Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous bound-state error estimates in the weak-field regime

Journal Article · Sat May 01 04:00:00 EDT 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.47.4143· OSTI ID:6873506

Falsaperla, P; Fonte, G ^[1]

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1. Dipartimento di Fisica, Universita di Catania, Corso Italia 57, I-95129 Catania (Italy) Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Corso Italia 57, I-95129 Catania (Italy)

Applying a method based on some results due to Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], we show that series of Rydberg eigenvalues and Rydberg eigenfunctions of hydrogen in a uniform magnetic field can be calculated with a rigorous error estimate. The efficiency of the method decreases as the eigenvalue density increases and as [gamma][ital n][sup 3][r arrow]1, where [gamma] is the magnetic-field strength in units of 2.35[times]10[sup 9] G and [ital n] is the principal quantum number of the unperturbed hydrogenic manifold from which the diamagnetic Rydberg states evolve. Fixing [gamma] at the laboratory value 2[times]10[sup [minus]5] and confining our calculations to the region [gamma][ital n][sup 3][lt]1 (weak-field regime), we obtain extremely accurate results up to states corresponding to the [ital n]=32 manifold.

• OSTI ID: 6873506
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 47:5; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664200* -- Spectra of Atoms & Molecules & their Interactions with Photons-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
CALCULATION METHODS
EIGENFUNCTIONS
EIGENVALUES
ELEMENTS
ENERGY LEVELS
ERRORS
EXCITED STATES
FUNCTIONS
HYDROGEN
NONMETALS
RYDBERG STATES
ZEEMAN EFFECT