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Atoms, Volume 13, Issue 7 (July 2025) – 2 articles

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18 pages, 332 KiB  
Article
Hydrogenic Matrix Elements with Different Effective Charges: Non-Relativistic and Relativistic Cases
by Héctor O. Di Rocco and Julio C. Aguiar
Atoms 2025, 13(7), 60; https://doi.org/10.3390/atoms13070060 - 20 Jun 2025
Abstract
This work explores the evaluation of hydrogenic matrix elements for non-relativistic and relativistic cases under the Screened Hydrogenic Model (SHM). It focuses on scenarios where the initial and final states have different effective charges Z1Z2, deriving closed-form solutions [...] Read more.
This work explores the evaluation of hydrogenic matrix elements for non-relativistic and relativistic cases under the Screened Hydrogenic Model (SHM). It focuses on scenarios where the initial and final states have different effective charges Z1Z2, deriving closed-form solutions for particular cases n1=n2 and Z1=Z2. In addition, analytical expressions for radial matrix elements nl|rβ|nl and their relativistic counterparts are presented. These are applicable for discrete–discrete transitions and allow simplifications for specific configurations using Laplace transforms. The study discusses generalizations of SHM for calculating cross-sections in hot and dense plasmas, employing the Plane Wave Born Approximation (PWBA). It also addresses the transition from LS to jj coupling for matrix elements, providing rules for such transformations. Full article
(This article belongs to the Special Issue Atom and Plasma Spectroscopy)
9 pages, 533 KiB  
Article
Comparison of Different Rydberg Atom-Based Microwave Electrometry Techniques
by Eliel Leandro Alves Junior, Manuel Alejandro Lefrán Torres, Jorge Douglas Massayuki Kondo and Luis Gustavo Marcassa
Atoms 2025, 13(7), 59; https://doi.org/10.3390/atoms13070059 - 20 Jun 2025
Abstract
In this study, we have compared different Rydberg atom-based microwave electrometry techniques under the same experimental conditions and using the same Rydberg states (68S1/2, 68P3/2, and 67P3/2). [...] Read more.
In this study, we have compared different Rydberg atom-based microwave electrometry techniques under the same experimental conditions and using the same Rydberg states (68S1/2, 68P3/2, and 67P3/2). The comparison was carried out for the following techniques: (i) auxiliary microwave field, (ii) microwave amplitude modulation, and (iii) polarization spectroscopy. Our results indicate that all three techniques have a similar minimum measurable microwave electric field. A slightly better result can be obtained by performing polarization spectroscopy using a Laguerre–Gauss coupling laser beam. Full article
(This article belongs to the Section Atom Based Quantum Technology)
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