Dynamical Reorganization of Two-Electron Correlation During Atomic Excitation and Relaxation A reduced-density-matrix framework for cascade pathways

Abstract

Electron correlation is central to the structure and dynamics of two-electron atoms. Excitation and radiative relaxation are usually described through energies, state populations, and transition probabilities, while the associated reorganization of genuine two-electron correlation provides complementary information. We formulate a reduced-density-matrix framework for following this reorganization during excitation and subsequent radiative relaxation. The two-particle reduced density matrix (2-RDM) is separated into the contribution reconstructed from the one-particle density matrix and a cumulant part, and a reference-state correlation distance is introduced to quantify the displacement of the instantaneous correlation structure from that of a chosen reference state. An analytically tractable two-configuration model shows why populations alone cannot determine the full two-electron density matrix. The framework is then formulated for the helium cascade . The purpose is not to introduce a new density matrix or a new cumulant measure, but to use established RDM quantities to define and test a correlation-space trajectory for an atomic relaxation pathway. No Cooper-like pairing assumption is made. The proposed quantities can be evaluated using time-dependent configuration interaction or time-dependent 2-RDM methods. The paper establishes a testable framework; no numerical correlation trajectory is claimed until a converged calculation is performed.