The ANKE@COSY data on the reaction of two-pion production in the GeV region are analyzed within the theoretical model by Platonova and Kukulin. The model includes excitation of the dibaryon resonance DIJ = D03(2380) with the spin J = 3 and isospin I = 0 observed by the WASA@COSY in the reaction pn → dπ0π0, and its decay D03 → D12 + π → d + π + π, where D12(2150) is another dibaryon resonance. Distributions on the invariant masses of the final dππ and ππ systems are calculated.

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The recent ANKE@COSY data on the differential cross section of reaction pd \to pd\pi\pipd→pdππ demonstrate a peak at invariant mass of the final d\pi\pidππ system 2.38~GeV2.38GeV, that corresponds to the isoscalar J^P = 3^+JP=3+ dibaryon D_{03}D03, and the enhancement in the distribution over the invariant mass of two final pions. The two-resonance model involving the tt-channel \sigmaσ-meson exchange between the proton and deuteron in the subprocess pd\to pD_{03}pd→pD03 and the sequential decays D_{03}\to D_{12}+\piD03→D12+π and D_{12}\to d +\piD12→d+π was applied to describe the shapes of these distributions with the lowest orbital angular momenta in the corresponding vertices. A possible role of higher orbital momenta in those vertices is studied here.

The three-body wave function built on the basis of the Gaussian function, calculated using the threebody Hamiltonian with the Pauli blocking operator is studied. As an example, the wave function of the ground state of the 9 Be was taken. Analytical expressions are presented for the overlap matrix elements of the basis function for both basic and alternative set of relative Jacobi coordinates. The correlation densities of the wave function are calculated and illustrated depending on the set of orbital quantum numbers.