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Approximate Atomic Green Functions.

Stephan Fritzsche^1,2,3, Andrey Surzhykov^4,5

¹Helmholtz-Institut Jena, Fröbelstieg 3, D-07743 Jena, Germany.

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Summary

This summary is machine-generated.

This study introduces a method to approximate relativistic Green functions for complex atoms. These advanced Green functions, crucial for atomic physics, can now be systematically improved for various atomic systems.

Keywords:

atom atomic Green function atomic cascade atomic structure excitation scheme ion multi-photon relativistic second-order

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Area of Science:

Atomic physics
Many-particle physics
Quantum chemistry

Background:

Green functions, or propagators, are vital for representing atomic Hamiltonians and describing perturbation processes.
However, Green functions have been under-explored and unclassified for complex atomic systems.
Existing methods lack systematic improvement for relativistic Green functions in atoms.

Purpose of the Study:

To develop and demonstrate a method for approximating and systematically improving relativistic Green functions for complex atoms and ions.
To classify these functions based on excitation schemes.
To enable the study of complex atomic processes using these improved Green functions.

Main Methods:

Approximation of relativistic (many-electron) Green functions using classes of virtual excitations (excitation schemes).
Application of multi-configuration Dirac-Hartree-Fock expansion for all involved atomic states.
Implementation within the Jena Atomic Calculator (Jac) framework.

Main Results:

Development of a novel approach to approximate and improve relativistic Green functions for few- and many-electron atoms and ions.
Successful implementation of these approximate Green functions in the Jac.
Establishment of a foundation for studying complex atomic phenomena.

Conclusions:

The developed method provides a pathway to systematically improve relativistic Green functions for complex atomic systems.
The implementation in Jac facilitates the investigation of multi-photon and multiple electron (emission) processes.
This work bridges a gap in the understanding and application of Green functions in atomic physics.