Investigation of the triple-α reaction in a full three-body approach

Nguyen, N. B.; Nunes, F. M.; Thompson, I. J.

doi:10.1103/PhysRevC.87.054615

Title: Investigation of the triple-α reaction in a full three-body approach

Journal Article · Wed May 22 00:00:00 EDT 2013 · Physical Review C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.87.054615· OSTI ID:1332506

Nguyen, N. B. ^[1]; Nunes, F. M. ^[1]; Thompson, I. J. ^[2]

Michigan State Univ., East Lansing, MI (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, the triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of ¹²C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible. Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the non-resonant reaction mechanisms on the same footing, to compute the triple-alpha reaction rate at low temperatures. Methods: We combine the R-matrix expansion, the R-matrix propagation method, and the screening technique in the hyperspherical harmonics basis. Both the 2⁺₁ bound state and the 0⁺₂resonant state in ¹²C are well reproduced. We also study the cluster structure of these states. We calculate the triple-alpha reaction rate for T = 0.01 - 0.1 GK. In conclusion, we obtain the same rate as NACRE for temperatures above 0.07 GK, but the new rate is largely enhanced at lower temperatures (≈ 10¹² at 0.02 GK). The differences are caused by the direct capture contribution to the reaction when three alpha particles can not reach the resonant energies.

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Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: FG52-08NA28552; AC52-07NA27344; PHY-0800026; SC0004087

OSTI ID:: 1332506

Alternate ID(s):: OSTI ID: 1102731

Journal Information:: Physical Review C, Nuclear Physics, Vol. 87, Issue 5; ISSN 0556-2813

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 36 works

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References (51)

