scholarly journals Interaction matrix element fluctuations in quantum dots

2008 ◽  
Author(s):  
L. Kaplan ◽  
Y. Alhassid ◽  
Pawel Danielewicz ◽  
Piotr Piecuch ◽  
Vladimir Zelevinsky
Keyword(s):  
Quantum Dots ◽  
Matrix Element ◽  
Interaction Matrix ◽  
Interaction Matrix Element

A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

1986 ◽  
Vol 41 (5) ◽  
pp. 704-714
Author(s):  
D. Campos ◽  
J. M. Tejeiro ◽  
F. Cristancho
Keyword(s):  
Matrix Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Inelastic Collisions ◽  
Interaction Matrix ◽  
Quantum Mechanical ◽  
Interaction Matrix Element ◽  
S Matrix ◽  
Hopping Model ◽  
Potential Curves

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

Interaction Matrix Element in a Shell Model

1963 ◽  
Vol 129 (6) ◽  
pp. 2643-2652 ◽  
Author(s):  
U. Fano ◽  
F. Prats ◽  
Z. Goldschmidt
Keyword(s):  
Matrix Element ◽  
Shell Model ◽  
Interaction Matrix ◽  
Interaction Matrix Element

Some Hartree–Fock Results for (3d + 4s)q+1 Configurations

1971 ◽  
Vol 49 (9) ◽  
pp. 1205-1210 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Matrix Element ◽  
Average Energy ◽  
Interaction Matrix ◽  
Neutral Atoms ◽  
Radial Functions ◽  
Interaction Matrix Element ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Self-consistent field calculations have been performed in three different ways for the average energy of the configurations 3dq−14s2, 3dq4s, and 3dq+1, q = 2,3,..., 9 of the neutral atoms scandium to nickel. The calculations differ in the way the radial functions depend on the configuration. Parameters which enter into the interaction matrix for states of these configurations are reported. It is shown that the lack of orthogonality of an orbital from one configuration with that of another may alter the interaction matrix element significantly, and that the parameters for radial functions independent of the configuration are significantly different from those that depend on the configuration.

Dynamic of the Optical Matrix Element in Type II GaAsSb/GaAs Quantum Dots for Laser Applications

2009 ◽  
Author(s):  
Tomasz J. Ochalski ◽  
Kamil Gradkowski ◽  
Nicola Pavarelli ◽  
David P. Willams ◽  
Eoin P. O’Reilly ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Matrix Element ◽  
Type Ii ◽  
Laser Applications ◽  
Optical Matrix Element

Characterization of the shallow state of iodine chloride

1984 ◽  
Vol 62 (12) ◽  
pp. 1947-1953 ◽  
Author(s):  
J. C. D. Brand ◽  
D. Bussières ◽  
A. R. Hoy ◽  
S. M. Jaywant
Keyword(s):  
Ground State ◽  
Spectroscopic Constants ◽  
Interaction Matrix ◽  
Electronic Interaction ◽  
Weakly Bound ◽  
Interaction Matrix Element ◽  
Vibrational Levels ◽  
State 1 ◽  
Shallow State

A weakly bound Ω = 1 state of ICl, [Formula: see text], which converges to the ground state 1(2P3/2) + Cl(2P3/2) of the separated atoms, has been identified and characterized. Spectroscopic constants of this state are Te = 17 338.0(13), ωe = 32.85(48), ωexe = 1.272(40), 103Be = 38.2(13), 104αe = 8.89(34), 105γe = −8.1(20) cm−1, and re = 4.01(6) Å. The dissociation energy De = 219.6 cm−1 is consistent with the value predicted for a Morse function, [Formula: see text]. Transitions [Formula: see text] are allowed owing to homogeneous coupling between ã and the well-defined A(3π1) state; in fact, at medium-long range (r = 6–6.5 Å, D–Gν = 20–30 cm−1), the diabatic ã and A curves cross at a small angle. Principal features of the crossing are explained if the electronic interaction matrix element is ca. 4 cm−1, corresponding to weak coupling. Heterogeneous perturbations of the A and ã states in the range D–Gν < 200 cm−1 are attributed to coupling with high vibrational levels of the ground state X(1Σ+).

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