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).

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.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

scholarly journals Optics of Chromites and Charge-Transfer Transitions

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Andrei V. Zenkov
Keyword(s):  
Charge Transfer ◽  
Simple Structure ◽  
Electric Dipole Transition ◽  
Wave Functions ◽  
Final States ◽  
Matrix Elements ◽  
Cluster Approach ◽  
Electron Wave ◽  
Charge Transfer Transitions ◽  
Transition Modeling

Specific features of the charge-transfer (CT) states and O2p→Cr3d transitions in the octahedral (CrO6)9− complex are considered in the cluster approach. The reduced matrix elements of the electric-dipole transition operator are calculated on many-electron wave functions of the complex corresponding to the initial and final states of a CT transition. Modeling the optic spectrum of chromites has yielded a complicated CT band. The model spectrum is in satisfactory agreement with experimental data which demonstrates the limited validity of the generally accepted concept of a simple structure of CT spectra.

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