Computational aspects of the continuum quaternionic wave functions for hydrogen

2014 ◽  
Vol 349 ◽  
pp. 171-188 ◽  
Author(s):  
J. Morais
Keyword(s):  
Wave Functions ◽  
Computational Aspects ◽  
The Continuum

scholarly journals DISCRETIZED LAPLACIANS ON AN INTERVAL AND THEIR RENORMALIZATION GROUP

1994 ◽  
Vol 09 (25) ◽  
pp. 4485-4509 ◽  
Author(s):  
E. ERCOLESSI ◽  
P. TEOTONIO-SOBRINHO ◽  
G. BIMONTE
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Continuum Limit ◽  
Wave Functions ◽  
The Other ◽  
Scale Invariant ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
The Laplace Operator ◽  
The Continuum

The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how these extensions can be recovered by studying the continuum limit of certain discretized versions of the Laplace operator on a lattice. Associated to this limiting procedure, there is a renormalization flow in the finite-dimensional parameter space describing the discretized operators. This flow is shown to have infinite fixed points, corresponding to the self-adjoint extensions characterized by scale-invariant boundary conditions. The other extensions are recovered by looking at the other trajectories of the flow.

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.

Mikroskopische Theorie der Kernreaktionen für einen Mehrteilchen-Aufbruch / Microscopic Theory of Nuclear Reactions for a Multi-particle-break-up

1974 ◽  
Vol 29 (6) ◽  
pp. 859-866 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Nuclear Reactions ◽  
Microscopic Theory ◽  
Bound State ◽  
Wave Functions ◽  
Matrix Elements ◽  
S Matrix ◽  
The Matrix ◽  
Nucleon Emission ◽  
The Continuum ◽  
Continuum Wave

Introducing correlated continuum wave functions for the two- and re-particle-continuum a microscopic theory of nuclear reactions based on a method of Fano is developed. The S-matrix-elements are given by the matrix-elements between correlated continuum wave functions and bound state wave functions. The antisymmetrization of the continuum wave functions with more than one particle in the continuum is included. The theory can be straightforwardly applied on the n-nucleon-emission process following photo- and particle excitations.

RHO PRODUCTION IN PROTON-NUCLEUS COLLISION

1999 ◽  
Vol 08 (03) ◽  
pp. 243-256 ◽  
Author(s):  
SWAPAN DAS ◽  
B. K. JAIN ◽  
A. B. SANTRA
Keyword(s):  
Reaction Mechanism ◽  
Cross Sections ◽  
Target Nucleus ◽  
Beam Energy ◽  
Plane Waves ◽  
Bound State ◽  
Wave Functions ◽  
Decay Probability ◽  
Hadron Masses ◽  
The Continuum

With the final aim to explore the effect of the medium on hadron masses we study the reaction mechanism for the (p,p′ρ0) reaction on nuclei. We focus on the amplitudes which are dominated by the N*(1720)P13 resonance in intermediate state. This resonance has about 80% decay probability to Nρ channel. A nonrelativistic formalism is written for different amplitudes. The theoretical cross sections are presented for the 12 C target nucleus around 3 GeV beam energy. These results are found to be sensitive to the N* as well as ρ mass modifications in the medium. These two effects in the p′ spectrum can be separated experimentally as they are found to occur at different values of the p′ momentum. Because of the exploratory nature of this investigation, simple forms are used for the bound-state wave functions, and the continuum particles are approximated by plane waves.

Angular Distribution of Products from Photodissociation of Diatomic Molecules

1971 ◽  
Vol 49 (19) ◽  
pp. 2425-2431 ◽  
Author(s):  
S. H. Lin ◽  
C. J. Koizumi
Keyword(s):  
Angular Distribution ◽  
Electronic Transition ◽  
Function Approximation ◽  
Adiabatic Approximation ◽  
Diatomic Molecules ◽  
Delta Function ◽  
Wave Functions ◽  
Transition Moment ◽  
Radial Wave ◽  
The Continuum

The angular distribution of dissociation products in the photodissociation of diatomic molecules has been calculated quantum-mechanically. It is shown that in the adiabatic approximation the angular distribution of the electronic transition with the transition moment along the molecular axis can be expressed as σ(θ0) = (σ0/4π) [1 + βP2 (cos θ0)], and the angular distribution for the case of perpendicular transitions is very complicated and can be approximately expressed in the same form as that for the case of parallel transitions only in the limiting conditions. Approximate calculations of the angular distribution of photodissociation are also carried out by using the delta function approximation to the continuum radial wave functions, and it is found that in this approximation β = 2 for the parallel transition; that is, the angular distribution of dissociation products is of the form cos2 θ0.

Theoretical and computational aspects of extended wave functions

2001 ◽  
Vol 84 (3) ◽  
pp. 331-337 ◽  
Author(s):  
R. Carbó-Dorca ◽  
J. Karwowski
Keyword(s):  
Wave Functions ◽  
Computational Aspects
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