Reproducing heavy-ion fusion cross sections at extreme sub-barrier energies with a simple formula: Analysis of fusion hindrance with a Gaussian barrier distribution

Jiang, C. L.; Rehm, K. E.; Back, B. B.; Stefanini, A. M.; Montagnoli, G.

doi:10.1140/epja/i2018-12655-6

Title: Reproducing heavy-ion fusion cross sections at extreme sub-barrier energies with a simple formula: Analysis of fusion hindrance with a Gaussian barrier distribution

Journal Article · Mon Dec 17 00:00:00 EST 2018 · European Physical Journal. A

DOI:https://doi.org/10.1140/epja/i2018-12655-6· OSTI ID:1498066

Jiang, C. L. ^[1]; Rehm, K. E. ^[1]; Back, B. B. ^[1]; Stefanini, A. M. ^[2]; Montagnoli, G. ^[3]

Argonne National Lab. (ANL), Argonne, IL (United States)
Lab Nazionali di Legnaro, Legnaro (Italy)
Univ. di Padova, Padova (Italy)

Heavy-ion fusion hindrance occurs at extreme sub-barrier energies. This behavior is well reproduced with a simple cross section formula, which was developed by Siwek-Wilczynska et al., based on a single-Gaussian distribution of fusion barrier heights, before the discovery of the hindrance phenomenon. This expression has not yet been widely used and referenced in the literature. An analysis by using this simple formula is presented for 29 systems, from ¹⁶O + ¹⁸O to ⁶⁴Ni + ¹²⁴Sn , all being measured down to less than 10μb. The agreement with the data is even better than the ones from sophisticated Coupled-channels calculations. This simple expression also applies to fusion reactions in lighter systems. Here, the three parameters contained in this formula vary in a relatively smooth fashion over the whole mass range, and can be used to extrapolate cross sections or to obtain an estimate of the excitation function for systems which have not been measured. Extensions and restrictions of this method are also discussed.

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Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1498066

Journal Information:: European Physical Journal. A, Vol. 54, Issue 12; ISSN 1434-6001

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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References (60)

