Absence of hindrance in a microscopic 12C + 12C fusion study

Godbey, Kyle; Simenel, Cedric; Umar, A. S.

doi:10.1103/physrevc.100.024619

Title: Absence of hindrance in a microscopic ¹²C + ¹²C fusion study

Abstract

Studies of low-energy fusion of light nuclei are important in astrophysical modeling, with small variations in reaction rates having a large impact on nucleosynthesis yields. Due to the lack of experimental data at astrophysical energies, extrapolation and microscopic methods are needed to model fusion probabilities. To investigate deep sub-barrier ¹²C+¹²C fusion cross sections and establish trends for the S factor. Microscopic methods based on static Hartree-Fock and time-dependent Hartree-Fock (TDHF) mean-field theory are used to obtain ¹²C+¹²C ion-ion fusion potentials. Fusion cross sections and astrophysical S factors are then calculated using the incoming wave boundary condition method. Both density-constrained frozen Hartree-Fock (DCFHF) and density-constrained TDHF (DC-TDHF) predict a rising S factor at low energies, with DC-TDHF predicting a slight damping in the deep sub-barrier region (≈1 MeV). Comparison between DC-TDHF calculations and maximum experimental cross sections in the resonance peaks are good. However, the discrepancy in experimental low-energy results inhibits interpretation of the trend. Using the fully microscopic DCFHF and DC-TDHF methods, no S factor maximum is observed in the ¹²C+¹²C fusion reaction. In addition, no extreme sub-barrier hindrance is predicted at low energies. Furthermore, the development of a microscopic theory of fusion including resonance effects, as well as furthermore »« less

Authors:

Godbey, Kyle ^[1]; Simenel, Cedric ^[2];

^[1]

Vanderbilt Univ., Nashville, TN (United States)
The Australian National Univ., Canberra (Australia)

Publication Date:: Wed Aug 21 00:00:00 EDT 2019

Research Org.:: Vanderbilt Univ., Nashville, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1612036

Alternate Identifier(s):: OSTI ID: 1558151

Grant/Contract Number:: SC0013847

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 100; Journal Issue: 2; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Physics; Low & intermediate energy heavy-ion reactions; Nuclear astrophysics; Nuclear density functional theory; Nuclear fusion; Nuclear reactions

Citation Formats


                    Godbey, Kyle, Simenel, Cedric, and Umar, A. S. Absence of hindrance in a microscopic 12C + 12C fusion study.  United States: N. p., 2019. 
Web.  doi:10.1103/physrevc.100.024619.

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                    Godbey, Kyle, Simenel, Cedric, & Umar, A. S. Absence of hindrance in a microscopic 12C + 12C fusion study.  United States.  https://doi.org/10.1103/physrevc.100.024619

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                    Godbey, Kyle, Simenel, Cedric, and Umar, A. S. Wed .  
"Absence of hindrance in a microscopic 12C + 12C fusion study".  United States.  https://doi.org/10.1103/physrevc.100.024619.  https://www.osti.gov/servlets/purl/1612036.

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@article{osti_1612036,

  title        = {Absence of hindrance in a microscopic 12C + 12C fusion study},

  author       = {Godbey, Kyle and Simenel, Cedric and Umar, A. S.},

  abstractNote = {Studies of low-energy fusion of light nuclei are important in astrophysical modeling, with small variations in reaction rates having a large impact on nucleosynthesis yields. Due to the lack of experimental data at astrophysical energies, extrapolation and microscopic methods are needed to model fusion probabilities. To investigate deep sub-barrier 12C+12C fusion cross sections and establish trends for the S factor. Microscopic methods based on static Hartree-Fock and time-dependent Hartree-Fock (TDHF) mean-field theory are used to obtain 12C+12C ion-ion fusion potentials. Fusion cross sections and astrophysical S factors are then calculated using the incoming wave boundary condition method. Both density-constrained frozen Hartree-Fock (DCFHF) and density-constrained TDHF (DC-TDHF) predict a rising S factor at low energies, with DC-TDHF predicting a slight damping in the deep sub-barrier region (≈1 MeV). Comparison between DC-TDHF calculations and maximum experimental cross sections in the resonance peaks are good. However, the discrepancy in experimental low-energy results inhibits interpretation of the trend. Using the fully microscopic DCFHF and DC-TDHF methods, no S factor maximum is observed in the 12C+12C fusion reaction. In addition, no extreme sub-barrier hindrance is predicted at low energies. Furthermore, the development of a microscopic theory of fusion including resonance effects, as well as further experiments at lower energies must be done before the deep sub-barrier behavior of the reaction can be established.},

  doi          = {10.1103/physrevc.100.024619},

  journal      = {Physical Review C},

  number       = 2,

  volume       = 100,

  place        = {United States},

  year         = {Wed Aug 21 00:00:00 EDT 2019},

  month        = {Wed Aug 21 00:00:00 EDT 2019}

}

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Works referencing / citing this record:

