The R-matrix theory

Abstract

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schrödinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.

93 pages, 26 figures. Rep. Prog. Phys., in press

References in corpus (9)

• Recent developments in no-core shell-model calculations
• Ab Initio Many-Body Calculations of n-3H, n-4He, p-{3,4}He, and n-10Be Scattering
• Quantum Monte Carlo calculations of neutron-alpha scattering
• Four-body continuum-discretized coupled-channels calculations using a transformed harmonic oscillator basis
• Structure of low-lying 12C-resonances
• Local versus nonlocal $\alpha \alpha$ interactions in $3\alpha$ description of ${}^{12}$C
• A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case
• Spectroscopy of 9C via resonance scattering of protons on 8B
• Two- and three-alpha systems with nonlocal potential

Cited by in corpus (155)

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• The Future of Solar Neutrinos
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• Bound state techniques to solve the multiparticle scattering problem
• An R-matrix package for coupled-channel problems in nuclear physics
• Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework
• Two-proton emission and related phenomena
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• Ab initio study of the photoabsorption of ${}^4$He
• Alpha clustering and alpha-capture reaction rate from ab initio symmetry-adapted description of ${}^{20}$Ne
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• Structure of the exotic ${}^9$He nucleus from the no-core shell model with continuum
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• Coulomb breakup of 22C in a four-body model
• Elastic scattering of 17F, 17O and 19F on a heavy target in microscopic continuum discretized coupled-channels method
• Nucleon-nucleon scattering with the Complex Scaling Method and realistic interactions
• From nucleons to nuclei to fusion reactions
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• The study of the alpha formation probability in 10Be and 12Be within the microscopic cluster model
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• Radiative Capture of proton 14N(p,γ) 15O at Low Energy
• R-Matrix Calculations for Few-Quark Bound States
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• Towards a comprehensive study of the 14N(p,g)15O astrophysical key reaction: Description of the experimental technique including novel target preparation
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• Interference Effect Between Neutron Direct and Resonance Capture Reactions For Neutron-Rich Nuclei
• Monotonic properties of the shift and penetration factors
• Towards an ab initio description of the light-nuclei radiative captures
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• The Cosmological Lithium Problem Revisited
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