Calcul des forces d'oscillateur des premières transitions permises des donneurs dans le silicium et comparaison avec l'expérience

1985 ◽  
Vol 63 (4) ◽  
pp. 437-444 ◽  
Author(s):  
M. Bara ◽  
M. Astier ◽  
B. Pajot
Keyword(s):  
Point Of View ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Linear Combinations ◽  
Electron Effective Mass ◽  
Angular Momenta ◽  
Hydrogenic Donor ◽  
Ritz Procedure ◽  
Donor States

The calculation of the oscillator strength of the optical transitions between two electronic states necessitates the knowledge of the wave functions of these states. In the case of hydrogenic donor impurities in semiconductors, these wave functions are eigenvectors of a matrix whose elements couple hydrogenic basis wave functions of appropriate parity, angular momenta, and projection of angular momentum through a one-electron effective mass Hamiltonian, provided the set of eigenvalues of interest has been minimized with respect to the variational parameters included in the basis wave functions. In his well-known paper, Faulkner has given the eigenvalues of the first donor states for Si and Ge, but neither the eigenvectors nor the variational parameters. We have reproduced the calculations of Faulkner for Si, finding quite similar results for the eigenvalues. The coefficients of the linear combinations of the basis functions show that except for the very first levels, the labeling of the eigenvectors does not correspond to the basis function with the greatest weight, and that the labeling is somewhat arbitrary from that point of view. The eigenvectors are used to calculate the electric-dipole matrix elements. The values so obtained for the oscillator strengths are in qualitative agreement with the relative intensities of the observed lines for substitutional donors in Si. This seems to demonstrate that the eigenvectors obtained through the Rayleigh–Ritz procedure are reliable enough for the evaluation of spectroscopical quantities where they are needed.

Relativistic corrections to He I transition ratesThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

2011 ◽  
Vol 89 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Donald C. Morton ◽  
Paul Moffatt ◽  
G. W.F. Drake
Keyword(s):  
Nuclear Charge ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Nuclear Mass ◽  
Atomic Systems ◽  
Relativistic Corrections ◽  
Doubly Excited ◽  
Accurate Wave ◽  
The Continuum

The relativistic corrections to the theoretical oscillator strengths of light elements such as helium are typically less than 0.1% and usually are ignored. However, they can be important for comparisons with the most accurate experiments, and they rapidly increase in magnitude with increasing nuclear charge. We have begun with the spin-forbidden electric-dipole transitions of neutral helium, using calculations consisting of (1) extremely accurate wave functions without relativistic corrections for both infinite and finite nuclear mass, (2) spin-changing matrix elements through the perturbations of the wave functions by the spin-orbit and spin-other-orbit Breit operators, (3) the use of pseudostates in the sums over all the intermediate states including the continuum, and (4) the inclusion as perturbers of the 1S0 and 3S1 states the pseudostates corresponding to the doubly excited npn′p 3P 0e and npn′p 1P 1e terms, respectively. As examples of these calculations, we present oscillator strengths for the transitions 1 1S0–2 3P1, 2 1S0–2 3P1, 2 3S1–2 1P1, 2 1P1–3 3D1,2, and 2 3P1,2–3 1D2.

ON A SELECTION RULE FOR ELECTRIC TRANSITIONS IN AXIALLY-SYMMETRIC NUCLEI

2010 ◽  
Vol 19 (04) ◽  
pp. 685-691 ◽  
Author(s):  
A. DOBROWOLSKI ◽  
A. GÓŹDŹ ◽  
J. DUDEK
Keyword(s):  
Transition Matrix ◽  
Selection Rule ◽  
Wave Functions ◽  
Matrix Elements ◽  
Axially Symmetric ◽  
Many Body ◽  
Absolute Value ◽  
Angular Momenta ◽  
Abrupt Changes ◽  
Transition Matrix Elements

We consider many-body E-l transition matrix-elements between two nuclear states of different axially-symmetric deformations characterised by two different (mutually non-orthogonal) sets of single-particle wave-functions. Yet, when varying the deformations of the initial, final, or both these states one notices abrupt changes in the form of vanishing and possibly reappearance of the transition matrix elements calculated between the corresponding Slater determinants. The mechanism is explained in terms of the conservation of the |m| quantum number (absolute value of the projection of individual-nucleonic angular-momenta); consequences for the more general calculations of this type also without axial symmetry are discussed.

