scholarly journals Computing Dirac’s atomic hydrogen wave functions of the continuum, using summation of mathematically divergent series

1991 ◽  
Vol 5 (3) ◽  
pp. 319 ◽  
Author(s):  
F. J. Belinfante
Keyword(s):  
Atomic Hydrogen ◽  
Wave Functions ◽  
Divergent Series ◽  
The Continuum

Resonant electron scattering by atoms

1963 ◽  
Vol 274 (1357) ◽  
pp. 253-266 ◽  
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Atomic Hydrogen ◽  
Resonant State ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Inelastic Threshold ◽  
Atomic Systems ◽  
Resonance Energies ◽  
Resonant Electron

The Kapur-Peierls resonance formalism adapted for electron scattering by atomic systems is modified to allow for the exclusion principle, and a variational principle is derived for calculating the complex resonance energies. The theory is applied to calculate the first four resonance levels in the 1 S state of the electron/atomic hydrogen system by using a trial wave function made up from singleparticle functions which are modified (1 s ), (2 s ) and (2 p ) hydrogen wave functions. We find two levels (at approximately — 13 and — 10 eV) whose widths are of the order of a few volts. There are also two levels (at about — 3 and 0 eV) which have very narrow widths, less than 10 -2 eV, if they occur below the inelastic threshold, shooting up to widths of several volts at threshold. Such a narrow level occurs if the resonant state is energetically unable to decay to a state of the residual atom of which it contains a substantial component.

The application of variational methods to atomic scattering problems II. Impact excitation of the 2s level of atomic hydrogen-distorted wave treatment

1952 ◽  
Vol 212 (1111) ◽  
pp. 521-530 ◽  
Keyword(s):  
Cross Section ◽  
Atomic Hydrogen ◽  
Plane Waves ◽  
Wave Functions ◽  
Impact Excitation ◽  
Wave Method ◽  
Distorted Wave ◽  
Scattering Problems ◽  
The Cross ◽  
Distorted Wave Method

The cross-section for excitation of the 2 S level of atomic hydrogen by electrons is calculated using the distorted wave method with full allowance for exchange. The distorted wave functions used in the calculations are determined by Hulthèn’s variational method. The initial wave functions, representing the motion of an electron in the field of a normal atom with allowance for exchange, are taken to be those calculated by Massey & Moiseiwitsch (1950). The final wave functions, representing the motion of an electron in the field of a hydrogen atom in the 2 S state, have been obtained by a modification of the same method. Exchange effects are found to be less important in determining the forms of these wave functions. The cross-sections obtained are considerably smaller than those calculated by the Born-Oppenheimer method, in which the electron wave functions are undistorted plane waves. This is largely because the symmetrical cross-section, which has the greater weight in determining the mean cross-section, is much greater than the antisymmetrical according to the Born-Oppenheimer method, but the reverse is true if distortion is allowed for. In no case does the distorted wave method give results exceeding the theoretical upper limit, whereas with plane waves this limit is exceeded at certain electron energies by the symmetrical cross-section.

Sign in / Sign up

Export Citation Format

Share Document