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Related Experiment Video

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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High-precision, variational, bound-state calculations in coulomb three-body systems

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

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|January 4, 2001

Summary

This study presents highly accurate calculations for Coulomb three-body systems, including helium atoms and muonic ions. The advanced multiprecision FORTRAN package ensures reliable bound-state properties for few-body systems.

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Area of Science:

Atomic and Molecular Physics
Quantum Chemistry
Few-Body Systems

Background:

Coulomb three-body systems are fundamental in atomic and molecular physics.
Accurate calculation of bound-state properties is essential for understanding these systems.
Previous methods faced limitations in numerical stability and precision.

Purpose of the Study:

To compute high-precision variational results for bound states in various Coulomb three-body systems.
To investigate the bound-state properties of specific systems like helium atoms and muonic molecular ions.
To demonstrate the efficacy of a multiprecision FORTRAN package for few-body calculations.

Main Methods:

Utilized a multiprecision FORTRAN package and pretranslator developed by D. H. Bailey.
Employed high-precision variational methods for bound-state calculations.
Applied the package to systems including helium atoms (2(3)S state) and muonic molecular ions (S and P states).

Main Results:

Achieved significantly higher accuracy in total energy calculations compared to previous works.
Successfully computed bound-state properties for the 2(3)S state of helium, symmetric muonic molecular ions, and specific muonic atoms (3He2+μ(-)e(-) and 4He2+μ(-)e(-)).
Demonstrated the elimination of numerical instabilities crucial for high-precision few-body bound-state calculations.

Conclusions:

The multiprecision FORTRAN package provides a robust solution for numerical instabilities in few-body calculations.
This approach opens new possibilities for studying bound states in complex few-body systems with unprecedented accuracy.
The study establishes new benchmarks for the precision of bound-state properties in the investigated Coulomb three-body systems.