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# Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the ^{7}Be system

## Abstract

R-matrix theory is used to present nuclear reactions in the resolved resonance region. It uses information on bound states and low energy resonances to accurately parametrize cross sections on the resonances as well as the non-resonant background. Since the seminal work of Lane and Thomas (1958), the method has been widely used to analyze experimental cross-section data in a broad range of fields spanning nuclear reaction dynamics, nuclear astrophysics, ion beam analysis and their applications. Different R-matrix codes have been developed and used in these different applications with very little communication among the developers or practitioners on the capabilities, achievements or limitations of the codes. A limited comparison among three R-matrix codes on neutron-induced reactions was performed by the International Atomic Energy Agency (IAEA) International Evaluation of Neutron Cross Section Standards project (2007). Since then, significant progress has been made in their implementation of the R-matrix algorithms, and R-matrix codes have enhanced capabilities. In this paper we introduce, for the first time, the results of a comprehensive effort to verify the most widely used R-matrix codes in the various fields of nuclear science and applications: AMUR, AZURE2, CONRAD, EDA, FRESCO, GECCCOS, and SAMMY. In addition to the description of themore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Notre Dame, IN (United States)
- Intl Atomic Energy Agency (IAEA), Vienna (Austria)
- Japan Atomic Energy Agency (JAEA), Tokai (Japan)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Technische Univ. Wien, Vienna (Austria)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Alternative Energies and Atomic Energy Commission (CEA), Cadarache (France)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

- OSTI Identifier:
- 1526854

- Alternate Identifier(s):
- OSTI ID: 1528694

- Report Number(s):
- LLNL-JRNL-765198

Journal ID: ISSN 1434-6001; 955052

- Grant/Contract Number:
- AC52-07NA27344; Phys-0822648; Phys-0758100; AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- European Physical Journal. A

- Additional Journal Information:
- Journal Volume: 55; Journal Issue: 6; Journal ID: ISSN 1434-6001

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Thompson, Ian J., deBoer, R. J., Dimitriou, Paraskevi, Kunieda, Satoshi, Pigni, Marco T., Arbanas, Goran, Leeb, H., Srdinko, Thomas, Hale, G., Tamagno, Pierre, and Archier, Pascal. Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system. United States: N. p., 2019.
Web. doi:10.1140/epja/i2019-12753-y.
```

```
Thompson, Ian J., deBoer, R. J., Dimitriou, Paraskevi, Kunieda, Satoshi, Pigni, Marco T., Arbanas, Goran, Leeb, H., Srdinko, Thomas, Hale, G., Tamagno, Pierre, & Archier, Pascal. Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system. United States. doi:10.1140/epja/i2019-12753-y.
```

```
Thompson, Ian J., deBoer, R. J., Dimitriou, Paraskevi, Kunieda, Satoshi, Pigni, Marco T., Arbanas, Goran, Leeb, H., Srdinko, Thomas, Hale, G., Tamagno, Pierre, and Archier, Pascal. Mon .
"Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system". United States. doi:10.1140/epja/i2019-12753-y.
```

