Analsis Tools for "The Relativistic Hydrogen-Like Atom in a Finite Magnetic Field"

This repository provides tools to parse, analyze and visualize the raw data associated with the study "The Relativistic Hydrogen-Like Atom in a Finite Magnetic Field". It includes the Python scripts used to generate the *_summary.csv and *_bfield.csv files, as well as the Jupyter notebooks used to produce all visualizations presented in the study.

Quick start

Download the raw data and place the scripts and Jupyter notebooks in the same parent directory.

Install the dependencies (Python 3.11.7):

pip install -r requirements.txt

To parse and analyze the data, run the script for the convergence analysis with respect to the highest angular-momentum function required for numerical convergence. In the parse directory, run:

python parse_lconv.py

This script generates the *_summary.csv files in the respective parent directories for the different ions.

To obtain the energy eigenvalues of various states at different magnetic field strengths, run in the parse directory:

python parse_bfield.py

This script generates the *_bfield.csv files in the respective parent directories for the different ions.

To reproduce the visualizations, execute the cells in the following Jupyter notebooks:

• avoided_crossing.ipynb: visualization of the avoided crossing between the $2E_{1/2,u}^{-}$ and $3E_{1/2,u}^{-}$ states.

• bfield_hydrogen_roesner.ipynb: comparison with the results of W. Rösner, G. Wunner, H. Herold, and H. Ruder, J. Phys. B: At. Mol. Phys. 17, 29 (1984).

• lconv_analysis.ipynb: plots illustrating basis-set convergence behavior.

• paschen_back_analysis.ipynb: analysis of the state energies of the $2p_{1/2}$- and $2p_{3/2}$-parent terms and the $3d_{3/2}$- and $3d_{5/2}$-parent terms in and beyond the Paschen–Back limit.