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Born-Oppenheimer and hyperspherical adiabatic approximations in the nuclear- and molecular-mass limits

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Il Nuovo Cimento B (1971-1996)

Summary

Ground-state energies of a three-particle system composed of a distinct and two equal-mass particles interacting via localS-wave potentials is studied using Born-Oppenheimer and hyperspherical adiabatic approximations in the nuclear-and molecular-mass limits. The nuclear situation is simulated when the ratiom of equal to distinct particle masses is of the order of unity. The molecular situation is simulated form≫1, when the potential among the equal-mass particles is switched off. The ratiom was varied between the limitsm∼1 andm≫1 and the depths and ranges of the potentials were varied to simulate intermediate situations. In all cases the extreme and the uncoupled hyperspherical adiabatic approximations, which are the lower and upper bounds for the exact ground-state energy, is found to define a very narrow band with the Born-Oppenheimer approximation lying very close to it. Thus the two types of approximations are always found to work surprisingly well.

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Author notes

  1. Sadhan K. Adhikari & H. T. Coelho

    Present address: Departamento de Física, Universidade Federal de Pernambuco, 50739, Recife, Pernambuco, Brasil

  2. V. P. Brito

    Present address: Departamento de Física, Universidade Federal do Piauí, Terezina, PI, Brasil

  3. T. K. Das

    Present address: Department of Physics, University of Calcutta, Calcutta, India

Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Pernambuco, 50739, Recife, Pernambuco, Brasil

    V. P. Brito & T. K. Das

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  1. Sadhan K. Adhikari
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  2. V. P. Brito
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  3. H. T. Coelho
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  4. T. K. Das
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Adhikari, S.K., Brito, V.P., Coelho, H.T. et al. Born-Oppenheimer and hyperspherical adiabatic approximations in the nuclear- and molecular-mass limits. Nuov Cim B 107, 77–89 (1992). https://doi.org/10.1007/BF02726887

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  • DOI: https://doi.org/10.1007/BF02726887

PACS 02.30

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