Doorway States in the Random-Phase Approximation

TL;DR

This paper develops a theory of doorway states within the random-phase approximation, revealing unique features and numerical results that differ from traditional shell model descriptions.

Contribution

It introduces a novel RPA-based framework for doorway states, deriving the Pastur equation and highlighting differences from standard models.

Findings

Coupling of doorway states causes mutual attraction of opposite energy states.

Numerical results show unexpected features in doorway state interactions.

The Pastur equation matches large space matrix diagonalization results.

Abstract

By coupling a doorway state to a see of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.