A ground-based neutron monitor is a standard tool to measure cosmic ray variability near Earth, and it is crucially important to know its yield function for primary cosmic rays. Although there are several earlier theoretically calculated yield functions, none of them agrees with experimental data of latitude surveys of sea-level neutron monitors, thus suggesting for an inconsistency. A newly computed yield function of the standard sea-level 6NM64 neutron monitor is presented here separately for primary cosmic ray protons and $alpha-$particles, the latter representing also heavier species of cosmic rays. The computations have been done using the GEANT-4 Planetocosmics Monte-Carlo tool and a realistic curved atmospheric model. For the first time, an effect of the geometrical correction of the neutron monitor effective area, related to the finite lateral expansion of the cosmic ray induced atmospheric cascade, is considered, that was neglected in the previous studies. This correction slightly enhances the relative impact of higher-energy cosmic rays (energy above 5--10 GeV/nucleon) in neutron monitor count rate. The new computation finally resolves the long-standing problem of disagreement between the theoretically calculated spatial variability of cosmic rays over the globe and experimental latitude surveys. The newly calculated yield function, corrected for this geometrical factor, appears fully consistent with the experimental latitude surveys of neutron monitors performed during three consecutive solar minima in 1976--77, 1986--87 and 1996--97. Thus, we provide a new yield function of the standard sea-level neutron monitor 6NM64 that is validated against experimental data.
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