Nuclear Reactions in Stars Without Hydrogen. Salpeter, E. E. The Astrophysical Journal, Vol. 115 https://doi.org/10.1086/145546	journal	March 1952
On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel. Hoyle, F. The Astrophysical Journal Supplement Series, Vol. 1 https://doi.org/10.1086/190005	journal	September 1954
The 7.68-Mev State in C 12 Dunbar, D. N. F.; Pixley, R. E.; Wenzel, W. A. Physical Review, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRev.92.649	journal	November 1953
$B^{12}$ , $C^{12}$ , and the Red Giants Cook, C. W.; Fowler, W. A.; Lauritsen, C. C. Physical Review, Vol. 107, Issue 2 https://doi.org/10.1103/PhysRev.107.508	journal	July 1957
Thermonuclear reaction rates V Caughlan, Georgeanne R.; Fowler, William A. Atomic Data and Nuclear Data Tables, Vol. 40, Issue 2 https://doi.org/10.1016/0092-640X(88)90009-5	journal	November 1988
A compilation of charged-particle induced thermonuclear reaction rates Angulo, C.; Arnould, M.; Rayet, M. Nuclear Physics A, Vol. 656, Issue 1 https://doi.org/10.1016/S0375-9474(99)00030-5	journal	August 1999
Quantum Three-Body Calculation of the Nonresonant Triple- Reaction Rate at Low Temperatures Ogata, K.; Kan, M.; Kamimura, M. Progress of Theoretical Physics, Vol. 122, Issue 4 https://doi.org/10.1143/PTP.122.1055	journal	October 2009
Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions Austern, N.; Iseri, Y.; Kamimura, M. Physics Reports, Vol. 154, Issue 3 https://doi.org/10.1016/0370-1573(87)90094-9	journal	October 1987
Coupled-Discretized-Continuum-Channels Method for Deuteron Breakup Reactions Based on Three-Body Model: Justification of the Method for Truncation and Discretization of the p-n Continuum Yahiro, M.; Nakano, M.; Iseri, Y. Progress of Theoretical Physics, Vol. 67, Issue 5 https://doi.org/10.1143/PTP.67.1467	journal	May 1982
Evolutionary implications of the new triple- α nuclear reaction rate for low mass stars Dotter, A.; Paxton, B. Astronomy & Astrophysics, Vol. 507, Issue 3 https://doi.org/10.1051/0004-6361/200912998	journal	September 2009
Stellar Evolution Constraints on the Triple-α Reaction rate Suda, Takuma; Hirschi, Raphael; Fujimoto, Masayuki Y. The Astrophysical Journal, Vol. 741, Issue 1 https://doi.org/10.1088/0004-637X/741/1/61	journal	October 2011
Effects of a New Triple- Reaction Rate on the Helium Ignition of Accreting White Dwarfs Saruwatari, M.; Hashimoto, M. -a. Progress of Theoretical Physics, Vol. 124, Issue 5 https://doi.org/10.1143/PTP.124.925	journal	November 2010
Effects of a New Triple- Reaction on X-Ray Bursts of a Helium-Accreting Neutron Star Matsuo, Y.; Tsujimoto, H.; Noda, T. Progress of Theoretical Physics, Vol. 126, Issue 6 https://doi.org/10.1143/PTP.126.1177	journal	December 2011
Helium Ignition on Accreting Neutron Stars with a new Triple-α Reaction rate Peng, Fang; Ott, Christian D. The Astrophysical Journal, Vol. 725, Issue 1 https://doi.org/10.1088/0004-637X/725/1/309	journal	November 2010
Algebraic model for scattering in three- $s$ -cluster systems. I. Theoretical background Vasilevsky, V.; Nesterov, A. V.; Arickx, F. Physical Review C, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevC.63.034606	journal	February 2001
Relative production rates of ⁶ He, ⁹ Be, ¹² C in astrophysical environments de Diego, R.; Garrido, E.; Fedorov, D. V. EPL (Europhysics Letters), Vol. 90, Issue 5 https://doi.org/10.1209/0295-5075/90/52001	journal	June 2010
Structure of low-lying 12C resonances Álvarez-Rodrıguez, R.; Garrido, E.; Jensen, A. S. The European Physical Journal A, Vol. 31, Issue 3 https://doi.org/10.1140/epja/i2006-10298-x	journal	March 2007
Direct and sequential radiative three-body reaction rates at low temperatures Garrido, E.; de Diego, R.; Fedorov, D. V. The European Physical Journal A, Vol. 47, Issue 8 https://doi.org/10.1140/epja/i2011-11102-8	journal	August 2011
Ab initio no-core full configuration calculations of light nuclei Maris, P.; Vary, J. P.; Shirokov, A. M. Physical Review C, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevC.79.014308	journal	January 2009
Quantum Monte Carlo Calculations of Light Nuclei Pieper, Steven C. Nuclear Physics A, Vol. 751 https://doi.org/10.1016/j.nuclphysa.2005.02.018	journal	April 2005
Structure of the Hoyle State in ${}^{12}C$ Chernykh, M.; Feldmeier, H.; Neff, T. Physical Review Letters, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevLett.98.032501	journal	January 2007
FaCE: a tool for three body Faddeev calculations with core excitation Thompson, I. J.; Nunes, F. M.; Danilin, B. V. Computer Physics Communications, Vol. 161, Issue 1-2 https://doi.org/10.1016/j.cpc.2004.03.007	journal	August 2004
$N$ - $d$ scattering above the deuteron breakup threshold Kievsky, A.; Viviani, M.; Rosati, S. Physical Review C, Vol. 56, Issue 6 https://doi.org/10.1103/PhysRevC.56.2987	journal	December 1997
Momentum-space treatment of the Coulomb interaction in three-nucleon reactions with two protons Deltuva, A.; Fonseca, A. C.; Sauer, P. U. Physical Review C, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevC.71.054005	journal	May 2005
