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

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.