Sub-barrier fusion of ${}^{28, 30}{Si}$ with ${}^{24, 26}{Mg}$ Morsad, A.; Kolata, J. J.; Tighe, R. J. Physical Review C, Vol. 41, Issue 3 https://doi.org/10.1103/PhysRevC.41.988	journal	March 1990
Fusion reactions of ${}^{58, 64}{Ni} + {}^{124}{Sn}$ Jiang, C. L.; Stefanini, A. M.; Esbensen, H. Physical Review C, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevC.91.044602	journal	April 2015
Fusion of ${}^{16}O$ + ${}^{148, 150, 152, 154}{Sm}$ at sub-barrier energies Stokstad, R. G.; Eisen, Y.; Kaplanis, S. Physical Review C, Vol. 21, Issue 6 https://doi.org/10.1103/PhysRevC.21.2427	journal	June 1980
Expectations for ${}^{12}C$ and ${}^{16}O$ induced fusion cross sections at energies of astrophysical interest Jiang, C. L.; Rehm, K. E.; Back, B. B. Physical Review C, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevC.75.015803	journal	January 2007
Fusion of ${}^{28}{Si} + {}^{28, 30}{Si}$ : Different trends at sub-barrier energies Montagnoli, G.; Stefanini, A. M.; Esbensen, H. Physical Review C, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevC.90.044608	journal	October 2014
Fusion near the threshold: A comparative study of the systems 40Ar + 112, 116, 122sn and 40Ar + 144, 148, 154Sm Reisdorf, W.; Hessberger, F. P.; Hildenbrand, K. D. Nuclear Physics A, Vol. 438, Issue 1 https://doi.org/10.1016/0375-9474(85)90125-3	journal	May 1985
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
Neutron flow between nuclei as the principal enhancement mechanism in heavy-ion subbarrier fusion Stelson, P. H. Physics Letters B, Vol. 205, Issue 2-3 https://doi.org/10.1016/0370-2693(88)91647-4	journal	April 1988
Fusion hindrance for ${}^{58}{Ni} + {}^{54}{Fe}$ Stefanini, A. M.; Montagnoli, G.; Corradi, L. Physical Review C, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevC.82.014614	journal	July 2010
Fusion Hindrance for a Positive- $Q$ -Value System ${}^{24}{Mg} + {}^{30}{Si}$ Jiang, C. L.; Stefanini, A. M.; Esbensen, H. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.022701	journal	July 2014
Effects of transfer channels on near- and sub-barrier fusion of $^{32}$ S $+$ $^{48}$ Ca Montagnoli, G.; Stefanini, A. M.; Esbensen, H. Physical Review C, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevC.87.014611	journal	January 2013
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
Empirical nucleus-nucleus potential deduced from fusion excitation functions Siwek-Wilczyńska, K.; Wilczyński, J. Physical Review C, Vol. 69, Issue 2 https://doi.org/10.1103/PhysRevC.69.024611	journal	February 2004
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
First evidence of fusion hindrance for a small Q-value system Jiang, C. L.; Back, B. B.; Esbensen, H. Physics Letters B, Vol. 640, Issue 1-2 https://doi.org/10.1016/j.physletb.2006.07.007	journal	August 2006
Fusion and compound nuclei decay for light and intermediate-mass systems: ${}^{24}{Mg}$ , ${}^{28}{Si}$ + ${}^{12}C$ , ${}^{24}{Mg}$ + ${}^{24, 26}{Mg}$ , ${}^{28}{Si}$ + ${}^{24}{Mg}$ , ${}^{28, 29, 30}{Si}$ Gary, S.; Volant, C. Physical Review C, Vol. 25, Issue 4 https://doi.org/10.1103/PhysRevC.25.1877	journal	April 1982
Exploring Fusion at Extreme Sub-Barrier Energies with Weakly Bound Nuclei Shrivastava, A.; Navin, A.; Lemasson, A. Physical Review Letters, Vol. 103, Issue 23 https://doi.org/10.1103/PhysRevLett.103.232702	journal	December 2009
Fusion of 40Ca + 96Zr revisited: Transfer couplings and hindrance far below the barrier Stefanini, A. M.; Montagnoli, G.; Esbensen, H. Physics Letters B, Vol. 728 https://doi.org/10.1016/j.physletb.2013.12.048	journal	January 2014
Indications of a shallow potential in ${}^{48}{Ca} + {}^{96}{Zr}$ fusion reactions Esbensen, H.; Jiang, C. L. Physical Review C, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevC.79.064619	journal	June 2009
Fusion hindrance for ${}^{27}{Al} + {}^{45}{Sc}$ and other systems with a positive $Q$ value Jiang, C. L.; Rehm, K. E.; Esbensen, H. Physical Review C, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevC.81.024611	journal	February 2010
Fusion of the positive $Q$ -value system ${}^{36}S + {}^{48}{Ca}$ well below the Coulomb barrier Stefanini, A. M.; Montagnoli, G.; Silvestri, R. Physical Review C, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevC.78.044607	journal	October 2008
