Bound states in screened and bare Coulomb potentials: A nonorthogonal CI-based route to effective Hamiltonians for two-electron systems

1999 ◽  
Vol 74 (2) ◽  
pp. 153-161 ◽  
Author(s):  
Pinaki Chaudhury ◽  
S. P. Bhattacharyya
Keyword(s):  
Bound States ◽  
Electron Systems ◽  
Effective Hamiltonians ◽  
Coulomb Potentials

scholarly journals Scattering and Its Applications to Various Atomic Processes: Elastic Scattering, Resonances, Photoabsorption, Rydberg States, and Opacity of the Atmosphere of the Sun and Stellar Objects

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 78
Author(s):  
Anand K. Bhatia
Keyword(s):  
Elastic Scattering ◽  
Long Range ◽  
Short Range ◽  
Bound States ◽  
Rydberg States ◽  
Stellar Atmospheres ◽  
Electron Systems ◽  
Short Range Correlations ◽  
Hybrid Theory ◽  
Scattering Resonances

A scattering process can be a natural process or a process carried out in a laboratory. The scattering of particles from targets has resulted in important discoveries in physics. We discuss various scattering theories of electrons and positrons and their applications to elastic scattering, resonances, photoabsorption, excitation, and solar and stellar atmospheres. Among the most commonly employed approaches are the Kohn variational principle, close-coupling approximation, method of polarized orbitals, R-matrix formulation, and hybrid theory. In every formulation, an attempt is made to include exchange, long-range and short-range correlations, and to make the approach variationally correct. The present formulation, namely, hybrid theory, which is discussed in greater detail compared to other approximations, includes exchange, long-range correlations, and short-range correlations at the same time, and is variationally correct. It was applied to calculate the phase shifts for elastic scattering, the resonance parameters of two-electron systems, photoabsorption in two-electron systems, excitation of atomic hydrogen by an electron and positron impact, and to study the opacity of the Sun’s atmosphere. Calculations of polarizabilities, Rydberg states, and bound states of atoms are also discussed.

DISCUSSION OF A KNOWN SPHERICAL BASIS FOR DIRAC WAVE FUNCTIONS

2013 ◽  
Vol 28 (08) ◽  
pp. 1350022
Author(s):  
WERNER SCHEID
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Expectation Values ◽  
Original Boundary ◽  
Mit Bag Model ◽  
Slight Extension ◽  
Spherical Basis ◽  
Coulomb Potentials

The paper considers the free spherical Dirac equation with a boundary condition at r = R which is a slight extension of the original boundary condition of the MIT bag model. We discuss the basis states and apply them for a diagonalization of Coulomb potentials. The obtained results agree quite well with the lowest bound states with κ = -1, +1 and -2 and their expectation values [Formula: see text]. There appear basis states with energies -mc2 < E < mc2 under certain circumstances of the boundary condition. These states are concentrated at the boundary.

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