scholarly journals Application of Reaction Matrix Theory to Meson Processes

1968 ◽  
Vol 21 (6) ◽  
pp. 769
Author(s):  
JL Cook
Keyword(s):  
Boundary Conditions ◽  
Matrix Theory ◽  
Matrix Formalism ◽  
Pion Cloud ◽  
R Matrix ◽  
Reaction Matrix ◽  
Pion Nucleon ◽  
Full Analysis

The possible application of reaction matrix theory to pion-nucleon processes is discussed. It is found that suitable boundary conditions can remove the effects of the nucleon-pion cloud, leading to the conventional R-matrix formalism. A simple dynamical channel.coupling scheme is proposed which permits full analysis of experiments.

Resonance Widths and Unitarity

1972 ◽  
Vol 50 (2) ◽  
pp. 84-92 ◽  
Author(s):  
C. T. Tindle
Keyword(s):  
Energy Dependence ◽  
Cross Section ◽  
Matrix Theory ◽  
Neutron Cross Section ◽  
Matrix Formalism ◽  
R Matrix ◽  
Level Width ◽  
S Matrix ◽  
The Difference ◽  
Energy Dependent

The low energy neutron cross section of 135Xe is analyzed using both the R-matrix theory of Wigner and Eisenbud and the S-matrix theory of Humblet and Rosenfeld. Particular attention is given to the role played by the total resonance level width for it is well known that the R-matrix widths are energy dependent but the S-matrix widths are not. This different energy dependence leads to different analytic forms for the cross section and the n + 135Xe reaction offers what may be the simplest and best physical example for comparing these two forms. To the accuracy of the present data the difference is not detectable. The different energy dependence of the resonance widths is shown to be related to unitarity. A general proof that the R-matrix formalism is always unitary is given. The difficulty of satisfying unitarity in the S-matrix formalism is discussed and it is shown for the n + 135Xe reactions that this can lead to physically unacceptable solutions. This "lack of unitarity" does not, however, lead to any difficulties in fitting the present experimental data.

scholarly journals A Method for Inverting the Channel Matrix in R-Matrix Theory

1972 ◽  
Vol 25 (3) ◽  
pp. 253
Author(s):  
WK Bertram
Keyword(s):  
Recurrence Relation ◽  
Matrix Theory ◽  
Matrix Formalism ◽  
R Matrix ◽  
Channel Matrix

A technique is presented for inverting the channel matrix which occurs in R-matrix theory. The collision matrix is expressed in a form which does not involve matrix inversions; it is evaluated by the application of a recurrence relation. The connection between this method and the level matrix formalism is examined.

scholarly journals Developments regarding three-body reaction channels within the R-matrix formalism

2020 ◽  
Vol 239 ◽  
pp. 03002
Author(s):  
Benedikt Raab ◽  
Thomas Srdinko ◽  
Helmut Leeb
Keyword(s):  
Cross Sections ◽  
Matrix Theory ◽  
Resonance Region ◽  
Reaction Cross ◽  
Resonance Structure ◽  
Matrix Formalism ◽  
Matrix Formulation ◽  
R Matrix ◽  
Reaction Channels ◽  
Three Body

At low incident energies of nucleon-induced reaction cross sections exhibit a striking resonance structure which cannot properly be described by (semi-) microscopic models. Usually R-matrix theory is applied which provides a sufficiently accurate but phenomenological description of the resonance region. However, standard R-matrix theory is only suited for two-particle channels. Three- and many-particle channels which may occur at rather low incident energies and are usually treated in approximative or effective way. In this contribution an extension to unequal masses of the R-matrix formulation of Glockle based on the Faddeev equation is performed and proper expressions for numerical implementation are given.

The calculation of photoionization of highly-ionized iron using R-matrix theory

1997 ◽  
Vol 58 (4-6) ◽  
pp. 491-493 ◽  
Author(s):  
G. Black ◽  
S.J. Rose ◽  
K.L. Bell ◽  
F.P. Keenan
Keyword(s):  
Matrix Theory ◽  
R Matrix

Wave function approach to reaction matrix theory. II

1977 ◽  
Vol 15 (4) ◽  
pp. 1257-1260 ◽  
Author(s):  
B. Talukdar ◽  
N. Mallick ◽  
S. B. Sarkar ◽  
L. Mondal
Keyword(s):  
Wave Function ◽  
Matrix Theory ◽  
Function Approach ◽  
Reaction Matrix

Implementation of the CCGM approximation for surface diffraction using Wigner R‐matrix theory

1983 ◽  
Vol 79 (8) ◽  
pp. 4062-4068 ◽  
Author(s):  
Jack G. Lauderdale ◽  
C. William McCurdy
Keyword(s):  
Matrix Theory ◽  
R Matrix ◽  
Surface Diffraction
Sign in / Sign up

Export Citation Format

Share Document