Dissipative quantum dynamics in low-energy collisions of complex nuclei Diaz-Torres, A.; Hinde, D. J.; Dasgupta, M. Physical Review C, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevC.78.064604	journal	December 2008
The fusion of 12C and 16O with 28,29,30Si Jordan, W. J.; Maher, J. V.; Peng, J. C. Physics Letters B, Vol. 87, Issue 1-2 https://doi.org/10.1016/0370-2693(79)90012-1	journal	October 1979
Reconciling deformation parameters from fusion with those from Coulomb excitation Leigh, J. R.; Rowley, N.; Lemmon, R. C. Physical Review C, Vol. 47, Issue 2 https://doi.org/10.1103/PhysRevC.47.R437	journal	February 1993
Hindrance of Heavy-Ion Fusion due to Nuclear Incompressibility Mişicu, Ş.; Esbensen, H. Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.112701	journal	March 2006
How the Pauli exclusion principle affects fusion of atomic nuclei Simenel, C.; Umar, A. S.; Godbey, K. Physical Review C, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevC.95.031601	journal	March 2017
Signature of Smooth Transition from Sudden to Adiabatic States in Heavy-Ion Fusion Reactions at Deep Sub-Barrier Energies Ichikawa, Takatoshi; Hagino, Kouichi; Iwamoto, Akira Physical Review Letters, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevLett.103.202701	journal	November 2009
Signature of shallow potentials in deep sub-barrier fusion reactions Mişicu, Ş.; Esbensen, H. Physical Review C, Vol. 75, Issue 3 https://doi.org/10.1103/PhysRevC.75.034606	journal	March 2007
Dynamic Influence of Valence Neutrons upon the Complete Fusion of Massive Nuclei Beckerman, M.; Salomaa, M.; Sperduto, A. Physical Review Letters, Vol. 45, Issue 18 https://doi.org/10.1103/PhysRevLett.45.1472	journal	November 1980
How does fusion hindrance show up in medium-light systems? The case of 48Ca+48Ca Stefanini, A. M.; Montagnoli, G.; Silvestri, R. Physics Letters B, Vol. 679, Issue 2 https://doi.org/10.1016/j.physletb.2009.07.017	journal	August 2009
Fusion hindrance for Ca $+$ Ca systems: Influence of neutron excess Jiang, C. L.; Stefanini, A. M.; Esbensen, H. Physical Review C, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevC.82.041601	journal	October 2010
Fusion hindrance at deep sub-barrier energies for the ${}^{11}B + {}^{197}{Au}$ system Shrivastava, A.; Mahata, K.; Nanal, V. Physical Review C, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevC.96.034620	journal	September 2017
Damping of quantum vibrations revealed in deep sub-barrier fusion Ichikawa, Takatoshi; Matsuyanagi, Kenichi Physical Review C, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevC.88.011602	journal	July 2013
Fusion cross section behavior for ${}^{12}C$ + ${}^{24}{Mg}$ and ${}^{12}C$ + ${}^{26}{Mg}$ Daneshvar, K.; Kovar, D. G.; Krieger, S. J. Physical Review C, Vol. 25, Issue 3 https://doi.org/10.1103/PhysRevC.25.1342	journal	March 1982
Fusion hindrance for a positive $Q$ -value system Jiang, C. L.; Back, B. B.; Esbensen, H. Physical Review C, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevC.78.017601	journal	July 2008
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
Analysis of heavy-ion fusion reactions at extreme sub-barrier energies using the proximity formalism Ghodsi, O. N.; Gharaei, R. Physical Review C, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevC.88.054617	journal	November 2013
Role of the cluster structure of 7Li in the dynamics of fragment capture Shrivastava, A.; Navin, A.; Diaz-Torres, A. Physics Letters B, Vol. 718, Issue 3 https://doi.org/10.1016/j.physletb.2012.11.064	journal	January 2013
Fission following fusion of Ni + Sn Lesko, K. T.; Henning, W.; Rehm, K. E. Physical Review C, Vol. 34, Issue 6 https://doi.org/10.1103/PhysRevC.34.2155	journal	December 1986
Coupled-channels analysis of the $^{16} O +^{208} Pb$ fusion barrier distribution Morton, C. R.; Berriman, A. C.; Dasgupta, M. Physical Review C, Vol. 60, Issue 4 https://doi.org/10.1103/PhysRevC.60.044608	journal	August 1999
Angular Momentum Distributions in Subbarrier Fusion Reactions Vandenbosch, R. Annual Review of Nuclear and Particle Science, Vol. 42, Issue 1 https://doi.org/10.1146/annurev.ns.42.120192.002311	journal	December 1992
