Expression of Relativistic Expectation Values of Powers of r in Terms of Clebsch–Gordan Coefficients

2020/03/31 by Jean-Christophe Pain, J.-C. Pain
Physics and Astronomy · #Atomic and Molecular Physics #Expression (computer science) #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Relativistic quantum chemistry #Theory of relativity #Type (biology) #nucl-th #physics.atom-ph #quant-ph

paper · pdf · doi:10.1134/s0030400x20080275

submitted to "Optics ans spectroscopy"

openalex created_date 2020/04/10 · openalex publication_date 2020/08/01 · arxiv created 2020/11/17 · arxiv updated 2020/11/18 · openalex updated_date 2026/08/05

Abstract

It is shown that, in the relativistic hydrogenic approximation, expectation values of the type ⟨ nℓ j |r^k| nℓ j ⟩ can be expressed in terms of Clebsch–Gordan coefficients or 3jm symbols. This generalizes the results obtained by Varshalovich and Karpova [Opt. Spectrosc. 118, 1–5 (2015); Opt. Spektrosk. 118, 3–7 (2015)] in the non-relativistic hydrogenic case.

Citations

• The Application of Group theory to the Quantum Dynamics of Monatomic Systems
• Recurrence relations for relativistic atomic matrix elements
• Mathematical structure of relativistic Coulomb integrals
• Modeling penetrating collisions in the standard line broadening impact theory for hydrogen
• Quantum Theory of Angular Momentum
• Theory of Complex Spectra. II