Pade approximants for the ground-state energy of closed-shell quantum dots

TL;DR

This paper introduces two-point Pade approximants to estimate the ground-state energy of closed-shell quantum dots across various densities, achieving less than 3% maximum error and indicating an unpolarized ground state.

Contribution

It presents a novel analytic method using two-point Pade approximants based on density limits to accurately approximate quantum dot energies.

Findings

Maximum error less than 3% at intermediate densities

Ground state found to be unpolarized

Method effective for electron numbers 2 to 210

Abstract

Analytic approximations to the ground-state energy of closed-shell quantum dots (number of electrons from 2 to 210) are presented in the form of two-point Pade approximants. These Pade approximants are constructed from the small- and large-density limits of the energy. We estimated that the maximum error, reached for intermediate densities, is less than 3%. Within the present approximation the ground-state is found to be unpolarized.