Unexpected Behavior of Heavy-Ion Fusion Cross Sections at Extreme Sub-Barrier Energies Jiang, C. L.; Esbensen, H.; Rehm, K. E. Physical Review Letters, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevLett.89.052701	journal	July 2002
Influence of Nuclear Structure on Sub-Barrier Hindrance in $N i + N i$ Fusion Jiang, C. L.; Rehm, K. E.; Janssens, R. V. F. Physical Review Letters, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevLett.93.012701	journal	June 2004
Fusion hindrance for the positive $Q$ -value system ${}^{12}C + {}^{30}{Si}$ Montagnoli, G.; Stefanini, A. M.; Jiang, C. L. Physical Review C, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevC.97.024610	journal	February 2018
Measuring Barriers to Fusion Dasgupta, M.; Hinde, D. J.; Rowley, N. Annual Review of Nuclear and Particle Science, Vol. 48, Issue 1 https://doi.org/10.1146/annurev.nucl.48.1.401	journal	December 1998
$^{64} Ni +^{64} Ni$ fusion reaction calculated with the density-constrained time-dependent Hartree-Fock formalism Umar, A. S.; Oberacker, V. E. Physical Review C, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevC.77.064605	journal	June 2008
Analysis of heavy-ion fusion reactions at extreme sub-barrier energies Jiang, C. L.; Esbensen, H.; Back, B. B. Physical Review C, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevC.69.014604	journal	January 2004
Fusion of $^{40} Ca +^{40} Ca$ and other $Ca + Ca$ systems near and below the barrier Montagnoli, G.; Stefanini, A. M.; Jiang, C. L. Physical Review C, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevC.85.024607	journal	February 2012
On the “distribution of barriers” interpretation of heavy-ion fusion Rowley, N.; Satchler, G. R.; Stelson, P. H. Physics Letters B, Vol. 254, Issue 1-2 https://doi.org/10.1016/0370-2693(91)90389-8	journal	January 1991
Subbarrier fusion of atomic nuclei Beckerman, M. Physics Reports, Vol. 129, Issue 3 https://doi.org/10.1016/0370-1573(85)90058-4	journal	December 1985
Effect of Nuclear Deformation on Heavy-Ion Fusion Stokstad, R. G.; Eisen, Y.; Kaplanis, S. Physical Review Letters, Vol. 41, Issue 7 https://doi.org/10.1103/PhysRevLett.41.465	journal	August 1978
Beyond the Coherent Coupled Channels Description of Nuclear Fusion Dasgupta, M.; Hinde, D. J.; Diaz-Torres, A. Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.192701	journal	November 2007
Barrier distributions from the fusion of oxygen ions with ${}^{144, 148, 154}{Sm}$ and ${}^{186}W$ Leigh, J. R.; Dasgupta, M.; Hinde, D. J. Physical Review C, Vol. 52, Issue 6 https://doi.org/10.1103/PhysRevC.52.3151	journal	December 1995
Interaction Barrier in Charged-Particle Nuclear Reactions Wong, C. Y. Physical Review Letters, Vol. 31, Issue 12 https://doi.org/10.1103/PhysRevLett.31.766	journal	September 1973
Recent experimental results in sub- and near-barrier heavy-ion fusion reactions Montagnoli, Giovanna; Stefanini, Alberto M. The European Physical Journal A, Vol. 53, Issue 8 https://doi.org/10.1140/epja/i2017-12350-2	journal	August 2017
Existence of a one-body barrier revealed in deep subbarrier fusion Ichikawa, Takatoshi; Hagino, Kouichi; Iwamoto, Akira Physical Review C, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevC.75.057603	journal	May 2007
Channel-coupling effects in heavy-ion fusion reactions Dasso, C. H.; Landowne, S.; Winther, A. Nuclear Physics A, Vol. 405, Issue 2 https://doi.org/10.1016/0375-9474(83)90578-X	journal	August 1983
Fusability and fissionability in 86Kr-induced reactions near and below the fusion barrier Reisdorf, W.; Hessberger, F. P.; Hildenbrand, K. D. Nuclear Physics A, Vol. 444, Issue 1 https://doi.org/10.1016/0375-9474(85)90296-9	journal	October 1985
A study of Q-value effects on barrier penetration Dasso, C. H.; Landowne, S.; Winther, A. Nuclear Physics A, Vol. 407, Issue 1-2 https://doi.org/10.1016/0375-9474(83)90316-0	journal	October 1983
Density-constrained time-dependent Hartree-Fock calculation of 16O + 208Pb fusion cross-sections Umar, A. S.; Oberacker, V. E. The European Physical Journal A, Vol. 39, Issue 2 https://doi.org/10.1140/epja/i2008-10712-5	journal	January 2009

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