ANCs of the bound states of $^{16}$O deduced from elastic $\alpha$-$^{12}$C scattering data

Shung-Ichi Ando

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arXiv · 2311.14999

ANCs of the bound states of $^{16}$O deduced from elastic $\alpha$-$^{12}$C scattering data

Shung-Ichi Ando

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Abstract

Asymptotic normalization coefficients (ANCs) of the $0_1^+$, $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ ($l_{i th}^\pi$) bound states of $^{16}$O are deduced from the phase shift data of elastic $\alpha$-$^{12}$C scattering at low energies. $S$ matrices of elastic $\alpha$-$^{12}$C scattering are constructed within cluster effective field theory (EFT), in which both bound and resonant states of $^{16}$O are considered. Parameters in the $S$ matrices are fitted to the precise phase shift data below the $p$-$^{15}$N breakup energy for the partial waves of $l=0,1,2,3,4,5,6$, and the ANCs are calculated by using the wave function normalization factors of $^{16}$O propagators for $l=0,1,2,3$. We review the values of ANCs, which are compared with other results in the literature, and discuss uncertainties of the ANCs obtained from the elastic $\alpha$-$^{12}$C scattering data in cluster EFT.

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Shung-Ichi Ando. 2023-11-25. ANCs of the bound states of $^{16}$O deduced from elastic $\alpha$-$^{12}$C scattering data. https://arxiv.org/abs/2311.14999

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