DOI: https://doi.org/10.30970/jps.04.124
PRECISE VARIATIONAL CALCULATIONS OF ENERGY SPECTRA OF COULOMB-TYPE THREE- AND FOUR-PARTICLE SYSTEMS
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Journal of Physical Studies 4(2), 124–140 (2000)
DOI: https://doi.org/10.30970/jps.04.124 PRECISE VARIATIONAL CALCULATIONS OF ENERGY SPECTRA OF COULOMB-TYPE THREE- AND FOUR-PARTICLE SYSTEMS |
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1Department of Physics, Taras Shevchenko Kyiv National
University,
6 Hlushkov Av., Kyiv, UA–03127, Ukraine
e-mail: bubin@i.am
2Bogolyubov Institute for
Theoretical Physics of the National Academy of Sciences of
Ukraine,
14-b Metrologichna Str., Kyiv, UA-03143, Ukraine
e-mail: isimenog@bitp.kiev.ua
We consider basing on the Galerkin variational method with the Gaussian basis, the bound states of the Coulomb-type quantum systems of gravitating identical particles. The approach is applied to the three–particle system with a varying permutational symmetry of wave functions and to the four-particle system with fully symmetrical wave functions. A qualitative analysis of the energy spectra is performed. The contribution of Jastrow's correlations to the ground-state energy of the three-boson system is studied. Precise calculations of the binding energies of the ground state and a few lowest states with zero angular momentum are carried out. The rms radii, density distributions and formfactors, pair correlation functions, and momentum distributions are calculated and analysed for different energy states. The energies of the systems with the Yukawa-type interaction potentials are estimated. Some methods of highly accurate variational calculations are discussed. A significant attention is given to the problem of selecting nonlinear variational parameters.
PACS numbers: 02.70.-c, 03.65.Ge, 31.15.Pf