A new solution for effective interaction

TL;DR

This paper introduces a novel method for model-space effective interaction that extends the Krenciglowa-Kuo approach, offering faster convergence and accurate eigenvalue reproduction through both iterative and non-iterative solutions.

Contribution

A new operator replaces the Q-box in the KK method, leading to an extended equation solvable iteratively or non-iteratively with improved convergence.

Findings

Iteration accelerates convergence compared to KK method

Non-iterative calculation accurately reproduces true eigenvalues

Method is effective regardless of overlaps and energy differences

Abstract

A new method is given for the model-space effective interaction. Introducing a new operator in place of the Q-box in the Krenciglowa-Kuo (KK) method, we derive a new equation for the effective interaction. This equation can be viewed as an extension of the KK method. We show that this equation can be solved both in iterative and non-iterative ways. We observe that the iteration procedure brings about fast acceleration of convergence compared to the KK approach. We also find that the non-iterative calculation reproduces successfully any set of the true eigenvalues of the original Hamiltonian. This non-iterative calculation can be made regardless of the magnitudes of the overlaps with the model space and the energy differences between the unperturbed energy and the eigenvalues to be solved.