On threshold resonances

1970 ◽  
Vol 48 (15) ◽  
pp. 1747-1758 ◽  
Author(s):  
C. T. Tindle
Keyword(s):  
Cross Sections ◽  
Matrix Theory ◽  
Threshold Level ◽  
R Matrix ◽  
Neutral Particles ◽  
S Matrix ◽  
Energy Neutron ◽  
Square Well ◽  
Neutron Cross Sections ◽  
Threshold Resonances

A comparison is made of the way R-matrix and S-matrix theories analyze the threshold resonances which occur in the scattering of neutral particles by a square well. Both approaches are found to provide very good approximate formulas. However, modifications of the usual S-matrix expansions must first be made. The behavior of the energy of the threshold level is quite different in the two alternatives. By comparing the two theories in their interpretation of the low-energy neutron cross sections of 1H, 16O, and 208Pb it is concluded that.R-matrix theory provides a better interpretation for unbound levels and S-matrix theory is preferable when the threshold level is bound.

The analysis of high-energy neutron cross-sections

1956 ◽  
Vol 236 (1204) ◽  
pp. 52-67 ◽  
Keyword(s):  
Spatial Distribution ◽  
Harmonic Oscillator ◽  
Density Distribution ◽  
Cross Sections ◽  
High Energy ◽  
Total Cross Sections ◽  
Upper Limit ◽  
Energy Neutron ◽  
Square Well ◽  
Neutron Cross Sections

The neutron inelastic cross-sections reported in the previous paper are interpreted in terms of the square-well and harmonic oscillator optical models, and also the tapered density-distribution. Neutron and proton inelastic cross-sections are compared, and are shown to suggest that the neutrons in a nucleus have a larger spatial distribution than the protons. Finally, neutron total cross-sections are used to put an upper limit to the permissible surface thickness of a nucleus.

Determination of Intermediate Energy Neutron Cross Sections Using the Ramsauer Model

2006 ◽  
Vol 152 (3) ◽  
pp. 320-324
Author(s):  
M. Azam ◽  
R. S. Gowda ◽  
S. Ganesan
Keyword(s):  
Cross Sections ◽  
Intermediate Energy ◽  
Energy Neutron ◽  
Neutron Cross Sections

R-matrix analysis of Cl neutron cross sections up to 1.2 MeV

2006 ◽  
Vol 73 (4) ◽  
Author(s):  
R. O. Sayer ◽  
K. H. Guber ◽  
L. C. Leal ◽  
N. M. Larson ◽  
T. Rauscher
Keyword(s):  
Cross Sections ◽  
Matrix Analysis ◽  
R Matrix ◽  
Neutron Cross Sections

R-matrix analysis of the239Pu neutron cross sections

1986 ◽  
Vol 96 (1-4) ◽  
pp. 293-296 ◽  
Author(s):  
G. de Saussure ◽  
R. B. Perez ◽  
R. L. (Roger) Macklin
Keyword(s):  
Cross Sections ◽  
Matrix Analysis ◽  
R Matrix ◽  
Neutron Cross Sections

Comparison of reaction theories for multilevel interference—the 14C + p reactions

1969 ◽  
Vol 47 (24) ◽  
pp. 2763-2777 ◽  
Author(s):  
C. T. Tindle ◽  
E. Vogt
Keyword(s):  
Compound Nucleus ◽  
Cross Sections ◽  
Curve Fitting ◽  
Low Energy ◽  
Analytic Method ◽  
R Matrix ◽  
Strong Interference ◽  
S Matrix ◽  
Fitting Procedures ◽  
Good Agreement

A comparison is made between the R-matrix and S-matrix theories of low-energy compound nucleus resonances for the particular case of two-level interference. The (p,γ) and (p,n) cross sections of 14C for proton energies between 0.7 and 1.5 MeV are analyzed using both theories. The 15N compound nucleus in this region exhibits strong two-level interference. The two theories provide equally good fits to the data, but the parameters describing the compound-nucleus levels are quite different. A general analytic method of relating the two sets of parameters is derived and shown to give good agreement with the results obtained by curve-fitting procedures. Remarks are made concerning the general behavior of the parameters under strong interference conditions and also on the inclusion of many channels into the analysis.

Low-Energy Neutron Cross Sections of Fissionable Nuclei

1960 ◽  
Vol 118 (3) ◽  
pp. 724-733 ◽  
Author(s):  
Erich Vogt
Keyword(s):  
Cross Sections ◽  
Low Energy ◽  
Energy Neutron ◽  
Neutron Cross Sections

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.

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