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CONDENSED MATTER
Ground-state energy of quantum liquids
A. M. Dyugaevab,
P. D. Grigor'evb,
E. V. Lebedevac a Max Planck Institute for the Physics of Complex Systems
b Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Institute of Solid State Physics, Russian Academy of Sciences
Abstract:
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.
Received: 10.04.2013
Revised: 04.06.2013
DOI:
10.7868/S0370274X13130080
Fulltext:
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