In-Medium Similarity Renormalization Group Approach for Closed-Shell Atoms

Area of Science:

• Nuclear Physics
• Quantum Chemistry

Background:

• The in-medium similarity renormalization group (IMSRG) is a powerful ab initio method for nuclear structure calculations.
• Continuous unitary transformations are key to the IMSRG approach, enabling systematic approximations.

Purpose of the Study:

• To apply the IMSRG approach to closed-shell atoms (Helium and Neon).
• To investigate the convergence properties of different IMSRG formulations.

Main Methods:

• Solving the IMSRG flow equation for the Hamiltonian.
• Utilizing imaginary-time or White generators.
• Employing fourth-order Runge-Kutta and Magnus expansion methods.
• Analyzing the flow behavior with respect to step size.

Main Results:

• IMSRG calculations for Helium and Neon ground state energies closely match full configuration interaction results.
• The IMSRG approach using the Magnus expansion and White generator demonstrated the fastest convergence.
• The study carefully examined the flow behavior as a function of step size.

Conclusions:

• The IMSRG method is a reliable tool for calculating ground state energies of atoms.
• The Magnus expansion combined with the White generator provides an efficient pathway for IMSRG calculations.
• Further investigation into step-size dependence is crucial for optimizing IMSRG applications.