Asymptotics of three-body bound state radial wave functions of halo nuclei Original Research Article

Asymptotic expressions for the radial partial waves of a bound-state wave function of a three-body system in relative coordinates are obtained in explicit form, when the relative distance between two particles tends to infinity. This formula can be applied, for instance, to wave functions of halo nuclei for large distances of one of the valence neutrons and the core. Besides a well-known exponential decrease as a function of a hyperradius, the derived asymptotic expressions involve factors that can influence noticeably the asymptotic values of the three-body radial wave functions for some directions in the configuration space. The obtained asymptotic forms are applied to the analysis of the asymptotic behaviour of accurate 6He three-body αnn wave functions derived with the Lagrange-mesh method. The agreement between the calculated wave function and the asymptotic formula is excellent up to distances close to 20 fm. Information is extracted about the values of the three-body asymptotic normalization factors.