Influence of the tensor interaction on heavy-ion fusion cross sections
journal, November 2019

Godbey, K.; Guo, Lu; Umar, A. S.
Physical Review C, Vol. 100, Issue 5
DOI: 10.1103/physrevc.100.054612

Influence of the tensor interaction on heavy-ion fusion cross sections
text, January 2019

Godbey, K.; Guo, Lu; Umar, A. S.
arXiv
DOI: 10.48550/arxiv.1909.04005

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Microscopic study of the fusion reactions ^40,48Ca+⁷⁸Ni and the effect of the tensor force

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In this work, we provide a microscopic description of the fusion reactions between ^40,48Ca and ⁷⁸Ni. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of ⁴⁸Ca+⁷⁸Ni is more obvious than those of ⁴⁰Ca+⁷⁸Ni. By comparing the calculated fusion cross sections between ⁴⁰Ca+⁷⁸Ni and ⁴⁸Ca+⁷⁸Ni, an interesting enhancement of subbarriermore »« less
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Pauli energy contribution to the nucleus-nucleus interaction

Journal Article Umar, A. S. ; Simenel, C. ; Godbey, K. - Physical Review C

Background: The Pauli exclusion principle plays a crucial role as a building block of many-body quantal systems comprised of fermions. It also induces a “Pauli repulsion” in the interaction between di-nuclear systems. It has been shown in [Phys. Rev. C 95, 031601(R) (2017)] that the Pauli repulsion widens the nucleus-nucleus potential barrier, thus hindering sub-barrier fusion. Purpose: To investigate the proton and neutron contributions to the Pauli repulsion, both in the bare potential neglecting shape polarization and transfer between the reactants, as well as in the dynamical potential obtained by accounting for such dynamical rearrangements. Methods: As the basis ofmore »« less
https://doi.org/10.1103/physrevc.104.034619

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Fusion of ¹²C+²⁴Mg far below the barrier: Evidence for the hindrance effect

Journal Article Montagnoli, G. ; Stefanini, A. M. ; Jiang, C. L. ; ... - Physical Review C

Background: The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behavior of heavy-ion fusion at extreme subbarrier energies, including reactions involving lighter systems, e.g., reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S-factor vs energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q value is an experimentally challenging question. Purpose: Our aim has been to search for evidence of fusion hindrance inmore »« less
Cited by 10
https://doi.org/10.1103/physrevc.101.044608

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Calculation of the C 12 + C 12 sub-barrier fusion cross section in an imaginary-time-dependent mean field theory

Journal Article Bonasera, A. ; Natowitz, J. B. - Physical Review. C

The ¹²C + ¹²C sub-barrier fusion cross section is calculated within the framework of a time-dependent Hartree-Fock-based classical model using the Feynman path-integral method. The modified astrophysical S* factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower-energy region where recent analyses of experimental data obtained with the Trojan horse method (THM) lead to contrasting results, the model predicts a nonresonant S* factor half-way between those results. Low-energy resonances revealed in the THM data are added to the calculation, and the relative reaction rate in the Gamow region ismore »« less
https://doi.org/10.1103/physrevc.102.061602

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Density constrained TDHF [Book Chapter]

Other Oberacker, V. E. ; Umar, A. Sait

In this manuscript we provide an outline of the numerical methods used in implementing the density constrained time-dependent Hartree-Fock (DC-TDHF) method and provide a few examples of its application to nuclear fusion. In this approach, dynamic microscopic calculations are carried out on a three-dimensional lattice and there are no adjustable parameters, the only input is the Skyrme effective NN interaction. After a review of the DC-TDHF theory and the numerical methods, we present results for heavy-ion potentials V (R), coordinate-dependent mass parameters M(R), and precompound excitation energies E*(R) for a variety of heavy-ion reactions. Using fusion barrier penetrabilities, we calculatemore »« less
https://doi.org/10.2174/9781681087641119020006

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Title: Absence of hindrance in a microscopic 12C + 12C fusion study

Abstract

Citation Formats

A possible quark mechanism for the saturation of nuclear matter journal, January 1988

Heavy-ion interaction potential deduced from density-constrained time-dependent Hartree-Fock calculation journal, August 2006

Three-dimensional nuclear dynamics in the quantized ATDHF approach journal, October 1983

