Wave function of Be 9 in the three-body ( α α n ) model
Résumé
A simple analytic expression of the three-body wave function describing the system $(\ensuremath{\alpha}\ensuremath{\alpha}n)$ in the ground state ${\frac{3}{2}}^{\ensuremath{-}}$ of $^{9}\mathrm{Be}$ is obtained. In doing this, it is assumed that the $\ensuremath{\alpha}$ particles interact with each other via the $S$-wave Ali-Bodmer potential including the Coulomb term, and the neutron-$\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}\ensuremath{\alpha}$ 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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