```
@article{osti_1526854,
```

title = {Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system},

author = {Thompson, Ian J. and deBoer, R. J. and Dimitriou, Paraskevi and Kunieda, Satoshi and Pigni, Marco T. and Arbanas, Goran and Leeb, H. and Srdinko, Thomas and Hale, G. and Tamagno, Pierre and Archier, Pascal},

abstractNote = {R-matrix theory is used to present nuclear reactions in the resolved resonance region. It uses information on bound states and low energy resonances to accurately parametrize cross sections on the resonances as well as the non-resonant background. Since the seminal work of Lane and Thomas (1958), the method has been widely used to analyze experimental cross-section data in a broad range of fields spanning nuclear reaction dynamics, nuclear astrophysics, ion beam analysis and their applications. Different R-matrix codes have been developed and used in these different applications with very little communication among the developers or practitioners on the capabilities, achievements or limitations of the codes. A limited comparison among three R-matrix codes on neutron-induced reactions was performed by the International Atomic Energy Agency (IAEA) International Evaluation of Neutron Cross Section Standards project (2007). Since then, significant progress has been made in their implementation of the R-matrix algorithms, and R-matrix codes have enhanced capabilities. In this paper we introduce, for the first time, the results of a comprehensive effort to verify the most widely used R-matrix codes in the various fields of nuclear science and applications: AMUR, AZURE2, CONRAD, EDA, FRESCO, GECCCOS, and SAMMY. In addition to the description of the capabilities of the codes and their specifications, we discuss the results of a joint exercise which was coordinated by the International Atomic Energy Agency. The aim of the exercise was to compare calculations of charged-particle reaction cross sections for the light composite system 7Be. The calculations were performed by the codes using identical input R-matrix parameters and other specifications and were limited to charged-particle channels.},

doi = {10.1140/epja/i2019-12753-y},

journal = {European Physical Journal. A},

number = 6,

volume = 55,

place = {United States},

year = {2019},

month = {6}

}

Works referenced in this record:

##
Databases and tools for nuclear astrophysics applications: BRUSsels Nuclear LIBrary (BRUSLIB), Nuclear Astrophysics Compilation of REactions II (NACRE II) and Nuclear NETwork GENerator (NETGEN)

journal, January 2013

- Xu, Y.; Goriely, S.; Jorissen, A.
- Astronomy & Astrophysics, Vol. 549

##
R-Matrix Theory of Nuclear Reactions

journal, April 1958

- Lane, A. M.; Thomas, R. G.
- Reviews of Modern Physics, Vol. 30, Issue 2

##
Towards a More Complete and Accurate Experimental Nuclear Reaction Data Library (EXFOR): International Collaboration Between Nuclear Reaction Data Centres (NRDC)

journal, June 2014

- Otuka, N.; Dupont, E.; Semkova, V.
- Nuclear Data Sheets, Vol. 120

##
Multilevel Formula for the Fission Process

journal, August 1958

- Reich, C. W.; Moore, M. S.
- Physical Review, Vol. 111, Issue 3

##
Scattering of ${\mathrm{He}}^{3}$ by ${\mathrm{He}}^{4}$ and of ${\mathrm{He}}^{4}$ by Tritium

journal, November 1967

- Spiger, R. J.; Tombrello, T. A.
- Physical Review, Vol. 163, Issue 4

##
Coupled reaction channels calculations in nuclear physics

journal, April 1988

- Thompson, Ian J.
- Computer Physics Reports, Vol. 7, Issue 4

##
Generalized Nuclear Data: A New Structure (with Supporting Infrastructure) for Handling Nuclear Data

journal, December 2012

- Mattoon, C. M.; Beck, B. R.; Patel, N. R.
- Nuclear Data Sheets, Vol. 113, Issue 12

##
The *R* -matrix theory

journal, February 2010

- Descouvemont, P.; Baye, D.
- Reports on Progress in Physics, Vol. 73, Issue 3

##
Retroactive Generation of Covariance Matrix of Nuclear Model Parameters Using Marginalization Techniques

journal, November 2010

