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Multibox strategy for constructing highly accurate bound-state wave functions for three-body systems.

A M Frolov1

  • 1Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

A new variational, multibox method accurately calculates three-body system wave functions. This approach precisely determines properties of muonic molecular ions, solving a long-standing problem.

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Area of Science:

  • Atomic and Molecular Physics
  • Quantum Chemistry
  • Computational Physics

Background:

  • Accurate calculation of bound-state wave functions is crucial for understanding three-body systems.
  • Previous methods faced challenges in achieving high precision for complex systems like muonic molecular ions.

Purpose of the Study:

  • To develop a highly accurate and efficient variational method for constructing bound-state wave functions.
  • To apply this method to solve challenging problems, specifically determining the properties of weakly bound muonic molecular ions.

Main Methods:

  • A variational, multibox approach utilizing optimally chosen nonlinear parameters in exponential basis functions.
  • Incorporation of separately optimized cluster fragments for enhanced flexibility and accuracy.

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  • Application to calculate bound-state properties of various three-body systems.

    • Main Results:

    • The developed method yields compact and highly accurate wave functions for arbitrary three-body systems.
    • Successfully solved the long-standing problem of determining precise binding energies for (1,1) states in ddmu and dtmu muonic molecular ions.
    • Achieved unprecedented accuracy in binding energy calculations: -1.974 988 088 0+/-5 x 10(-10) eV (ddmu) and -0.660 338 74+/-1 x 10(-8) eV (dtmu).

    Conclusions:

    • The proposed variational, multibox approach offers a flexible and powerful tool for high-precision calculations of three-body systems.
    • This method enables solving three-body problems with arbitrary precision, advancing the field of computational physics.
    • The accurate determination of muonic molecular ion properties provides critical data for fundamental physics research.