Asymptotics of three-body bound state radial wave functions of halo nuclei involving two charged particles

TL;DR

This paper derives explicit asymptotic expressions for three-body bound halo nuclear wave functions involving two charged particles, and applies them to analyze the $^6$Li wave function, revealing potential sensitivity and mirror symmetry.

Contribution

It provides explicit asymptotic formulas for three-body wave functions with charged particles and demonstrates their application to halo nuclei, highlighting potential potential-dependent effects.

Findings

Excellent agreement of asymptotic formulas with numerical wave functions up to 30 fm

Extraction of three-body asymptotic normalization functions and their sensitivity to potential forms

Revelation of mirror symmetry in asymptotic normalization functions for isobaric pairs

Abstract

Asymptotic expressions for the radial and full wave functions of a three{body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends to infinity. The obtained asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (pn?) wave functions for the halo ($E^*=3.562$ MeV, $J^{\pi}=0^+$, $T=1$) state of $^6$Li derived by D. Baye within the Lagrange-mesh method for two forms of the $\alpha N$ -potential. The agreement between the calculated wave function and the asymptotic formula is excellent for distances up to 30 fm. Information about the values of the three-body asymptotic normalization functions is extracted. It is shown that the extracted values of the three-body asymptotic normalization function are sensitive to the form of the $\alpha N$ -potential. The mirror symmetry is revealed for the three-body asymptotic normalization functions derived for the isobaric ($^6$He, $^6$Li) pair.