Potential model for nuclear astrophysical fusion reactions with a square-well potential

Ogura, R.; Hagino, K.; Bertulani, C. A.

doi:10.1103/PhysRevC.99.065808

Title: Potential model for nuclear astrophysical fusion reactions with a square-well potential

Journal Article · 25 June 2019 · Physical Review C

DOI: https://doi.org/10.1103/PhysRevC.99.065808 · OSTI ID:1529104

Ogura, R. ^[1]; Hagino, K. ^[2]; Bertulani, C. A. ^[3]

Tohoku Univ., Sendai (Japan); Texas A&M University-Commerce
Tohoku Univ., Sendai (Japan)
Texas A & M Univ.-Commerce, Commerce, TX (United States)

The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. Here, we discuss the origin of this apparently different behavior from that obtained with a smooth Woods-Saxon potential, for which a deep potential is often employed. We argue that due to the sharp change of the potential at the boundary the radius parameter tends to be large in the square-well model, which results in a large absorption radius. The wave function then needs to be suppressed in the absorption region, which can eventually be achieved by using a shallow potential. We thus clarify the reason why the square-well potential has been able to reproduce a large amount of fusion data.

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Research Organization:: Texas A & M Univ.-Commerce, Commerce, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-08ER41533

OSTI ID:: 1529104

Journal Information:: Physical Review C, Journal Name: Physical Review C Journal Issue: 6 Vol. 99; ISSN PRVCAN; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (21)

Nuclear heavy-ion reactions Hodgson, P. E. La Rivista Del Nuovo Cimento Series 3, Vol. 1, Issue 1 https://doi.org/10.1007/BF02724442	journal	January 1978
Nuclear heavy-ion reactions Beynon, T. D. Annals of Nuclear Energy, Vol. 6, Issue 11-12 https://doi.org/10.1016/0306-4549(79)90013-6	journal	January 1979
Gamma-ray yields from 12C + 13C reactions near and below the coulomb barrier Dayras, R. A.; Stokstad, R. G.; Switkowski, Z. E. Nuclear Physics A, Vol. 265, Issue 1 https://doi.org/10.1016/0375-9474(76)90121-4	journal	July 1976
Microscopic investigation of the 12C + 12C interaction Baye, D.; Pecher, N. Nuclear Physics A, Vol. 379, Issue 2 https://doi.org/10.1016/0375-9474(82)90396-7	journal	May 1982
A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions Hagino, K.; Rowley, N.; Kruppa, A. T. Computer Physics Communications, Vol. 123, Issue 1-3 https://doi.org/10.1016/S0010-4655(99)00243-X	journal	December 1999
Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-Energy Reactions Thompson, Ian J.; Nunes, Filomena M. https://doi.org/10.1017/CBO9781139152150	book	January 2009
Upper Limit on the molecular resonance strengths in the ¹² C+ ¹² C fusion reaction Tang, X.; Fang, X.; Bucher, B. EPJ Web of Conferences, Vol. 17 https://doi.org/10.1051/epjconf/20111716016	journal	January 2011
Fusion cross section of ¹² C+ ¹³ C at sub-barrier energies Zhang, N. T.; Tang, X. D.; Chen, H. EPJ Web of Conferences, Vol. 109 https://doi.org/10.1051/epjconf/201610909003	journal	January 2016
The real potential continuous ambiguity for 90 MeV Li ions Cook, J.; Barnwell, J. M.; Clarke, N. M. Journal of Physics G: Nuclear Physics, Vol. 6, Issue 10 https://doi.org/10.1088/0305-4616/6/10/011	journal	October 1980
Upper Limit on the molecular resonance strengths in the ¹² C+ ¹² C fusion reaction Tang, X. D.; Fang, X.; Bucher, B. Journal of Physics: Conference Series, Vol. 337 https://doi.org/10.1088/1742-6596/337/1/012016	journal	February 2012
Nuclear Optical Model and Wave Properties: Barrier Penetration, Reflection, Absorption, and Resonance Michaud, Georges; Scherk, Leonard; Vogt, Erich Physical Review C, Vol. 1, Issue 3 https://doi.org/10.1103/PhysRevC.1.864	journal	March 1970
Thermonuclear-Reaction Rates at High Temperature Michaud, Georges; Fowler, William A. Physical Review C, Vol. 2, Issue 6 https://doi.org/10.1103/PhysRevC.2.2041	journal	December 1970
Sub-barrier fusion of the oxygen isotopes: A more complete picture Thomas, J.; Chen, Y. T.; Hinds, S. Physical Review C, Vol. 33, Issue 5 https://doi.org/10.1103/PhysRevC.33.1679	journal	May 1986
Examination of fusion cross sections and fusion oscillations with a generalized Wong formula Rowley, N.; Hagino, K. Physical Review C, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevC.91.044617	journal	April 2015
Recent developments in heavy-ion fusion reactions Back, B. B.; Esbensen, H.; Jiang, C. L. Reviews of Modern Physics, Vol. 86, Issue 1 https://doi.org/10.1103/RevModPhys.86.317	journal	March 2014
Subbarrier Fusion Reactions and Many-Particle Quantum Tunneling Hagino, K.; Takigawa, N. Progress of Theoretical Physics, Vol. 128, Issue 6 https://doi.org/10.1143/PTP.128.1061	journal	December 2012
Repulsive Core of Effective - Potential Tamagaki, R.; Tanaka, H. Progress of Theoretical Physics, Vol. 34, Issue 1 https://doi.org/10.1143/PTP.34.191	journal	July 1965
Thermonuclear Reaction Rates, II Fowler, William A.; Caughlan, Georgeanne R.; Zimmerman, Barbara A. Annual Review of Astronomy and Astrophysics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev.aa.13.090175.000441	journal	September 1975
Upper Limit on the molecular resonance strengths in the ${}^{12}$C+${}^{12}$C fusion reaction Tang, X.; Fang, X.; Bucher, B. arXiv https://doi.org/10.48550/arxiv.1109.6078	text	January 2011
Subbarrier fusion reactions and many-particle quantum tunneling Hagino, K.; Takigawa, N. arXiv https://doi.org/10.48550/arxiv.1209.6435	text	January 2012
A program for coupled-channels calculations with all order couplings for heavy-ion fusion reactions Hagino, K.; Rowley, N.; Kruppa, A. T. arXiv https://doi.org/10.48550/arxiv.nucl-th/9903074	text	January 1999