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Calculations of the probability densities and energies of the ground states for α-cluster nuclei ${}^{12}$C (3α), ${}^{16}$O (4α), ${}^{20}$Ne (5α), ${}^{24}$Mg (6α), ${}^{28}$Si (7α) and for nuclear
molecules ${}^{9}$Be (2α + n), ${}^{10}$Be (2α + 2 n), ${}^{10}$B (2α + n + p), ${}^{10}$C(2α + 2 p), ${}^{11}$B(2α + 2 n + p), ${}^{11}$C(2α + n + 2 p) were performed by the Feynman Path Integral (FPI) method [1] using parallel computing based on NVIDIA CUDA technology. The FPI method is used because it is not limited by the number of the particles. The reason why FPI is a natural choice for studying spatial structures is because the asymptotic form of the FPI kernel contains density distributions explicitly (Fig. 1).
Fig. 1. The probability density for the ground state of the ${}^{16}$O nucleus as a 4α-system calculated by the FPI method along with the potential landscape (curves) (a-c) with the 3D models of some configurations (d) and Jacobi coordinates with x = y (e). The tetrahedron configuration 1 is the most probable; the square configuration 2 is of considerably lower probability; the dinuclear configurations 3, 4 (α + ${}^{12}$C) are even less probable.
- V. V. Samarin, Eur. Phys. J. A, 58:117 (2022).
