Collisional depolarization of light alkali atoms excited to their lowest 2P levels

1970 ◽  
Vol 48 (24) ◽  
pp. 3047-3058 ◽  
Author(s):  
M. Elbel
Keyword(s):  
Cross Sections ◽  
Transition Matrix ◽  
Inner Product ◽  
Matrix Elements ◽  
Angular Momenta ◽  
Rank Tensor ◽  
Alkali Atoms ◽  
The Matrix ◽  
Transition Matrix Elements ◽  
Depolarization Of Light

Transition matrix elements connecting the Zeeman sublevels of the lowest p doublets in light alkali atoms have been derived using methods of steady-state collision theory. The matrix elements generally consist of two parts which, under rotations of the quantization axis with respect to the scattering plane, behave like components of a first rank and a second rank tensor, respectively. Only the second rank tensor components lead to the selection rule j, mJ↔j, −mj, whereas the first rank tensor components do not. The latter can be ascribed to a formal interaction term which is proportional to the inner product of the orbital angular momenta of the valence electron and the colliding atoms, respectively, thus accounting for molecular coupling phenomena during the collision. Finally, the transition matrix elements are used to calculate the depolarizing cross sections from the van der Waals potential.

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.

HYPERGEOMETRIC FUNCTION REPRESENTATION OF RELATIVISTIC TRANSITION MATRIX ELEMENTS FOR HYDROGENIC ATOMS

2009 ◽  
Vol 23 (02) ◽  
pp. 111-119
Author(s):  
A. V. SOLDATOV ◽  
J. SEKE ◽  
G. ADAM ◽  
M. POLAK
Keyword(s):  
Transition Matrix ◽  
Numerical Evaluation ◽  
Hypergeometric Functions ◽  
Field Vector ◽  
Matrix Elements ◽  
Plane Wave Expansion ◽  
Computationally Efficient ◽  
The Matrix ◽  
Transition Matrix Elements ◽  
Computationally Efficient Algorithms

By using the plane-wave expansion for the electromagnetic-field vector potential, relativistic bound–bound, bound–unbound and unbound–unbound transition matrix elements for hydrogenic atoms are expressed universally in terms of hypergeometric functions. By applying the obtained formulas, these transition matrix elements can be evaluated analytically and numerically with arbitrarily high precision. The newfound representation for the matrix elements is very convenient for direct numerical evaluation of the Lamb shift because of its universality, conciseness and reliance on functions already built in the standard computational packages. All of this is highly favorable for programming of computationally efficient algorithms.

OPTICAL TRANSITIONS IN A PARABOLIC GaAs/Ga1-xAlxAs SUPERLATTICES

2001 ◽  
Vol 08 (03n04) ◽  
pp. 321-325
Author(s):  
ŞAKIR ERKOÇ ◽  
HATICE KÖKTEN
Keyword(s):  
Transition Matrix ◽  
Optical Transition ◽  
Matrix Elements ◽  
Electron States ◽  
Parabolic Potential ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Transition Matrix Elements ◽  
Scf Calculations

We have performed self-consistent field (SCF) calculations of the electronic structure of GaAs/Ga 1-x Al x As superlattices with parabolic potential profile within the effective mass theory. We have calculated the optical transition matrix elements involving transitions from the hole states to the electron states, and we have also computed the oscillator strength matrix elements for the transitions among the electron states.

scholarly journals Microscopic method for E0 transition matrix elements

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
B. A. Brown ◽  
A. B. Garnsworthy ◽  
T. Kibédi ◽  
A. E. Stuchbery
Keyword(s):  
Transition Matrix ◽  
Matrix Elements ◽  
Microscopic Method ◽  
Transition Matrix Elements

Neutron and proton transition matrix elements and inelastic hadron scattering

1981 ◽  
Vol 103 (4-5) ◽  
pp. 255-258 ◽  
Author(s):  
A.M. Bernstein ◽  
V.R. Brown ◽  
V.A. Madsen
Keyword(s):  
Transition Matrix ◽  
Matrix Elements ◽  
Transition Matrix Elements

scholarly journals Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
N. Ahmadiniaz ◽  
V. M. Banda Guzmán ◽  
F. Bastianelli ◽  
O. Corradini ◽  
J. P. Edwards ◽  
...  
Keyword(s):  
Cross Sections ◽  
Drop Out ◽  
Matrix Elements ◽  
Fermion Propagator ◽  
Particle Path ◽  
Path Integral Representation ◽  
Fermion Line ◽  
Electron Propagator ◽  
The Matrix ◽  
Standard Linear

Abstract In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications.We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

scholarly journals Floquet-state cooling

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Onno R. Diermann ◽  
Martin Holthaus
Keyword(s):  
Solid State ◽  
Ground State ◽  
Thermal Equilibrium ◽  
Transition Matrix ◽  
Fourier Spectrum ◽  
Dissipative System ◽  
Quasistationary State ◽  
Matrix Elements ◽  
Periodically Driven ◽  
Transition Matrix Elements

AbstractWe demonstrate that a periodically driven quantum system can adopt a quasistationary state which is effectively much colder than a thermal reservoir it is coupled to, in the sense that certain Floquet states of the driven-dissipative system can carry much higher population than the ground state of the corresponding undriven system in thermal equilibrium. This is made possible by a rich Fourier spectrum of the system’s Floquet transition matrix elements, the components of which are addressed individually by a suitably peaked reservoir density of states. The effect is expected to be important for driven solid-state systems interacting with a phonon bath predominantly at well-defined frequencies.

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