NACRE update and extension project Phenomenological analyses of radiative capture reactions

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NACRE update and extension project-
Phenomenological analyses of radiative capture
reactions -
22nd Meeting between Astrophysicists and Nuclear
PhysicistsBrussels, December 12-13, 2005

•  M. Katsuma1, M. Aikawa1, K. Arai2,1, M.
  Arnould1, K. Takahashi1 and H. Utsunomiya3
• 1 Université Libre de Bruxelles, Belgium
• 2 Nagaoka National College of Technology, Japan
• 3 Konan University, Japan

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Outline

• The NACRE compilation (1999)
• Widely used in studies of stellar evolution and
  concomitant nucleosynthesis processes.
• The NACRE update and extension project
• under way in the framework of a Konan-ULB
  convention.
• Make evaluation tools to analyze reactions.
• The potential model with parameter optimization
  routines
• The current status of the project by way of a few
  exemplifying results of our preliminary analyses
  of radiative capture reactions.

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NACRE

• Abbreviation of Nuclear Astrophysics
  Compilation of REaction rates
• Cross sections of 86 charged-particle induced
  reactions on targets in the range 1 ? Z ? 14
• The Maxwellian-averaged thermonuclear reaction
  rates from 106K to 1010K
• Good knowledge of nuclear reaction rates to
  astrophysicist
• Published as C. Angulo et al., NPA 656 (1999) 3

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NACRE update and extension project

• Konan-ULB joint project
• Photoreactions for astrophysics (g,n), (g,p)
  and (g,a)
• Konan (g,n) reactions, ULB (p, g) and (a,g)
  reactions
• Update of the NACRE compilation (late 2004)
• Collection of experimental data published in
  refereed journals (between 1997 and July 2005)
• Make an evaluation tool to analyze reactions
• Extension of the NACRE compilation (not yet)
• Extend three regions
• evaluate the existing experimental data
• make reliable extrapolations to the lower-energy
  region

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Extension of the NACRE compilation

• Stable targets in the Z ? 14 range
• Stable targets in the Z gt 14 range
• Unstable targets

Schematic view of the network - already
compiled in NACRE (1999) - to be compiled in the
project
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NACRE update and extension project

• Konan-ULB joint project
• Photoreactions for astrophysics (g,n), (g,p)
  and (g,a)
• Konan (g,n) reactions, ULB (p, g) and (a,g)
  reactions
• Update of the NACRE compilation (late 2004)
• Collection of experimental data published in
  refereed journals (between 1997 and July 2005)
• Make an evaluation tool to analyze reactions
• Extension of the NACRE compilation (not yet)
• Extend three regions
• evaluate the existing experimental data
• make reliable extrapolations to the lower-energy
  region

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Extrapolation of data to the low energy

• Problem
• how to extrapolate S-factors and reaction rates
  to the low energy
• Expansion
• S(E) S(0) (1 s1 E s2 E2 )
• Phenomenological models
• Potential model and R-matrix method
• with parameter optimization routines
• Microscopic models
• Cluster Models (GCM, RGM,)

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Potential model

• Radiative capture cross sections

• Schrödinger eq.

• Potential of the final state
• Same shape
• Separation energy

• Astrophysical S-factor

ParametersVi, Vf, r0, a, Cs
S(E) Cs E exp(2ph) sc(E)
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7Be(p,g)8B S-factor
(preliminary)
E1
Direct capture ? Resonance
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7Be(p,g)8B S-factor
S(0) values in NACRE
Extrapolation of data in NACRE

• Almost the same as the upper limit of S(0) values

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2H(p,g)3He S-factor
(preliminary)
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2H(p,g)3He S-factor
S(0) values in NACRE
Extrapolation of data in NACRE

• All the curves are in the S(0) value region.

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2H(p,g)3He S-factor - decomposition
(preliminary)
E1
M1
E1 dominant above 0.1 MeV
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3He(a,g)7Be S-factor
(preliminary)
E1
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3He(a,g)7Be S-factor
Large experimental uncertainty
Extrapolation of data in NACRE
E1
S(0) values in NACRE

• Approximately the same as the lower limit of S(0)
  values

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S-factors
(preliminary)
(preliminary)
0.4
0.4
M1
E2
M1
E2
E1
E1
(preliminary)
(preliminary)
Difference between our results and NACRE? (low
energy region)
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Summary

• The NACRE update and extension project has been
  pursued within a Konan-ULB collaboration since
  2004.
• Update of the NACRE compilation
• Collection of experimental data published in
  refereed journals (between 1997 and July 2005)
• Make evaluation tools to analyze radiative
  capture reactions
• potential model and R-matrix method
• with parameter optimization routines
• Experimental data are well reproduced.
• Extrapolations of data to low energies in
  7Be(p,g)8B, 2H(p,g)3He and 3He(a,g)7Be are
  consistent with NACRE.
• Error treatment of experimental data should be
  considered carefully.

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Parameters of the models
Potential model
1.3af1/3 lt r0 lt 1.3(a11/3a21/3 )
Spectroscopic factor 0.5 in the 6Li(p,g)7Be
and 7Be(p,g) 8B reactions 3H(4He,g)7Li
3He(4He,g)7Be