A derivation of Judd-Ofelt theory by second quantization of configuration interaction

Abstract

A derivation of the equations in the Judd-Ofelt theory for quantifying the intensities of 4f-4f transitions based on the second quantization or occupation number representation is presented. This derivation is more concise and compact, emphasizing some approximations employed and aims at simplifying the comprehension of the theory. It is almost self-contained, with the properties and relationships pertaining to the second quantization approach being introduced, and it requires some basic understanding of quantum mechanics, particularly, of angular momentum techniques (e.g. 3-j symbols and Racah operators). It is expected that this derivation can be followed and comprehended by students, researchers, and enthusiasts, hopefully encouraging new implementations, applications, and developments involving the intensities of 4f-4f transitions.