Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous error estimates for energy eigenvalues, energy eigenfunctions, and oscillator strengths

Journal Article · Sat Oct 01 04:00:00 EDT 1994 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.50.3051· OSTI ID:7203705

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)

A variational method, based on some results due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], and previously discussed is here applied to the hydrogen atom in uniform magnetic fields of tesla in order to calculate, with a rigorous error estimate, energy eigenvalues, energy eigenfunctions, and oscillator strengths relative to Rydberg states up to just below the field-free ionization threshold. Making use of a basis (parabolic Sturmian basis) with a size varying from 990 up to 5050, we obtain, over the energy range of [minus]190 to [minus]24 cm[sup [minus]1], all of the eigenvalues and a good part of the oscillator strengths with a remarkable accuracy. This, however, decreases with increasing excitation energy and, thus, above [similar to][minus]24 cm[sup [minus]1], we obtain results of good accuracy only for eigenvalues ranging up to [similar to][minus]12 cm[sup [minus]1].

• OSTI ID: 7203705
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 50:4; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ACCURACY
ATOMS
CALCULATION METHODS
EIGENSTATES
EIGENVALUES
ELEMENTS
ENERGY
ENERGY LEVELS
EXCITED STATES
HYDROGEN
IONIZATION
MAGNETIC FIELDS
NONMETALS
OSCILLATOR STRENGTHS
RYDBERG STATES
THRESHOLD ENERGY
VARIATIONAL METHODS
ZEEMAN EFFECT