Microscopic calculations for the 4He continuum

1980 ◽  
Vol 58 (3) ◽  
pp. 306-317 ◽  
Author(s):  
J. J. Bevelacqua
Keyword(s):  
Theoretical Model ◽  
Phase Shift ◽  
Harmonic Oscillator ◽  
Qualitative Agreement ◽  
Matrix Formalism ◽  
R Matrix ◽  
Internal States

A detailed theoretical model for the 4He system is constructed within the framework of the dynamical R-matrix formalism of Lane and Robson. The internal states are expanded on a basis of properly symmetrized translationally invariant harmonic oscillator eigenstates including all states up to [Formula: see text] of oscillator excitation. Scattering results for the 3H(p,p), 3He(n,n), 3H(p,n), 2H(d,d), 2H(d,p), and 2H(d,n) reactions are presented. Phase shift calculations for the p + 3H and n + 3He channels suggest a (1+, 0) assignment for the 25.5 MeV level. Detailed scattering calculations are in qualitative agreement with measured results. The results are also compared with resonating group and field theoretic models. Although each model has its advantages, none is able to provide a complete description of the 4He system.

scholarly journals 3+ States of 8Be

1978 ◽  
Vol 31 (4) ◽  
pp. 239 ◽  
Author(s):  
FC Barker ◽  
Nasima Ferdous
Keyword(s):  
Matrix Element ◽  
Phase Shift ◽  
Excitation Energy ◽  
Cross Sections ◽  
Qualitative Agreement ◽  
Energy Difference ◽  
Mixing Model ◽  
R Matrix ◽  
Mixing Matrix ◽  
The Cross

Level parameters for the 3+ doublet at about 19 MeV in "Be are obtained from a two-level R-matrix fit to the 7Li+p 5P3 phase shift, using the restrictions of the two-state isospin mixing model. The energy of the lower level is appreciably below the accepted value. Predicted contributions from the 3 + levels to the cross sections for the reactions 7Li(p, n), 7Li(p, y), lOBed, ex) and 9Be(d, t) are compared with measured values, and qualitative agreement is obtained. The new values of the level parameters give agreement with values of the isospin mixing matrix element and of the excitation energy difference of the 3 +, T = 1 states in "Li and "Be, calculated assuming that the charge-dependent nteraction is purely Coulomb.

Dynamics of charge density wave phase-slips in mesoscopic samples

2002 ◽  
Vol 12 (9) ◽  
pp. 165-168
Author(s):  
S. N. Artemenko
Keyword(s):  
Experimental Study ◽  
Theoretical Model ◽  
Charge Density ◽  
Qualitative Agreement ◽  
Charge Density Wave ◽  
Temporal Evolution ◽  
Density Wave ◽  
Thermal Fluctuations ◽  
Charge Density Wave Phase ◽  
Phase Slips

Theoretical model of current conversion from normal to collective current in mesoscopic samples of CDW conductors is presented. The current conversion is described in terms of phase slips (PS) induced by strain of the CDW and stimulated by thermal fluctuations. Kernels of PS situated near contacts are surrounded by long-range perturbations of the CDW phase. If spacing between contacts is shorter than decaying length of these perturbations then temporal evolution of PS at different contacts becomes correlated, and PS voltage decreases with spacing between the contacts decreasing. The results are in qualitative agreement with experimental study of current conversion in submicron NbSe3 wires.

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 ENERGY FUNCTIONS IN BOX BALL SYSTEMS

2000 ◽  
Vol 15 (09) ◽  
pp. 1379-1392 ◽  
Author(s):  
KAORI FUKUDA ◽  
YASUHIKO YAMADA ◽  
MASATO OKADO
Keyword(s):  
Phase Shift ◽  
Energy Function ◽  
Conserved Quantities ◽  
Energy Functions ◽  
R Matrix ◽  
Theory Formulation

The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or H function) in the combinatorial R matrix.

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.

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
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