Ground-state energy of quantum liquids

Abstract

The kinetic (K40 (n) and K30 (n)) and potential (V40 (n) and V30 (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 E40 (n) and E30 (n) on the density of the isotopes 4He and 3He. In the approximation of structureless quantum liquid, the potential energies are equal, V40V30 (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 V0 = 4E40 − 3E30 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 K40 = 3(E30 − E40), which agrees with the experimental data on neutron scattering in liquid 4He. The quantities K40 (n) and K30 (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.