This paper determines the fundamental thermodynamic potential of the healing and relaxation theory for helium II developed in previous papers in this series. The potential is founded on experimental data drawn from a variety of sources, e.g., neutron scattering, calorimetry, etc. This energy function is used in the calculation of the healing length near a plane wall and the vortex core parameter for a rectilinear line vortex over a wide range of the density-temperature plane for helium II. The coefficients of a cubic B-spline representation of the free energy is given over the same range, and a BASIC program is provided for the evaluation of that energy from the coefficients. © 1989 Plenum Publishing Corporation.