A simple analytic expression of the three-body wave function describing the system (ααn) in the ground state 3/2^- of ⁹Be is obtained. In doing this, it is assumed that the α particles interact with each other via the S-wave Ali-Bodmer potential including the Coulomb term, and the neutron-α forces act only in the P-wave state. This wave function is constructed by trial and error method via solving in this way a kind of inverse problem when the two-body αα potential is recovered from a postulated three-body wave function. As a result, the wave function is an exact solution of the corresponding three-body Schr\"odinger equation for experimentally known binding energy and for the αα potential whose difference from the Ali-Bodmer one is minimized by varying the adjustable parameters on which the postulated wave function depends.
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S. A. Rakityansky (2024) studied this question.