Limits on the molecular resonance
strengths in the 12C+12C fusion reaction
Xiao Fang
Department of Physics
University of Notre Dame
Outline
Carbon burning in stars
Molecular resonances in
12C+12C fusion
Fusion reactions of
carbon isotopes
Limits on the resonance
strengths
Future work
Carbon burning in stars
Massive star
Gamow peak energy
for 12C+12C:
E ≈ 1.5MeV
T: 0.2 - 1.2GK
Ecm:1 – 3 MeV
Cauldrons in the Cosmos, C.E. Rolfs et al.
Molecular resonances in 12C+12C fusion
Any more
resonance?
Molecular resonances in the 12C+12C fusion
reaction measured by Almqvist et al., in 1960
Most recent S(E)* factor (Modified S(E) factor)
of the fusion process 12C+12C measured by
Spillane et al., in 2007
50 years later….
Compare the 12C+12C reaction with carbon isotope fusion reactions,
12C+13C and 13C+13C. Because of their similarities in mass, charge,
and nuclear structure, comparing the cross sections of the 12C+12C with
these other two carbon isotope fusion reactions may help us better
understand the resonances in the 12C+12C fusion reaction.
To remove the Coulomb barrier penetration effect in the fusion
process, we have introduced the cross section factor:
S(E)=σ(E) E exp(87.21/E1/2)
Reduced
mass
Radius
(fm)
12C+12C
6
5.77
12C+13C
6.33
5.85
13C+13C
6.5
5.93
Fusion reactions of carbon isotopes
Before correction
Notre Dame
12C+12C(red,
Becker
et al., 1981)
12C+13C(blue, Notani
et al., 2009)
13C+13C(purple,
Trentalange 1982)
Isotope effect
1.E+17
12C+12C
12C+13C
13C+13C
9.E+16
8.E+16
Difference in mass and radius
Difference in cross section
(using CCFULL)
6.E+16
5.E+16
4.E+16
Elastic transfer enhancement in
12C+13C
3.E+16
2.E+16
1.E+16
0.E+00
2.5
4.5
6.5
8.5
Ecm(MeV)
1.4
1.2
1.0
Reduced
mass
Radius
(fm)
12C+12C
6
5.77
12C+13C
6.33
13C+13C
6.5
Ratio
S(MeV*b)
7.E+16
0.8
0.6
(12C+13C)/(12C+12C)
5.85
0.4
(13C+13C)/(12C+12C)
5.93
0.2
(12C+13C,including
transfer)/(12C+12C)
0.0
2.5
4.5
6.5
Ecm (MeV)
8.5
Fusion reactions of carbon isotopes
After correcting the isotope
effect (difference in mass and
radius)
Fusion reactions of carbon isotopes
After correcting the isotope and
couple channel effect to the
12C(2+,4.44 MeV)
Relative motion energy
Nogami-Yamanishi Model
2+
L
L-2
Radius
Limits on the resonance strengths
Cooper (2009)
12C+12C
S(E) (MeV*b)
Spillane (2007)
experiments:
Becker (1981)
Spillane (2007)
Kovar (1979)
Predicted 12C+12C
with cc
Becker (1981)
Predicted 12C+12C
without cc
Kovar (1979)
Ec.m. (MeV)
The predictions are compared with:
1) the resonance (Ecm=2.1 MeV) found by Spillane et al.;
2) the resonance (Ecm=1.5 MeV) suggested by Cooper et al..
Both resonance peaks are well above the upper limits, therefore additional measurements are needed for
verification.
Push measurement towards lower energies
High current accelerator (>40 pµA) + highly efficient Si/Ge array
A 5 MV Pelletron
with ECR source
in terminal.
Special Thanks
Group members: Xiao-dong Tang, Brian Bucher, Justin Browne, Adam Alongi
We’d like to extend special thanks to all of those involved in this project.
Especially Henning Esbensen and Cheng-lie Jiang in Argonne National Lab,
And Cheng-jian Lin in China Institute of Atomic Energy.