Abstract
The variational method in oscillator representation with individual parameters for each Jacobi coordinate is applied to the non-relativistic calculation of the ground state energy of a number of three-particle Coulomb systems, consisting of two identical particles and a different one. The accuracy and convergence rate of the calculations in the constructed oscillator basis are studied up to a total of 28 oscillator quanta. The results are compared with those of the traditional approach using only one such nonlinear variational parameter. The method with individual parameters for Jacobi coordinates is found to possess a number of advantages as compared to the traditional approach.
Highlights
The non-relativistic intrinsic Hamiltonian for the three-particle bound-state system with two identical particles and a different one coupled by Coulomb interaction can be written as [2]
Where ρ1 and ρ2 are the translation-invariant Jacobi coordinates, γ1 and γ2 are the individual parameters for each Jacobi coordinate, in contrast to one such parameter used in the traditional approach, ν1 and ν2 are the reduced masses for the introduced Jacobi coordinates, and ν12 = ν1/ν2
The ground state energies of a number of three-particle Coulomb systems involving up to 28 oscillator quanta have been computed by means of the present method
Summary
https://doi.org/10.1051/epjconf/201817302006 systems [4,5,6,7,8,9], it appears possible to perform an actually rigorous evaluation of the advantage of the method [2] over the traditional approach.
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