  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.
