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

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 Schrödinger 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.

arXiv comment16 pages, 4 figures; to appear in Physical Review C

References in corpus (6)

• Astrophysical reaction rate for ${}^9$Be formation within a three-body approach
• Low-energy photodisintegration of 9Be and alpha + alpha + n <-> 9Be + gamma reactions at astrophysical conditions
• 9Be scattering with microscopic wave functions and the CDCC method
• Low-energy photodisintegration of ${}^9$Be with the molecular orbit model
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• Direct capture cross section of ${}^9$Be(n,$\gamma$)${}^{10}$Be

Cited by in corpus (1)

• Molecular 9Be+p Fusion Reaction