Natural and Dyson orbitals in small helium drops

TL;DR

This study investigates natural and Dyson orbitals in small helium drops using the hyperspherical cluster model, analyzing their properties and convergence as the number of helium atoms increases.

Contribution

It provides a detailed comparison of natural and Dyson orbitals in helium drops and demonstrates the superiority of natural orbitals for representing system density.

Findings

Natural orbitals are more effective than Dyson orbitals in representing the system density.

The difference between Dyson and natural orbitals diminishes as the number of helium atoms increases.

Both orbitals can describe the density, but natural orbitals offer a better representation.

Abstract

The natural and Dyson orbitals are studied for small helium drops comprising 5 to 20 helium atoms interacting via a soft two-body gaussian potential. The wave functions of these drops have been obtained in the hyperspherical cluster model (HCM) which provides a correct description of the single-particle behaviour at large separations from the system. The natural orbitals are obtained from diagonalization of the nonlocal one-body density matrix, while Dyson orbitals are constructed by direct overlap of the wave functions of two drops differing by one boson. This overlap converges with increasing basis of the HCM. The shapes and occupancies of the natural orbitals as well as their link to Dyson overlaps and evolution with increasing number of atoms are discussed. Both natural and Dyson orbitals can be used to represent the density of the system. However, the natural orbitals representation is demonstrated to be superior. With increasing boson numbers the difference between Dyson and natural orbitals becomes less prominent and it is expected to disappear in infinitely large systems of identical bosons.