) are found by analytic continuation in energy of the $\alpha<sup>{12}$C $l$-wave partial scattering amplitudes, known from the phase-shift analysis of experimental data, to the pole corresponding to the $<sup>{16}$O bound state and lying in the unphysical region of negative energies. To determine $C_l$, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. For a more reliable determination of the ANCs, various forms of functions expressed in terms of phase shifts were used in analytical approximation and subsequent extrapolation.