Eur. Phys. J. A (2023) 59: 162
https://doi.org/10.1140/epja/s10050-023-01079-4

Regular Article - Theoretical Physics

Determination of asymptotic normalization coefficients for the channel ${}^{16}$O$\to \alpha {+}^{12}$C. II. Excited states ${}^{16}$O($3^{-},2^{+},1^{-}$)

¹ Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
² Department of Physics and Astronomy, Curtin University, GPO Box U1987, 6845, Perth, WA, Australia
³ Institute of Nuclear Physics, Ulugbek, 100214, Tashkent, Uzbekistan
⁴ Cyclotron Institute, Texas A &M University, 77843, College Station, TX, USA

^b a.kadyrov@curtin.edu.au

Received: 10 April 2023
Accepted: 7 July 2023
Published online: 18 July 2023

Abstract

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a recent 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)$\to \alpha {+}^{12}$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$(J^{\pi })\to \alpha {+}^{12}$C(g.s.) corresponding to the other three bound excited states of ${}^{16}$O ($J^{\pi }=3^{-}$, $2^{+}$, $1^{-}$, $l=J$). ANCs $C_l$ ($l=3,2,1$) are found by analytic continuation in energy of the ${\alpha }^{12}$C l-wave partial scattering amplitudes, known from the phase-shift analysis of experimental data, to the pole corresponding to the ${}^{16}$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.