The R-matrix formalism for two-particle scattering problems

2021 ◽  
pp. 127865
Author(s):  
Dragoş-Victor Anghel ◽  
Amanda Teodora Preda ◽  
George Alexandru Nemnes
Keyword(s):  
Matrix Formalism ◽  
Particle Scattering ◽  
Scattering Problems ◽  
R Matrix

scholarly journals The Ghost Anomaly in the 9Be(p, d)8Be Reaction

1976 ◽  
Vol 29 (4) ◽  
pp. 245 ◽  
Author(s):  
FC Barker ◽  
GM Crawley ◽  
PS Miller ◽  
WF Steele
Keyword(s):  
Ground State ◽  
Matrix Formalism ◽  
R Matrix

The ghost of the 8Be ground state has been observed in the 9Be(p, d)8Be reaction, and fitted using a many-level R-matrix formalism.

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

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.

Transport through semiconductor quantum systems in the R-matrix formalism

1998 ◽  
Vol 11 (2) ◽  
pp. 117-121 ◽  
Author(s):  
U. Wulf ◽  
J. Kučera ◽  
E. Sigmund
Keyword(s):  
Quantum Systems ◽  
Matrix Formalism ◽  
R Matrix

scholarly journals Experimental Investigation and R-matrix Analysis of Low-lying Levels in 5He and 5Li

1988 ◽  
Vol 41 (4) ◽  
pp. 525 ◽  
Author(s):  
CL Woods ◽  
FC Barker ◽  
WN Catford ◽  
LK Fifield ◽  
NA Orr
Keyword(s):  
Matrix Analysis ◽  
Scattering Data ◽  
Matrix Formalism ◽  
Satisfactory Description ◽  
Model Calculations ◽  
R Matrix ◽  
Channel Radius ◽  
Direct Reactions ◽  
Method Of Production ◽  
Parameter Values

The ~cle-unstable nuclei SHe and Su have been studied via the 4He<,U,6U)SHe and 4He( Li,6He)SU stripping reactions at beam energies of 50 MeV and the 6U(12C, 13N)SHe and 6Li(13C, 14C)SU pickup reactions at 90 MeV. The experimental data clearly demonstrate a dependence of the lineshapes on the method of production of the mass-5 nuclei (in this case pickup or stripping). The observed lineshapes were analysed using the R-matrix formalism in a two-level approximation for each r value, with parameter values deduced from fits to the available 4He + nucleon scattering data. A best channel radius of 5�5 � 1� 0 fm was determined from the stripping data, and the corresponding set of R-matrix parameters also provided a satisfactory description of the pickup data. This channel radius is significantly larger than that employed in most previous analyses. Properties of the lowest ~ - and ! - sta~s of SHe and sU, observed via direct reactions, ate deduced from the parameter values. These properties are compared with results from earlier experimental analyses and the inferred properties of positive-parity states are compared with the results of recent shell-model calculations.

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