https://doi.org/10.1140/epjd/s10053-021-00183-8
Regular Article - Atomic Physics
Excited states of the Gaussian two-electron quantum dot
1
School of Chemistry, University of Hyderabad, 500 046, Hyderabad, India
2
Chemistry Program, Centre College, 40422, Danville, Kentucky, USA
3
Guangdong Technion - Israel Institute of Technology, Shantou, Guangdong, China
4
Department of Chemistry, Technion, Israel Institute of Technology, Haifa, Israel
Received:
17
December
2020
Accepted:
19
May
2021
Published online:
8
June
2021
We consider the 
states of the two-electron three-dimensional quantum dot with a Gaussian one-body potential, 
. For a single electron, a simple scaling relation allows the reduction into a one-parameter problem in terms of 
. However, for the two-electron system, the interelectronic repulsion term, 
, frustrates this simple scaling transformation, so we face a genuine two-parameter system. We pay particular attention to the location and nature of the critical well-depths, at which the binding energy of the second electron vanishes. Several observations are noteworthy: For all 
, the triplet critical well-depth is lower than that in the singly excited singlet state. Hence, there exists a finite range of well-depths for which the triplet is bound and the singlet is not, a feature that can possibly be applied in some device. Above its critical well-depth, the triplet state energy is always lower than that of the singly excited singlet. Both well-depths are considerably higher than the critical well-depth in the ground state. The expectation value of the interelectronic repulsion is always lower in the triplet, like the harmonic quantum dot but unlike He-like atoms, the two-particle Debye (Yukawa) atom, or the confined He atom. In the infinite well-depth (
) limit, keeping the well-width 
constant, the energies and other expectation values of the bound states of the two-electron Gaussian quantum dot approach those of a non-interacting harmonic two-electron system.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
