Ground-state energy of quantum liquids

The kinetic ($K^{0}_{4}(n)$ and $K^{0}_{3}(n)$) and potential ($V^{0}_{4}(n)$ and $V^{0}_{3}(n)$) energies of $^4$He and $^3$He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies $E^{0}_{4}(n)$ and $E^{0}_{3}(n)$ on the density of the isotopes $^4$He and $^3$He. In the approximation of structureless quantum liquid, the potential energies are equal, $V^{0}_{4}(n)=V^{0}_{3}(n)$, and the kinetic energies are inversely proportional to the atomic mass, $K^{0}_{4}(n)=\frac{3}{4}K^{0}_{3}(n)$ . The potential energy given by the expression $V^{0}=4E^{0}_{4}-3E^{0}_{3}$ to a high accuracy is linear in the density $n$, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid $^4$He is given by the expression $K^{0}_{4} = 3 (E^{0}_{3}-E^{0}_{4})$, which agrees with the experimental data on neutron scattering in liquid $^4$He. The quantities $K^{0}_{4}(n)$ and $K^{0}_{3}(n)$ determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.