- Habert, B.; Jean, C. De Saint; Noguere, G.
- Nuclear Science and Engineering, Vol. 166, Issue 3

##
Elastic Scattering of Protons from ${\mathrm{Li}}^{6}$ Nuclei

journal, June 1963

- McCray, J. A.
- Physical Review, Vol. 130, Issue 5

##
CONRAD Evaluation Code: Development Status and Perspectives

journal, April 2014

- Archier, P.; De Saint Jean, C.; Litaize, O.
- Nuclear Data Sheets, Vol. 118

##
The Boundary Condition Parameter in R-Matrix Theory

journal, January 1972

- Barker, Fo
- Australian Journal of Physics, Vol. 25, Issue 4

##
Update of the α−n Yields for Reactor Fuel Materials for the Interest of Nuclear Safeguards

journal, January 2017

- Simakov, S. P.; van den Berg, Q. Y.
- Nuclear Data Sheets, Vol. 139

##
The jina Reaclib Database: its Recent Updates and Impact on Type-I X-Ray Bursts

journal, June 2010

- Cyburt, Richard H.; Amthor, A. Matthew; Ferguson, Ryan
- The Astrophysical Journal Supplement Series, Vol. 189, Issue 1

##
SigmaCalc recent development and present status of the evaluated cross-sections for IBA

journal, March 2016

- Gurbich, A. F.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 371

##
A compilation of charged-particle induced thermonuclear reaction rates

journal, August 1999

- Angulo, C.; Arnould, M.; Rayet, M.
- Nuclear Physics A, Vol. 656, Issue 1

##
Generalized Reich-Moore *R* -matrix approximation

journal, January 2017

- Arbanas, Goran; Sobes, Vladimir; Holcomb, Andrew
- EPJ Web of Conferences, Vol. 146

##
Status of the R-matrix Code AMUR toward a consistent cross-section evaluation and covariance analysis for the light nuclei

journal, January 2017

- Kunieda, Satoshi
- EPJ Web of Conferences, Vol. 146

##
Cross sections for the ${}_{}{}^{6}{}_{}{}^{}\mathrm{Li}$ ( $p$ , ${}_{}{}^{3}{}_{}{}^{}\mathrm{He}$ ) ${}_{}{}^{4}{}_{}{}^{}\mathrm{He}$ reaction at energies between 0.1 and 3.0 MeV

journal, December 1979

- Elwyn, A. J.; Holland, R. E.; Davids, C. N.
- Physical Review C, Vol. 20, Issue 6

##
Precise Coulomb wave functions for a wide range of complex ℓ, η and z

journal, February 2007

- Michel, N.
- Computer Physics Communications, Vol. 176, Issue 3

##
Alternative parametrization of *R* -matrix theory

journal, October 2002

- Brune, C. R.
- Physical Review C, Vol. 66, Issue 4

##
The ${}^{12}\mathbf{C}(\alpha ,\gamma ){}^{16}\mathbf{O}$ reaction and its implications for stellar helium burning

journal, September 2017

- deBoer, R. J.; Görres, J.; Wiescher, M.
- Reviews of Modern Physics, Vol. 89, Issue 3

##
The scattering of He3 by He4

journal, January 1964

- Barnard, A. C. L.; Jones, C. M.; Phillips, G. C.
- Nuclear Physics, Vol. 50

##
Polarization of Fast Nucleons

journal, December 1956

- Wolfenstein, L.
- Annual Review of Nuclear Science, Vol. 6, Issue 1

##
Simultaneous Evaluation of Fission Cross Sections of Uranium and Plutonium Isotopes for JENDL-3.3

journal, April 2000

- Kawano, Toshihiko; Matsunobu, Hiroyuki; Murata, Torn
- Journal of Nuclear Science and Technology, Vol. 37, Issue 4

##
Scattering of ${\mathrm{He}}^{3}$ from ${\mathrm{He}}^{4}$

journal, May 1963

- Tombrello, T. A.; Parker, P. D.
- Physical Review, Vol. 130, Issue 3

##
On the use of the covariance matrix to fit correlated data

journal, July 1994

- D'Agostini, G.
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 346, Issue 1-2

##
Higher Angular Momenta and Long Range Interaction in Resonance Reactions

journal, July 1947

- Wigner, E. P.; Eisenbud, L.
- Physical Review, Vol. 72, Issue 1

##
AZURE: An $R$ -matrix code for nuclear astrophysics

journal, April 2010

- Azuma, R. E.; Uberseder, E.; Simpson, E. C.
- Physical Review C, Vol. 81, Issue 4

##
COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments

journal, June 1985

- Thompson, I. J.; Barnett, A. R.
- Computer Physics Communications, Vol. 36, Issue 4

##
Nuclear data for ion beam analysis applications

journal, January 2017

- Dimitriou, Paraskevi; Semkova, Valentina; Zerkin, Viktor
- EPJ Web of Conferences, Vol. 146