scholarly journals The Boundary Condition Parameter in R-Matrix Theory

1972 ◽  
Vol 25 (4) ◽  
pp. 341 ◽  
Author(s):  
FO Barker
Keyword(s):  
Boundary Condition ◽  
Finite Number ◽  
Cross Sections ◽  
Nuclear Reactions ◽  
Matrix Theory ◽  
R Matrix ◽  
The Cross

In the general R-matrix theory of nuclear reactions, all measurable quantities such as the cross sections scc' should be independent of the choice of the boundary condition parameters Bc although the values of the level parameters E? and ??c depend on the Bc. For applications involving only a finite number of levels ?, it is not obvious that this is still the case as completeness arguments can no longer be used. It is shown here that scc' can be made independent of the choice Bc of for any finite number of levels and any number of channels, and the resulting formulae giving the dependence of E? and ??c on Bc are derived. An application is made to the pair of 5/2- levels of 7Li near 7 MeV excitation.

scholarly journals Interference Between Levels in Nuclear Reactions

1967 ◽  
Vol 20 (3) ◽  
pp. 341 ◽  
Author(s):  
FC Barker
Keyword(s):  
Nuclear Reaction ◽  
Cross Section ◽  
Nuclear Reactions ◽  
Matrix Theory ◽  
R Matrix ◽  
Single Level ◽  
The Cross

In this note we consider the cross section for a nuclear reaction in which one of the product nuclei is unstable, with two or more levels contributing to its decay. Previously a formula had been derived from R-matrix theory for the case where contributions come from only a single level of the nucleus with a given spin and parity.

scholarly journals 2- States of 8Be

1977 ◽  
Vol 30 (2) ◽  
pp. 113 ◽  
Author(s):  
FC Barker
Keyword(s):  
Shell Model ◽  
Cross Sections ◽  
Matrix Theory ◽  
Matrix Approximation ◽  
Model Calculations ◽  
R Matrix ◽  
Rapid Changes ◽  
The Cross ◽  
Proper Account

The cross sections for several reactions populating sBe in the region of the 7Be+n threshold show rapid changes, which have been attributed to a 2- threshold state. An analysis of these data using R matrix theory shows that there is considerable isospin mixing in the threshold state, implying another 2 - state nearby. A two-level R matrix approximation provides a good fit to all the relevant data, with parameters consistent with shell model calculations and with properties of sLi. Proper account must be taken of the neutron threshold in order to explain the isospin mixing. The threshold state is expected to show different widths in different reactions.

scholarly journals Isospin Mixing in 4¯ States of 12C

1983 ◽  
Vol 36 (5) ◽  
pp. 649 ◽  
Author(s):  
FC Barker
Keyword(s):  
Shell Model ◽  
Cross Sections ◽  
Nuclear Reactions ◽  
Matrix Theory ◽  
Bound State ◽  
Model Calculations ◽  
R Matrix ◽  
Parameter Values

Fits are made to measured 12C(n�,no:)12C cross sections in terms of an isospin-mixed doublet of 4- 12C levels near 19�5 MeV, using the R-matrix theory of nuclear reactions. Parameter values are restricted by information from other reactions and from bound-state shell model calculations.

The cross sections for different channels in heavy ion nuclear reactions

1971 ◽  
Vol 32 (1) ◽  
pp. 7-9 ◽  
Author(s):  
J. Galin ◽  
D. Guerreau ◽  
M. Lefort ◽  
X. Tarrago
Keyword(s):  
Cross Sections ◽  
Nuclear Reactions ◽  
Heavy Ion ◽  
The Cross

scholarly journals Anthony Milner Lane. 27 July 1928—9 February 2011

2020 ◽  
Vol 68 ◽  
pp. 297-314
Author(s):  
Charles Clement
Keyword(s):  
Nuclear Physics ◽  
Collective Motion ◽  
Nuclear Reactions ◽  
Matrix Theory ◽  
Nuclear Data ◽  
Theoretical Physics ◽  
R Matrix ◽  
Good Account ◽  
Advanced Knowledge

Tony Lane came from humble beginnings to become one of the world's leading theoretical nuclear physicists. His career in the Theoretical Physics Division at the Atomic Energy Research Establishment (AERE) at Harwell was characterized by his outstanding successes in explaining experimental nuclear data. He pioneered the understanding of the important nucleon capture reactions by introducing new mechanisms of direct and semi-direct capture and, together with colleagues, he greatly advanced knowledge of nuclear analogue states, and the role of isospin in nuclear physics. With R. G. Thomas, he wrote a comprehensive review of R-matrix theory, applied to analyse resonances in nuclear reactions, which became one of the most cited papers in physics. His book Nuclear theory gave a good account of the use of pairing force theory in nuclear physics, and its application to nuclear collective motion.

A new empirical formula for cross-sections of (n,nα) reactions

2020 ◽  
Vol 29 (08) ◽  
pp. 2050062
Author(s):  
Mustafa Yiğit
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Empirical Formula ◽  
Nuclear Reactions ◽  
Measured Cross Section ◽  
Future Studies ◽  
Present Formalism ◽  
The Cross ◽  
Neutron Cross Sections ◽  
Good Agreement

Studies on the cross-sections of (n,n[Formula: see text]) reactions which are energetically possible, about 14 MeV neutrons are quite scarce. In this paper, the cross-sections of (n,n[Formula: see text] nuclear reactions at [Formula: see text]14–15 MeV are analyzed by using a new empirical formula based on the statistical theory. We show that neutron cross-sections are closely related to the [Formula: see text]-value of nuclear reaction, in particular for (n,n[Formula: see text]) channels. Results obtained with this empirical formula show good agreement with the available measured cross-section values. We hope that the estimations on the cross-sections using the present formalism may be helpful in future studies in this field.

R-Matrix Theory of Nuclear Reactions

1958 ◽  
Vol 30 (2) ◽  
pp. 257-353 ◽  
Author(s):  
A. M. Lane ◽  
R. G. Thomas
Keyword(s):  
Nuclear Reactions ◽  
Matrix Theory ◽  
R Matrix

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.

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.

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