unless the population is uniformly spread out across the landscape, making the assumption that you can translate "population density" to "population" within the buffer is a conceptual stretch, You also have floating point values for density which rules out "Tabulate Area" and "Zonal Statistics" or "Zonal Statistics as Table" would necessitate taking the average density, which might be ok if the buffer is relatively uniform. Use density values with caution. It would be better to acquire actual populations data on a polygon basis if it is at all possible.
... sort of retired...