Calculation of hydrodynamic mass for atomic impurities in helium

We present a simple numerical procedure for calculating the irrotational hydrodynamic flow around a spherical solute in super fluid helium. The results for alkali cations are compared to recent many-body variational Monte Carlo (VMC) calculations. The helium contribution to the effective masses calculated by the VMC and hydrodynamic methods are 12.9(4.6) versus 9.4 u for Li+, 48.2(5.6) versus 52.1 u for Na+, 69.6(4.8) versus 70.1 u for K+, and 6.4(8.8) versus 6.8 for Cs+. In all cases, the agreement of the two results are in within the error estimate of the VMC calculation, demonstrating the accuracy of hydrodynamic treatment of helium motion even on the atomic length scale.