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Asymptotic expressions for the radial and full wave functions of a three{bodybound halo nuclear system with two charged particles in relative coordinatesare obtained in explicit form, when the relative distance between two particlestends to infinity. The obtained asymptotic forms are applied to the analysis ofthe 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. Bayewithin the Lagrange-mesh method for two forms of the $\alpha N$ -potential. Theagreement between the calculated wave function and the asymptotic formula isexcellent for distances up to 30 fm. Information about the values of thethree-body asymptotic normalization functions is extracted. It is shown thatthe extracted values of the three-body asymptotic normalization function aresensitive to the form of the $\alpha N$ -potential. The mirror symmetry isrevealed for the three-body asymptotic normalization functions derived for theisobaric ($^6$He, $^6$Li) pair.

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