Ground-state energy of quantum liquids

Abstract

The kinetic (K ⁰₄ (n) and K ⁰₃ (n)) and potential (V ⁰₄ (n) and V ⁰₃ (n)) energies of ⁴He and ³He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E ⁰₄ (n) and E ⁰₃ (n) on the density of the isotopes ⁴He and ³He. In the approximation of structureless quantum liquid, the potential energies are equal, V ⁰₄ V ⁰₃ (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, $K_4^0 (n) = \frac{3} {4}K_3^0 (n)$. The potential energy given by the expression V ⁰ = 4E ⁰₄ − 3E ⁰₃ 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 ⁴He is given by the expression K ⁰₄ = 3(E ⁰₃ − E ⁰₄ ), which agrees with the experimental data on neutron scattering in liquid ⁴He. The quantities K ⁰₄ (n) and K ⁰₃ (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.