Dependence of fusion on isospin dynamics journal, January 2017

Expectations for C 12 and O 16 induced fusion cross sections at energies of astrophysical interest journal, January 2007

A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions journal, December 1999

Three-dimensional unrestricted time-dependent Hartree-Fock fusion calculations using the full Skyrme interaction journal, May 2006

Microscopic sub-barrier fusion calculations for the neutron star crust journal, May 2012

Barrier penetration and spontaneous fission in the time-dependent mean-field approximation journal, November 1980

POSSIBLE RESONANCES IN THE 12 C + 12 C FUSION RATE AND SUPERBURST IGNITION journal, August 2009

Microscopic study of 16 O + 16 O fusion journal, August 2013

The 12C + 12C sub-coulomb fusion cross section journal, May 1977

Skyrme tensor force in heavy ion collisions journal, May 2016

Microscopic study of noncentral effects in heavy-ion fusion reactions with spherical nuclei journal, December 2014

Dependence of the O 16 + O 16 nuclear potential on nuclear incompressibility journal, June 2015

Evidence for survival of the α cluster structure in light nuclei through the fusion process journal, December 2015

Nuclear fusion in dense matter: Reaction rate and carbon burning journal, August 2005

12 C( 16 O, γ ) 28 Si radiative capture: Structural and statistical aspects of the γ decay journal, March 2012

The role of tensor force in heavy-ion fusion dynamics journal, July 2018

Hindrance of Heavy-Ion Fusion due to Nuclear Incompressibility journal, March 2006

Cluster formation in precompound nuclei in the time-dependent framework journal, December 2017

Influence of the tensor force on the microscopic heavy-ion interaction potential journal, December 2018

How the Pauli exclusion principle affects fusion of atomic nuclei journal, March 2017

Clustering effects in reactions induced by light nuclei journal, April 2013

Energy dependence of potential barriers and its effect on fusion cross sections journal, March 2014

Microscopic study of the Sn 132 , 124 + Zr 96 reactions: Dynamic excitation energy, energy-dependent heavy-ion potential, and capture cross section journal, September 2010

Cross section measurements in the 12C+12C system journal, January 2017

C 12 + C 12 Fusion Reactions near the Gamow Energy journal, March 2007

An increase in the 12C + 12C fusion rate from resonances at astrophysical energies journal, May 2018

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions journal, November 2018

Microscopic calculation of precompound excitation energies for heavy-ion collisions journal, October 2009

New Theoretical Approach to Nuclear Heavy-Ion Scattering journal, September 1968

Nuclear energy density optimization: Large deformations journal, February 2012

Microscopic study of Ca + Ca fusion journal, April 2012

Fusion of deformed nuclei: C 12 + C 12 journal, February 2010

Three-dimensional time-dependent Hartree-Fock calculations of O 16 + O 16 and Ca 40 + Ca 40 fusion cross sections journal, May 1978

Absolute cross sections measurement for the 12C + 12C system at astrophysically relevant energies journal, November 2006

Origin and Consequences of C 12 + C 12 Fusion Resonances at Deep Sub-barrier Energies journal, February 2013

Experimental Investigation of the Stellar Nuclear Reaction ^{12}C + ^{12}C at Low Energies journal, July 1969

Time-Dependent Hartree-Fock Description of Heavy ions Fusion journal, January 2008

Configuration transition effect in heavy-ion fusion reactions with deformed nuclei journal, October 2015

Spin–orbit splitting and the tensor component of the Skyrme interaction journal, March 2007

Characterizing the astrophysical S factor for C 12 + C 12 fusion with wave-packet dynamics journal, May 2018

Experimental Measurements of the C 12 + C 12 Nuclear Reactions at Low Energies journal, April 1973

On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel. journal, September 1954

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier journal, August 2008

Approximate Independence of Optical-Model Elastic Scattering Calculations on the Potential at Small Distances journal, August 1964

The role of nucleon structure in finite nuclei journal, May 1996

Dynamical effects in fusion with exotic nuclei journal, August 2016

Dynamical deformation effects in subbarrier fusion of Ni 64 + Sn 132 journal, December 2006

Low energy fusion of 12C + 12C and 16O + 16O systems journal, February 1981

Semiclassical theory of large amplitude collective excitations journal, September 1980

Effects of mutual excitations in the fusion of carbon isotopes journal, December 2011

CVII. The nuclear surface journal, November 1956

Heavy ion fusion reactions in stars conference, January 2018

Reaction rate for carbon burning in massive stars journal, January 2018

São Paulo potential as a tool for calculating S factors of fusion reactions in dense stellar matter journal, October 2007

Nuclear quantum many-body dynamics: From collective vibrations to heavy-ion collisions journal, November 2012

