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arXiv · 2407.17371

Wave function of $^9$Be in the three-body (alpha-alpha-n)-model

S. A. Rakityansky
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Abstract

A simple analytic expression of the three-body wave function describing the system $(\alpha\alpha n)$ in the ground state $\frac{3}{2}^-$ of ${}^9\mathrm{Be}$ is obtained. In doing this, it is assumed that the $\alpha$ particles interact with each other via the $S$-wave Ali-Bodmer potential including the Coulomb term, and the neutron-$\alpha$ 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 $\alpha\alpha$ 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 $\alpha\alpha$ potential whose difference from the Ali-Bodmer one is minimized by varying the adjustable parameters which the postulated wave function depends on.

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S. A. Rakityansky. 2024-07-24. Wave function of $^9$Be in the three-body (alpha-alpha-n)-model. https://doi.org/10.1103/physrevc.110.024001

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