Low-Temperature Triple-Alpha Rate in a Full Three-Body Nuclear Model Nguyen, N. B.; Nunes, F. M.; Thompson, I. J. Physical Review Letters, Vol. 109, Issue 14 https://doi.org/10.1103/PhysRevLett.109.141101	journal	October 2012
The Helium Wave Equation Gronwall, T. H. Physical Review, Vol. 51, Issue 8 https://doi.org/10.1103/PhysRev.51.655	journal	April 1937
Hyperspherical coordinate approach to atomic and other Coulombic three-body systems Lin, C. D. Physics Reports, Vol. 257, Issue 1 https://doi.org/10.1016/0370-1573(94)00094-J	journal	June 1995
Tertiary and general-order collisions Delves, L. M. Nuclear Physics, Vol. 9, Issue 3 https://doi.org/10.1016/0029-5582(58)90372-9	journal	January 1958
Three-particle photo-disintegration of the triton Delves, L. M. Nuclear Physics, Vol. 29 https://doi.org/10.1016/0029-5582(62)90179-7	journal	January 1962
Bound state properties of Borromean halo nuclei: 6He and 11Li Zhukov, M. V.; Danilin, B. V.; Fedorov, D. V. Physics Reports, Vol. 231, Issue 4 https://doi.org/10.1016/0370-1573(93)90141-Y	journal	August 1993
Study of 14Be with core excitation Tarutina, T.; Thompson, I. J.; Tostevin, J. A. Nuclear Physics A, Vol. 733, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2003.12.003	journal	March 2004
Three-body systems with Lagrange-mesh techniques in hyperspherical coordinates Descouvemont, P.; Daniel, C.; Baye, D. Physical Review C, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevC.67.044309	journal	April 2003
Core excitation in three-body systems: Application to 12Be Nunes, F. M.; Christley, J. A.; Thompson, I. J. Nuclear Physics A, Vol. 609, Issue 1 https://doi.org/10.1016/0375-9474(96)00284-9	journal	November 1996
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
Transformation coefficients in the hyperspherical approach to the three-body problem Raynal, J.; Revai, J. Il Nuovo Cimento A Series 10, Vol. 68, Issue 4 https://doi.org/10.1007/BF02756127	journal	August 1970
Three-body scattering in configuration space Merkuriev, S. P.; Gignoux, C.; Laverne, A. Annals of Physics, Vol. 99, Issue 1 https://doi.org/10.1016/0003-4916(76)90083-X	journal	July 1976
Higher Angular Momenta and Long Range Interaction in Resonance Reactions Wigner, E. P.; Eisenbud, L. Physical Review, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRev.72.29	journal	July 1947
R-Matrix Theory of Nuclear Reactions Lane, A. M.; Thomas, R. G. Reviews of Modern Physics, Vol. 30, Issue 2 https://doi.org/10.1103/RevModPhys.30.257	journal	April 1958
Pauli blocking in three-body models of halo nuclei Thompson, I. J.; Danilin, B. V.; Efros, V. D. Physical Review C, Vol. 61, Issue 2 https://doi.org/10.1103/PhysRevC.61.024318	journal	January 2000
The R -matrix theory Descouvemont, P.; Baye, D. Reports on Progress in Physics, Vol. 73, Issue 3 https://doi.org/10.1088/0034-4885/73/3/036301	journal	February 2010
An R matrix approach to the solution of coupled equations for atom–molecule reactive scattering Light, John C.; Walker, Robert B. The Journal of Chemical Physics, Vol. 65, Issue 10 https://doi.org/10.1063/1.432836	journal	November 1976
R ‐matrix solution of coupled equations for inelastic scattering Stechel, Ellen B.; Walker, Robert B.; Light, John C. The Journal of Chemical Physics, Vol. 69, Issue 8 https://doi.org/10.1063/1.437056	journal	October 1978
Phenomenological α-α potentials Ali, S.; Bodmer, A. R. Nuclear Physics, Vol. 80, Issue 1 https://doi.org/10.1016/0029-5582(66)90829-7	journal	May 1966
The three-body continuum Coulomb problem and the 3α structure of 12C Fedorov, D. V.; Jensen, A. S. Physics Letters B, Vol. 389, Issue 4 https://doi.org/10.1016/S0370-2693(96)80001-3	journal	December 1996
Energy levels of light nuclei A = 11−12 Ajzenberg-Selove, F. Nuclear Physics A, Vol. 506, Issue 1 https://doi.org/10.1016/0375-9474(90)90271-M	journal	January 1990
Variational calculations on a simple triton model using a complete hyperspherical function basis Erens, G.; Visschers, J. L.; van Wageningen, R. Annals of Physics, Vol. 67, Issue 2 https://doi.org/10.1016/0003-4916(71)90150-3	journal	October 1971
Alpha-chain states in ${}^{12}C$ Anagnostatos, G. S. Physical Review C, Vol. 51, Issue 1 https://doi.org/10.1103/PhysRevC.51.152	journal	January 1995
Cluster structures within Fermionic Molecular Dynamics Neff, T.; Feldmeier, H. Nuclear Physics A, Vol. 738 https://doi.org/10.1016/j.nuclphysa.2004.04.061	journal	June 2004
Ab Initio Calculation of the Hoyle State Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.192501	journal	May 2011
Microscopic cluster description of $^{12}$ C Vasilevsky, V.; Arickx, F.; Vanroose, W. Physical Review C, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevC.85.034318	journal	March 2012
Three-α continuum states Descouvemont, Pierre Journal of Physics G: Nuclear and Particle Physics, Vol. 37, Issue 6 https://doi.org/10.1088/0954-3899/37/6/064010	journal	March 2010

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