In the framework of a recently developed alpha-cluster model a nucleus is represented as a core (alpha-cluster liquid drop with dissolved excess neutron pairs in it) and a nuclear molecule on its surface. From analysis of experimental nuclear binding energies one can find the number of alpha-clusters in the molecule and calculate the nuclear charge radii. It was shown that for isotopes of one Z with growing A the number of alpha-clusters in the molecule decreases to three, which corresponds to the nucleus 12C for even Z and 15N for odd Z, and the specific density of the core binding energy \rho grows and reaches its saturation value. In this paper it is shown that the value \rho=2.55 MeV/fm^3 explains the particular number of excess neutrons in stable nuclei.

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