Determination of asymptotic normalization coefficients for the ${}^7$Li$\to \alpha {+}^3$He channel

Abstract

Asymptotic normalization coefficients (ANCs) $C_{3/2}$ and $C_{1/2}$ for the channels ${}^7$Li$(3/2^{-};0$ MeV)$\to \alpha {+}^3$H and ${}^7$Li$(1/2^{-};0.478$ MeV)$\to \alpha {+}^3$H, respectively, were determined by analyzing elastic ${\alpha }^3$H- scattering data using three different methods. All three methods yield similar results. The ANC values averaged over the three methods are $C_{3/2}=2.08\pm 0.10$ fm${}^{-1/2}$ and $C_{1/2}=2.00\pm 0.10$ fm${}^{-1/2}$. Comparison of the found ANCs with the previously obtained ANCs for ${}^7$Be confirms the relationship linking the ANC values for mirror nuclei. This research on determining the ANCs for the ${}^7$Li nucleus is, to some extent, a continuation of the previously completed study on its mirror nucleus, ${}^7$Be [ D. A. Savin, L. D. Blokhintsev, B. F. Irgaziev, A. S. Kadyrov, and A. M. Mukhamedzhanov, Phys. Rev. C 112, 065807 (2025)].

6 pages, 5 figures