  We study the solar-activity and solar-polarity dependence of galactic
cosmic-ray intensity (CRI) on the solar and heliospheric parameters playing a
significant role in solar modulation. We utilize the data for cosmic-ray
intensity as measured by neutron monitors, solar activity as measured by
sunspot number (SSN), interplanetary plasma/field parameters, solar-wind
velocity [V] and magnetic field [B], as well as the tilt of the heliospheric
current sheet [{\Lambda}] and analyse these data for Solar Cycles 20 - 24 (1965
- 2011). We divide individual Solar Cycles into four phases, i.e. low, high,
increasing, and decreasing solar activity. We perform regression analysis to
calculate and compare the CRI-response to changes in different
solar/interplanetary parameters during (i) different phases of solar activity
and (ii) similar activity phases but different polarity states. We find that
the CRI-response is different during negative (A<0) as compared to positive
(A>0) polarity states not only with SSN and {\Lambda} but also with B and V.
The relative CRI-response to changes in various parameters, in negative (A<0)
as compared to positive (A>0) state, is solar-activity dependent; it is ~2 to 3
times higher in low solar activity, ~1.5 to 2 times higher in moderate
(increasing/decreasing) activity, and it is nearly equal in high solar-activity
conditions. Although our results can be ascribed to preferential entry of
charged particles via the equatorial/polar regions of the heliosphere as
predicted by drift models, these results also suggest that we should look for,
any polarity-dependent response of solar wind and transport parameters in
modulating CRI in the heliosphere.
