Application of the $${2}\alpha{+}{n}$$ Three-Body Cluster Model of the $${}^{{9}}$$Be Nucleus in the Reaction $${}^{{9}}$$Be($${}^{{3}}$$He, $${}^{{3}}$$He)$${}^{{9}}$$Be

Elastic-scattering processes in the $${}^{3}\textrm{He}+{}^{9}$$ Be reaction are studied on the basis of the 2 $$\alpha+n$$ three-body cluster model of the $${}^{9}$$ Be nucleus. The $${}^{9}$$ Be three-body wave function obtained by the variational method in the Gaussian basis is used to derive an analytic representation of nuclear-matter density distribution. The interaction potential calculated for the $${}^{3}\textrm{He}+{}^{9}$$ Be system by the double-folding method is employed to analyze experimental data on the differential cross section for the elastic-scattering process $${}^{9}$$ Be ( $${}^{3}$$ He, $${}^{3}$$ He) $${}^{9}$$ Be at collision energies between 30 and 60 MeV.