Condensons and bicondensons in a one-dimensional systems

Abstract

The paper is devoted to the simulation of continual strong coupling condensons, and bicondensons states in one-dimensional systems by using the Gaussian basis with exponentially correlated multipliers. To determine the accuracy of variational calculations, it has been shown that using the variational function consisting of a sum of 5 Gaussians reproduces the exact value of energy and wave function of the one-dimensional condenson with the accuracy of 7 and 5 significant digits, respectively. Analytical expressions for the effective functional of the one-dimensional bicondenson have been obtained. Variational calculations of singlet condenson ground state energy were carried out with simultaneous accounting of single-center correlations and correlations caused by a direct dependence of the bicondenson wave function on the distance between electrons. The graphical dependence of the bicondenson energy on the Coulomb repulsion parameter Vᴄ has been represented. The region of existence of bicondenson was determined as a function of electron-electron repulsion parameter Vᴄ ≤ V*ᴄ ≈ 5.4. The one-center bicondenson model has been considered, and the distribution of the two-electron probability density (squared wave function of bicondenson) in the region 2 ≤Vᴄ has two maxima, the distance between which for Vᴄ = 2 is Rm = 1.8567. This distribution of the probability density is associated with the low dimensionality of the system under consideration.