Correlation-crystal-field delta-function analysis of Er3+ (4f11) energy-level structure

Full text: Inclusion of selective two-electron correlation-crystal-field (CCF) contributions in the energy-level (model) Hamiltonian has been shown to resolve disparities between calculated and observed energy-level splittings within problematic multiplet manifolds of Nd3+ and Er3+ systems. However, it has not been clear just why the particular CCF terms selected should be more important than other, neglected, terms. In this work, we make use of a simplified delta-function CCF model that assumes the dominant contributions to the correlation crystal-field interactions come from electrons having opposite spin that occupy the same position in space (hence the term 'delta-function'). In the present study, we examine the Er3+ (4f11) electronic energy-level structures for six different Er3+ systems. Inclusion of at most three effective 'delta-function' operators (beyond those needed to represent the standard one-electron CF interactions) resolves the disparities between observed and calculated energy-level splittings for the problematic multiplet manifolds for each of these systems. The relationship between these 'delta-function' terms and previously used selected CCF terms is shown