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The Strong nucleus-nucleus Potential (SnnP) is of principal importance for understanding nuclear molecules [1] and for the synthesis of the superheavy nuclei [2]. Nucleon density distributions are known to play a crucial role in finding the SnnP by means of the double folding model [2], [3]. The best way is to calculate the densities in a microscopic manner, i.g. by the Hartree-Fock approach [4]–[6]. However, such calculations are rather complicated and computer resources consuming.

That is why in the present work we develop a novel fast algorithm for evaluating the proton and neutron densities for spherical nuclei. The algorithm is based on five benchmarking densities coming from the Hartree-Fock approach: $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{36}\mathrm{S}$, $^{92}\mathrm{Zr}$, $^{144}\mathrm{Sm}$, $^{208}\mathrm{Pb}$. Each of these microscopic densities is approximated by a combination of a Woods-Saxon profile with an exponential tail having a variable (i.e. radial dependent) diffuseness (WST profile). For the nuclei with the charge number between the benchmarking ones we perform a linear interpolation of the parameters defining the WST profile.

As a test for the WST-algorithm we find the nuclear charge density distributions for several spherical nuclei and compare those with the experimental Fourier-Bessel distributions from [7]. The agreement seems to be rather good.

Then we calculate the barrier height and radii for several fusion reactions involving two spherical nuclei using the well-known M3Y nucleon-nucleon interaction. The calculated barrier parameters are compared with the experimental ones from [8]. The calculated barriers are systematically higher than the experimental ones indicating importance of the dissipative phenomena in the above-barrier collision process [5], [6].

[1] W.Greiner et al. // Nuclear Molecules. WORLD SCIENTIFIC, 1995.

[2] В.И.Загребаев и др. // ЭЧАЯ. 38 (2007) 893–938.

[3] G.R.Satchler et al. // Phys. Rep. 55 (1979) 183–254.

[4] R.Bhattacharya // Nucl. Phys. A. 913 (2013) 1–18.

[5] I.I.Gontchar et al. // Phys. Rev. C. 89 (2014) 034601.

[6] M.V.Chushnyakova et al. // Phys. Rev. C 90 (2014) 017603.

[7] H.DeVries et al. // At. Data Nucl. Data Tables 36 (1987) 495–536.

[8] I.I.Gontchar et al. // Phys. Rev. C 69 (2004) 024610.