REDUCED MATRIX ELEMENTS AND REPRESENTATION OF WAVE FUNCTIONS

1970 ◽  
Vol 31 (C4) ◽  
pp. C4-43-C4-46
Author(s):  
F. R. INNES
Keyword(s):  
Wave Functions ◽  
Matrix Elements

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

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.

Theoretical ionization energies and oscillator strengths for the sodium isoelectronic sequence

1969 ◽  
Vol 47 (8) ◽  
pp. 835-838 ◽  
Author(s):  
R. P. McEachran ◽  
C. E. Tull ◽  
M. Cohen
Keyword(s):  
Matrix Element ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Ionization Energies ◽  
Core Approximation

Orbital wave functions for a number of 2S, 2P0, 2D, and 2F0 states of Na, Mg+, and Al2+ have been calculated by means of the frozen core approximation. The oscillator strengths of all allowed dipole transitions have been determined using both length and velocity formulations for the transition matrix element; these results agree with each other to within a few percent.

MULTIPOLE MATRIX ELEMENTS 〈nl|rβ|El'〉v FOR H-LIKE ATOMS AND THEIR APPLICATIONS (AS β = 1, n ≤ 4, Enl < 0 ≤ E ≤ 1)

2008 ◽  
Vol 22 (08) ◽  
pp. 937-965 ◽  
Author(s):  
V. F. TARASOV
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Atomic Physics ◽  
Nuclear Charge ◽  
Dipole Moments ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Auxiliary Parameter ◽  
Radial Functions ◽  
Line Intensities

This article deals with the connection between multipole matrix elements 〈nl|rβ|n'l'〉ν and 〈nl|rβ|El'〉ν for H-like atoms, where ν is the so-called "auxiliary" parameter of Heun's differential equation and [Formula: see text] is the "effective" nuclear charge, and new properties of Appell's function F2(x,y) to the vicinity of the singular point (1, 1) and in addition, here, first V. A. Fock's idea for the continuous spectrum is taken into consideration. Such an approach allows us to get the explicit expressions for squares of the dipole moments and the certain physical characteristics in atomic physics and also their exact numerical values, e.g., the average oscillator strengths [Formula: see text] and the line intensities J(nl, El'), etc., as n ≤ 4, l'= l ± 1 and 0 ≤ E ≤ 1 (see Tables 1–3). Besides, diagrams of certain radial functions for the discrete-continuous transitions are given here.

scholarly journals Magnetic HexadecapoleγTransitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lotta Jokiniemi ◽  
Jouni Suhonen ◽  
Hiroyasu Ejiri
Keyword(s):  
Nuclear Matrix ◽  
Wave Functions ◽  
Matrix Elements ◽  
Heavy Nuclei ◽  
Magnetic Quadrupole ◽  
Order Of Magnitude ◽  
Nuclear Responses ◽  
Beta Decays ◽  
Gamow Teller ◽  
Phonon Model

Neutrino-nuclear responses in the form of squares of nuclear matrix elements, NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs,MEXP(M4), deduced from observed M4γtransition half-lives are compared with the single-quasiparticle (QP) NMEs,MQP(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEsMMQPM(M4). The experimentally derived M4 NMEs are found to be reduced by a coefficientk≈0.29with respect toMQP(M4) and byk≈0.33with respect toMMQPM(M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but mainly by other nucleonic and nonnucleonic correlations which are not explicitly included in the MQPM. The found reduction rates are of the same order of magnitude as those for magnetic quadrupoleγtransitions and Gamow-Teller (GT) and spin-dipole (SD)βtransitions. The impacts of the found reduction coefficients on the magnitudes of the NMEs involved in astroneutrino interactions and neutrinoless double beta decays are discussed.

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