A unified analytical framework for Mössbauer synchrotron sources

Area of Science:

• Nuclear Physics
• Materials Science
• Spectroscopy

Background:

• Next-generation Mössbauer spectroscopy requires advanced modeling for nuclear hyperfine interactions.
• Synchrotron and X-ray free-electron laser facilities necessitate rapid, accurate, and polarization-aware analysis.

Purpose of the Study:

• To present a unified analytical framework for modeling nuclear hyperfine interactions.
• To provide exact, rotationally invariant expressions for resonance energies and transition probabilities.
• To enable efficient global fitting and modeling of hyperfine interactions in complex materials.

Main Methods:

• Developed a unified analytical framework avoiding Hamiltonian diagonalization.
• Expressed intensities in terms of hyperfine invariants.
• Introduced a quantitative identifiability metric and used Monte Carlo sampling.

Main Results:

• Achieved exact, rotationally invariant expressions for simultaneous magnetic dipole and electric quadrupole interactions.
• Demonstrated efficient global fitting and modeling of hyperfine interaction distributions.
• Showed that polarization control significantly improves hyperfine parameter determination.

Conclusions:

• The presented framework offers a mathematically transparent and computationally efficient toolset for modern Mössbauer spectroscopy.
• Accelerates studies of iron-based compounds and magnetic/electronic/structural order.
• Applicable to extreme conditions and nanoscale geometries.