The NACRE II project

1
The NACRE II project
23rd Meeting between Astrophysicists and Nuclear
Physicists Brussels, December 11, 2006

•  M. Katsuma
• Université Libre de Bruxelles, Belgium

2
Compilation of Nuclear Reaction Rate for
Astrophysics

• Nucleosynthesis
• Big-Bang nucleosynthesis of elements
• Stellar evolution and concomitant nucleosynthesis
• This achievement has been supported by the
  experimental efforts and the compilation of
  nuclear reaction data.
• Compilation of Nuclear Reaction Rate
• W.A. Fowler et al. (1988)
• Less clear explanation of deduced reaction rates
• C. Angulo et al. (1999) NACRE
• Documentation about the procedure of evaluation
• Explicit references to the original experimental
  data
• Provide estimates of lower and upper limits of
  the rates
• Konan-ULB (2008?)
• NACRE II project
• Started Autumn 2004

3
Current status of data evaluation

• Radiative capture reactions Potential model ,
  R-matrix
• A(p,g)B, A(a,g)B
• Transfer reactions DWBA , R-matrix
• A(d,p)B, A(p,a)B, A(a,n)B
• Comparison of the astrophysical S-factors
• model calculations
• S-factor data in NACRE
• Extrapolation of data to the low energy
• Examples of the reaction rates
• test calculations
• Possibility of the extension to the heavy-mass
  region

4
Potential model

• Radiative capture cross sections

• Schrödinger eq.

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

• Boundary conditions
• Initial Scattering
• Final Bound state

ParametersVi, Vf, r0, a, Cs
5
DWBA Distorted-Waves Born Approximation

• Cross sections of transfer reactions

• Form factors

fa
fb

• Global optical potentials
• Potential strengths are adjusted.

fA
fB
6
Extrapolation of data to the low energy

• Astrophysical S-factor
• S(E) E exp(2ph) sc(E)
• Experimental difficulties
• Cross sections are very small.
• Atomic effects are non-negligible.
• How to extrapolate the S-factor down to the low
  energy
• Fit the experimental data by using the potential
  model, R-matrix method or DWBA.
• Calculate the astrophysical S-factor down to E
  1 keV.
• Extrapolation in NACRE

S0 value is used as the index of the
extrapolation.
S(E) S0 S1 E S2 E2
7
7Be(p,g)8B S-factor
Potential model R-matrix method Direct capture
OResonance O NACRE (E lt 0.1 MeV) S(E) 21
18E 38E2 19 lt S0 lt 23 eVb
S0 values are approximately inside of NACRE. S0
22.1 eVb (R-matrix method) S0 18.9
eVb (Potential model)
8
7Be(p,g)8B S-factor
Potential model R-matrix method Direct capture
OResonance O NACRE (E lt 0.1 MeV) S(E) 21
18E 38E2 19 lt S0 lt 23 eVb
S0 values are approximately inside of NACRE. S0
22.1 eVb (R-matrix method) S0 18.9
eVb (Potential model)
S0 values in NACRE
9
20Ne(p,g)21Na S-factor
Potential model Direct capture O E1
transition The transition to the sub- threshold
state is dominant. NACRE S0 gt 100 keVb The
potential model gives a small S0 value. Outside
Sum of transitions to
21Na
E
1/2 Eex 2.425 MeV
5/2 Eex 0.331 MeV 3/2 g.s.
10
3H(d,n)4He and 3He(d,p)4He S-factors
DWBA R-matrix method Resonance O 3H(d,n)4He
S0 11 MeVb NACRE All the curves are almost
the same value in low energies. Inside 3He(d,p)4He
Not included in NACRE
11
A2-9
12
A10 - 27
(keV b)
13
Current status of data evaluation
14
NACRE ratio of reaction rates
(Test calculations)
The reaction rates are calculated from the
potential model or DWBA.
Difference between NACRE and this work by factor
of 2-6.
15
Extension to the heavy-mass region (p,a)
16
Extension to the heavy-mass region (a,n)
17
Current status of data evaluation (Heavy-mass
region)

• Transfer reactions
• The DWBA could be used in the analyses of
  transfer reactions in the heavy-mass region.
• Radiative capture reactions
• Potential model X
• due to many levels

18
Summary

• Current status of the NACRE II project
• The astrophysical S-factors of 28 reactions have
  been analyzed with the potential model, R-matrix
  method and DWBA.
• about 50 S-factor data in NACRE
• Examples of the reaction rates
• Difference in the results of 20Ne(p,g)21Na,
  14N(p,a)11C, between the models and NACRE by
  factor of 2-6.
• Possibility of the extension to the heavy-mass
  region
• The DWBA have been applied to the cross section
  data in the heavy-mass region.
• Future
• Systematic research of the S-factor data
• a version based on the phenomenological models
• b version including the experimental
  information
• Spline interpolation of the S-factor data
• Resonance parameters

Così-Così
19
Collaborators

• Evaluation
• S-factors Potential Model M. Katsuma, K.
  Takahashi R-matrix (Capture reactions) M.
  Katsuma, K. Arai R-matrix (Transfer
  reactions) K. Arai, M. Katsuma DWBA M. Katsuma
• Rate M. Arnould, K. Takahashi, H. Utsunomiya, M.
  Katsuma
• Data collection
• M. Aikawa, M. Arnould, K. Takahashi, H.
  Utsunomiya
• This project has been proceeding in the framework
  of Konan-ULB convention.