PROBABILITY OF AUTO-IONIZATION IN LIGHT ATOMS

1950 ◽  
Vol 28a (5) ◽  
pp. 542-548 ◽  
Author(s):  
Ta-You Wu ◽  
Lorraine Ourom
Keyword(s):  
Perturbation Theory ◽  
Transition Probability ◽  
Initial Approximation ◽  
Wave Functions ◽  
Spectral Lines ◽  
Electron Interaction ◽  
Present Calculation ◽  
Continuous State ◽  
Light Atoms ◽  
Auger Effect

With a view to testing the adequacy of the perturbation theory as applied to radiationless transitions in light atoms, the probability of such a transition in the Be atom from the 1s22p3s3P state to the continuum 1s22s + ejected p electron has been calculated. The wave functions employed for the discrete states are obtained by the variational method and the wave function for the continuous state by numerical integration of the Schrodinger equation. The transition probability obtained is 5 × 1013 per second, leading to a width of ~ 290 cm.−1 for the level 1s22p3s3P. This is at least 103 times larger than what is indicated by the observed widths of the spectral lines. Thus the present calculation, together with similar earlier calculations for the He atom, shows that the perturbation theory is inadequate for the light atoms.It is also pointed out that there is an inconsistency in the use of the perturbation theory in these calculations and those on the Auger effect in the literature since the use of variational or "screened" wave functions implies that a part of the electron–electron interaction has already been included in the initial approximation, and it is hence incorrect to treat this whole interaction as the perturbation causing the transition.

Zur Theorie der Auger-Prozesse in III — V-Halbleitern

1969 ◽  
Vol 24 (11) ◽  
pp. 1752-1759
Author(s):  
Dieter Schöne
Keyword(s):  
Transition Probability ◽  
Wave Functions ◽  
Matrix Elements ◽  
Bloch Functions ◽  
Radiative Transitions ◽  
Excess Electrons ◽  
Approximate Wave ◽  
Auger Effect

Abstract This paper presents a calculation of the lifetimes of excess electrons in the III -V compounds InSb, InAs and GaSb, assuming the Auger effect between bands. Following the theory of Beattie and Landsberg matrix elements are calculated by using approximate wave functions instead of Bloch functions. The ninefold integration of the transition probability can be reduced to a four-fold one which then is numerically calculated with the aid of a computer. The results are compared with the lifetimes of radiative transitions. It is shown that the Auger processes are dominant in small gap semiconductors, but not in semiconductors with larger gaps (more than about 0.5 eV).

scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

scholarly journals Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight-binding model

2015 ◽  
Author(s):  
Masudul Haque ◽  
jiang min zhang
Keyword(s):  
Perturbation Theory ◽  
Transition Probability ◽  
Tight Binding ◽  
Coarse Graining ◽  
Sinc Function ◽  
Tight Binding Model ◽  
Binding Model ◽  
Periodically Driven ◽  
Perturbative Regime ◽  
Simple Equality

Abstract We point out that in the first-order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function sinc x ≡ sin x/x. These physical effects appear in many systems with approximately equally spaced spectra, and are also robust for larger amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.

scholarly journals On the electromagnetic fields due to variable electric charges and the intensities of spectrum lines according to the quantum theory

1935 ◽  
Vol 150 (870) ◽  
pp. 416-421 ◽  
Keyword(s):  
Quantum Theory ◽  
Wave Functions ◽  
Spectral Lines ◽  
Quantum Mechanical ◽  
Final States ◽  
Electric Moment ◽  
Mechanical Method ◽  
Quantum Mechanical Method ◽  
Consistent Method ◽  
Time Average

In a recent paper Schott has criticized the quantum mechanical method of finding the intensities of spectral lines, and in particular the assumption that the intensity may be derived by treating the atom as a dipole, radiating classically. The electric moment of this dipole is taken as p = e -2 πivt ∫ Ψ* f rΨ i d τ + Conjugate complex, (1A) where Ψ i and Ψ f are the wave functions of the initial and final states of the atom respectively, and in the Quantum Theory the usual assumption is that the energy radiated per unit time is given by R = 2 |p¨ ¯ | 2 /3 c 2 , (1B) where p¨ ¯ is the time average of p¨. A more consistent method is suggested in which the electric density ρ and the current j, corresponding to the transition, are found, and the electromagnetic field due to these two is examined.

Optical Absorptions in Metal Sodium: The Temperature Dependence in the Liquid State

1974 ◽  
Vol 29 (3) ◽  
pp. 462-468
Author(s):  
N. C. Haider
Keyword(s):  
Perturbation Theory ◽  
Solid State ◽  
Temperature Dependence ◽  
Electron Density ◽  
Electron Energy ◽  
Density Of States ◽  
Optical Conductivity ◽  
Liquid State ◽  
Present Calculation ◽  
Electron Density Of States

The temperature dependence of optical absorptions in liquid Na is calculated. The electron energy values are obtained to second order in perturbation theory which are then used to determine the electron density of states. The density of states plots show some structure similar to those noted in the solid state. The optical conductivity in the liquid state is found to increase with the temperature as in the solid state. The present calculation for the optical conductivity gives a rather sharp peak around ħ ω = 1.7 eV. These results are in better agreement with the existing experimental results

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