Variational description of the 3-body Coulomb problem through a correlated Eckart-Gaussian wavefunction

Abstract

The quantum mechanical problem posed by the internal motion of three particles subject to Coulomb i n teractions is variationally solved by means of an Eckart-Gaussian EG ansatz that exhibits an exponential behavior with respect to the radial coordinates fr1,r2g, and a harmonic Gaussian-type dependence on the interparticle distance r12, thereby providing explicit correlation. The proposed wavefunction is of the form e , 1 r 1 , 1 r 2 + e , 2 r 1 , 2 r 2 r l 12 e , r 12 ,u 0 2 , through which ground state energies are calculated for a few two-electron atoms,considering nite nuclear mass e ects,and molecular ions corresponding to electronic and mesonic systems. The physical interpretation and advantages of the EG wavefunction are discussed in terms of the relative masses of the particles in the analyzed systems. A useful application of the variational method is presented where the underlying structure of the 3-body wavefunction combines an atomic-and a molecularlike description of the system. The obtained energies agree with the exact results within 10 ,4 ,10 ,2Hartrees.

On the limit of existence of Borromean binding in three-particle systems with screened Coulomb interactions

“…However, for the case of μ + μ + e − , where m e = 1, one expects that the heavier mass of muon the lower energy of the system. Thus, for μ + μ + e − (table 2) the least accurate results are those by Flores-Riveros and Rivas-Silva [5] and by Frolov and Bishop [2]. Our result is in great agreement with that of Frolov [4], which is the best one.…”

“…Where possible they are compared with the accessible literature data. The screening-free (λ = 0) results for the muonic systems are compared (tables 2 and 3) with the results of Flores-Riveros and Rivas-Silva [5], Frolov and Bishop [2],…”

“…The positronium negative ion, e + e − e − , has been investigated by many researchers, not only with the pure Coulomb interactions but with the screened Coulomb potentials as well. Table 4 presents comparison of present ground-state energies and the ones of Saha et al [8], Bhattacharyya et al [17], Ghoshal and Ho [15], Kar and Ho [10], Frolov and Yeremin [1], Frolov and Bishop [2], Drake et al [7], Flores-Riveros and Rivas-Silva [5], and Dutta et al [24] for λ 0. Our results are the best for the strong and medium screening, λ 0.15 au.…”

Characterization of the continuous transition from atomic to molecular shape in the three-body Coulomb system

“…We employed the trial function of Flores-Riveros and Rivas-Silva [47] Φ(r 13 , r 23 , r 12 ) = (e −αr13−βr23 + e −βr13−αr23 )…”

“…Realistic systems. Eexact is the 'exact' energy (the sources of these values can be found in ref [47]…”