Effective Hamiltonian for near‐degenerate states in direct relativistic perturbation theory. I. Formalism

1996 ◽  
Vol 104 (21) ◽  
pp. 8546-8552 ◽  
Author(s):  
A. Rutkowski ◽  
W. H. E. Schwarz
Keyword(s):  
Perturbation Theory ◽  
Effective Hamiltonian ◽  
Relativistic Perturbation Theory ◽  
Degenerate States

Effective Hamiltonian for near-degenerate states in relativistic direct perturbation theory. II. H2+-like systems

1998 ◽  
Vol 109 (6) ◽  
pp. 2135-2143 ◽  
Author(s):  
A. Rutkowski ◽  
W. H. E. Schwarz ◽  
R. Kozłowski ◽  
J. Bȩczek ◽  
R. Franke
Keyword(s):  
Perturbation Theory ◽  
Effective Hamiltonian ◽  
Direct Perturbation ◽  
Degenerate States

Analytical formulas for the Stark effect on intensity of hydrogen radiation lines

2003 ◽  
Vol 81 (5) ◽  
pp. 755-769 ◽  
Author(s):  
A A Kamenski ◽  
V D Ovsiannikov
Keyword(s):  
Perturbation Theory ◽  
Green Function ◽  
Field Strength ◽  
Stark Effect ◽  
Selection Rule ◽  
Magnetic Quantum Number ◽  
Matrix Elements ◽  
Analytical Formulas ◽  
Degenerate States ◽  
Analytical Expressions

A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced Coulomb–Green function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.–n, 32.70.Fw

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