AMELI: Angular matrix elements of lanthanide ions

Area of Science:

• Atomic and Molecular Physics
• Quantum Chemistry
• Spectroscopy

Background:

• Matrix elements of spherical tensor operators are essential for interpreting lanthanide spectra in various materials.
• Existing methods for calculating these elements can be computationally intensive and prone to numerical errors.
• Racah's classification provides a theoretical basis for transforming matrix elements between coupling schemes.

Purpose of the Study:

• To develop a comprehensive framework for calculating angular matrix elements of spherical tensor operators.
• To create a universally applicable and computationally efficient method for these calculations.
• To provide an open-access repository of pre-calculated matrix elements for fN configurations.

Main Methods:

• Utilized a Slater determinant basis for calculating angular matrix elements.
• Transformed matrix elements to the LS-coupling scheme using Racah's classification.
• Employed exact arithmetic in the AMELI repository to eliminate numerical artifacts.

Main Results:

• Developed general rules for calculating angular matrix elements for spherical tensor operators in fN configurations.
• Created the AMELI repository containing exact matrix elements for unit and angular momentum operators, and perturbation Hamiltonians.
• Demonstrated the repository's utility through comparisons with classic tables and application examples using the YALIP Python implementation.

Conclusions:

• The presented framework and AMELI repository offer a more accurate and efficient alternative to legacy tables for semi-empirical calculations.
• The use of exact arithmetic and exploitation of symmetry properties leads to compact and reliable data.
• This work facilitates advanced analysis of lanthanide spectra in both amorphous and crystalline environments.