Finite Nuclei in the Quark-Meson Coupling Model journal, February 2016

Carbon Flashes in the Heavy-Element Ocean on Accreting Neutron Stars journal, October 2001

New γ-ray measurements for C 12 + C 12 sub-Coulomb fusion: Toward data unification journal, June 2006

Multinucleon transfer in O 16 , 18 , F 19 + Pb 208 reactions at energies near the fusion barrier journal, August 2016

Localization in light nuclei journal, March 2011

The mean-field theory of nuclear structure and dynamics journal, October 1982

Long Type I X‐Ray Bursts and Neutron Star Interior Physics journal, July 2006

A Remarkable 3 Hour Thermonuclear Burst from 4U 1820−30 journal, February 2002

THE 12 C + 12 C REACTION AND THE IMPACT ON NUCLEOSYNTHESIS IN MASSIVE STARS journal, December 2012

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities journal, May 1998

Global and consistent analysis of the heavy-ion elastic scattering and fusion processes journal, March 2004

Thermonuclear Reaction Rates, II journal, September 1975

Three-dimensional TDHF calculations for reactions of unstable nuclei journal, October 1997

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory journal, June 2014

Microscopic approach to coupled-channels effects on fusion journal, December 2013

Density-constrained time-dependent Hartree-Fock calculation of 16O + 208Pb fusion cross-sections journal, January 2009

New Theoretical Approach to Nuclear Heavy-Ion Scattering journal, October 1970

Density-constrained time-dependent Hartree-Fock calculation of $^{16}$O+$^{208}$Pb fusion cross sections text, January 2008

Energy dependence of nucleus-nucleus potential close to the Coulomb barrier text, January 2008

Title: Absence of hindrance in a microscopic ¹²C + ¹²C fusion study

A possible quark mechanism for the saturation of nuclear matter
journal, January 1988

Heavy-ion interaction potential deduced from density-constrained time-dependent Hartree-Fock calculation
journal, August 2006

Three-dimensional nuclear dynamics in the quantized ATDHF approach
journal, October 1983

Dependence of fusion on isospin dynamics
journal, January 2017

Expectations for ${}^{12}C$ and ${}^{16}O$ induced fusion cross sections at energies of astrophysical interest
journal, January 2007

A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions
journal, December 1999

Three-dimensional unrestricted time-dependent Hartree-Fock fusion calculations using the full Skyrme interaction
journal, May 2006

Microscopic sub-barrier fusion calculations for the neutron star crust
journal, May 2012

Barrier penetration and spontaneous fission in the time-dependent mean-field approximation
journal, November 1980

POSSIBLE RESONANCES IN THE ¹² C + ¹² C FUSION RATE AND SUPERBURST IGNITION
journal, August 2009

Microscopic study of $^{16} O +^{16} O$ fusion
journal, August 2013

The 12C + 12C sub-coulomb fusion cross section
journal, May 1977

Skyrme tensor force in heavy ion collisions
journal, May 2016

Microscopic study of noncentral effects in heavy-ion fusion reactions with spherical nuclei
journal, December 2014

Dependence of the ${}^{16}O + {}^{16}O$ nuclear potential on nuclear incompressibility
journal, June 2015

Evidence for survival of the $α$ cluster structure in light nuclei through the fusion process
journal, December 2015

Nuclear fusion in dense matter: Reaction rate and carbon burning
journal, August 2005

$^{12}$ C( $^{16}$ O, $γ$ ) $^{28}$ Si radiative capture: Structural and statistical aspects of the $γ$ decay
journal, March 2012

The role of tensor force in heavy-ion fusion dynamics
journal, July 2018

Hindrance of Heavy-Ion Fusion due to Nuclear Incompressibility
journal, March 2006

Cluster formation in precompound nuclei in the time-dependent framework
journal, December 2017

Influence of the tensor force on the microscopic heavy-ion interaction potential
journal, December 2018

How the Pauli exclusion principle affects fusion of atomic nuclei
journal, March 2017

Clustering effects in reactions induced by light nuclei
journal, April 2013

Energy dependence of potential barriers and its effect on fusion cross sections
journal, March 2014

Microscopic study of the ${}^{132, 124}{Sn}$ $+$ ${}^{96}{Zr}$ reactions: Dynamic excitation energy, energy-dependent heavy-ion potential, and capture cross section
journal, September 2010

Cross section measurements in the 12C+12C system
journal, January 2017

${}^{12}C + {}^{12}C$ Fusion Reactions near the Gamow Energy
journal, March 2007

An increase in the 12C + 12C fusion rate from resonances at astrophysical energies
journal, May 2018

