It is assumed that the total potential of proton interaction with a hydrogen atom is the sum of the short-range nuclear soft-core Reid potential and the long-range Thomas-Fermi potential. A quantum mechanical analysis of low-energy features of the phase shift and cross section for elastic proton scattering on a hydrogen atom is given for the case of zero total angular momentum. The calculations performed in the present study within a nonlinear version of the variable-phase approach ultimately revealed that, because of a long-range character of the asymptotic behavior of the Thomas-Fermi potential, the respective cross section at low energies oscillates but has a finite number of zeros.
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