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions
journal, November 2018

Microscopic calculation of precompound excitation energies for heavy-ion collisions
journal, October 2009

New Theoretical Approach to Nuclear Heavy-Ion Scattering
journal, September 1968

Nuclear energy density optimization: Large deformations
journal, February 2012

Microscopic study of Ca $+$ Ca fusion
journal, April 2012

Fusion of deformed nuclei: ${}^{12}C + {}^{12}C$
journal, February 2010

Three-dimensional time-dependent Hartree-Fock calculations of ${}^{16}O$ + ${}^{16}O$ and ${}^{40}{Ca}$ + ${}^{40}{Ca}$ fusion cross sections
journal, May 1978

Absolute cross sections measurement for the 12C + 12C system at astrophysically relevant energies
journal, November 2006

Origin and Consequences of ${}^{12}C + {}^{12}C$ Fusion Resonances at Deep Sub-barrier Energies
journal, February 2013

Experimental Investigation of the Stellar Nuclear Reaction ^{12}C + ^{12}C at Low Energies
journal, July 1969

Time-Dependent Hartree-Fock Description of Heavy ions Fusion
journal, January 2008

Configuration transition effect in heavy-ion fusion reactions with deformed nuclei
journal, October 2015

Spin–orbit splitting and the tensor component of the Skyrme interaction
journal, March 2007

Characterizing the astrophysical $S$ factor for ${}^{12}C + {}^{12}C$ fusion with wave-packet dynamics
journal, May 2018

Experimental Measurements of the ${}^{12}C$ + ${}^{12}C$ Nuclear Reactions at Low Energies
journal, April 1973

On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel.
journal, September 1954

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier
journal, August 2008

Approximate Independence of Optical-Model Elastic Scattering Calculations on the Potential at Small Distances
journal, August 1964

The role of nucleon structure in finite nuclei
journal, May 1996

Dynamical effects in fusion with exotic nuclei
journal, August 2016

Dynamical deformation effects in subbarrier fusion of ${}^{64}{Ni} + {}^{132}{Sn}$
journal, December 2006

Low energy fusion of 12C + 12C and 16O + 16O systems
journal, February 1981

Semiclassical theory of large amplitude collective excitations
journal, September 1980

Effects of mutual excitations in the fusion of carbon isotopes
journal, December 2011

CVII. The nuclear surface
journal, November 1956

Heavy ion fusion reactions in stars
conference, January 2018

Reaction rate for carbon burning in massive stars
journal, January 2018

São Paulo potential as a tool for calculating $S$ factors of fusion reactions in dense stellar matter
journal, October 2007

Nuclear quantum many-body dynamics: From collective vibrations to heavy-ion collisions
journal, November 2012

Finite Nuclei in the Quark-Meson Coupling Model
journal, February 2016

Carbon Flashes in the Heavy-Element Ocean on Accreting Neutron Stars
journal, October 2001

New γ-ray measurements for ${}^{12}C + {}^{12}C$ sub-Coulomb fusion: Toward data unification
journal, June 2006

Multinucleon transfer in ${}^{16, 18}O, {}^{19}F + {}^{208}{Pb}$ reactions at energies near the fusion barrier
journal, August 2016

Localization in light nuclei
journal, March 2011

The mean-field theory of nuclear structure and dynamics
journal, October 1982

Long Type I X‐Ray Bursts and Neutron Star Interior Physics
journal, July 2006

A Remarkable 3 Hour Thermonuclear Burst from 4U 1820−30
journal, February 2002

THE ¹² C + ¹² C REACTION AND THE IMPACT ON NUCLEOSYNTHESIS IN MASSIVE STARS
journal, December 2012

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities
journal, May 1998

Global and consistent analysis of the heavy-ion elastic scattering and fusion processes
journal, March 2004

Thermonuclear Reaction Rates, II
journal, September 1975

Three-dimensional TDHF calculations for reactions of unstable nuclei
journal, October 1997

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory
journal, June 2014

Microscopic approach to coupled-channels effects on fusion
journal, December 2013

Density-constrained time-dependent Hartree-Fock calculation of 16O + 208Pb fusion cross-sections
journal, January 2009

New Theoretical Approach to Nuclear Heavy-Ion Scattering
journal, October 1970

Density-constrained time-dependent Hartree-Fock calculation of $^{16}$O+$^{208}$Pb fusion cross sections
text, January 2008

Energy dependence of nucleus-nucleus potential close to the Coulomb barrier
text, January 2008

Localization in light nuclei
text, January 2010

Effects of mutual excitations in the fusion of carbon isotopes
text, January 2011