Determination of the cross sections for the astrophysical reaction 14Cn,15C12 from the width of the

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Determination of the cross sections for the
astrophysical reaction 14C(n,?)15C(1/2) from the
width of the proton resonance 15F(1/2)
N.K. Timofeyuk University of Surrey, UK In
collaboration with D.Baye, P.Descouvemont, R.
Kamouni (ULB, Belgium) and I.J. Thompson (UniS,
UK)
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• Astrophysical applications for the 14C(n, ?)15C
  reaction
• Inhomogeneous big bang nucleosynthesis
• Neutron-induced CNO cycle
• Supernovae explosions

Possible reaction chains in neutron-rich zones
7Li(n, ?)8Li(?,n)11B(n, ?)12B(??)12C
7Li(t,n)9Be(t,n)11B(n, ?)12B(??)12C Then
12C(n, ?)13C(n, ?)14C and 14C(n, ?)15C
12C(n,?)13C(n,?) 14C(n,?)15C
(??)15N(n,?)16N(??)16O(n,?)17O(?,n)14C
14N(n,p) 14C(n, ?)15C (??)15N (n,
?)16N(??)16O(n,?)17O(?,n)14C
?(?n,?)9Be(?,n)12C(n,?)13C(n,?) 14C(n,?)15C
?(?n,?)9Be(n,?)10Be(?,?) 14C(n,?)15C
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What is known about the low-energy 14C(n, ?)15C
cross sections?

sn? (23.3keV) Direct measurements at 23.3 keV
(1992) 1.1 ? 0.28
µb Potential model calculations (1990)
5.1 µb Folding model
calculations (1999) (?s??/kT at 30 keV)
10.14 µb Microscopic cluster model (2000)
6.38 µb Coulomb
dissociation of 15C (MSU, 2002)
2.6 ? 0.9 µb Coulomb dissociation of 15C (GSI,
2002) 4.4 ? 0.6
µb Coulomb dissociation of 15C (RIKEN, 2002)
4.1 ? 0.4 µb Direct measurements at
23.3 keV (2005) 2.7 ?
0.22 µb
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Direct 14C(n,?)15C(½) capture at low energies
The main contribution gives E1 capture from
initial p-wave to final s-wave bound state
Amplitude
the overlap integral between the wave functions
of 14C and 15C
the neutron scattering wave functions in the
entrance channel
At large distances
Asymptotic normalisation coefficient (ANC)
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Mirror nucleon decays
15C
15F
14C
14O
p
n
real
virtual
ANC
Proton width Gp
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For bound-unbound mirror vertices If charge
symmetry of the NN interactgions is valid and the
wave functions in mirror nuclei are exactly the
same then for narrow resonances
(N.K. Timofeyuk, R.C. Johnson and A.M.
Mukhamedzhanov, PRL 91, 0232501 (2003))
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MCM calculations with exactly the same NN
interactions in mirror nuclei.
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MCM calculations with NN interactions which fit
proton resonance energies and neutron separation
energies in mirror nuclei. Core excitations
included.
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Microscopic cluster calculations (MCM)
15C 14C n, 15F 14O p ?15 ? ( ?14 ?
gN(r) ) gn(r) ? Cn exp (-?r)/r , r ?
? Microscopic R-matrix approach is used to find
Cn. and Gp Nuclei 14C and 14O are described in
the one-centre oscillator shell model Core
excitations are taken into account Effective NN
potentials used Volkov (V2) (describes
binding energies of triton and 4He) Minnesota
(MN) (describes the two-nucleon low-energy
scattering data but also the essential properties
of the deuteron, triton and 4He)
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ER 1.47 MeV
Ratio ?? (in MeV fm) calculated in the
single-channel and multi-channel MCM with two
different oscillator radii b and two different NN
potentials single-channel MCM
multi-channel MCM b 1.5 fm b 1.75 fm b
1.5 fm b 1.75 fm V2 0.297 0.280 0.301
0.286 MN 0.309 0.291 0.313 0.297
?? 0.297 ? 0.017 MeV fm
Gp 0.56 MeV
C2n Gp/ ??
1.89 ? 0.11 fm-1
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?14C15C? ? S1/2 fs.p.(r) ? S1/2bs.p. exp(-?r)/r
, r ? ? bs.p. is the single-particle
ANC C S1/2bs.p. r0 a bs.p. Sexp C2exp
(fm-1) Potential model (n, ?) 1.261
0.7 1.48 0.88 1.92 14C(d,p) 1.3 0.7 1.49 0
.88 1.96 15C breakup 1.228 0.6 1.38 1.0
1.91 15C breakup (GSI, DW) 1.25 0.7 1.47 0.97?
0.08 2.10?0.15 15C breakup (GSI, PW)
1.25 0.7 1.47 0.73?0.05 1.58?0.11 15C breakup
(GSI, PW) 1.15 0.5 1.28 0.92?0.07
1.50?0.08 15C breakup (MSU) 1.223 0.5 1.30 0.90
1.53 PM for 15C spectrum 1.
17 0.71 1.45 1.0 2.10 from mirror
symmetry C2mir 1.89 ? 0.11 fm-1
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ER Gp ??
C2mir Smir p14O 1.47 0.56
0.297?0.017 1.89?0.11 1.01?0.21 p14O
1.45 0.7 0.295?0.073 2.37
1.39?0.54 16O(14N,15C)15F 1.41?0.15
0.8?0.3 0.260?0.073 3.08
2.15?1.48 20Ne(3He,8Li)15F 1.37?0.18
0.8?0.3 0.250?0.089 3.20 2.41?1.75
p14O 1.23?0.05 0.67? 0.03 0.194?0.029
3.45 2.06?1.06 p14O 1.51?0.11 1.2
0.307?0.067 4.10?0.88 2.25?0.81 20Ne(3He,8Li)1
5F 1.6?0.2 ? 0.9 0.352?0.111
? 1.94 ?0.87 p14O 1.29
0.7 0.218?0.012 3.30 1.72?0.36
0.16 -0.10
0.78 -0.47
2.83 -1.57
3.59 -1.73
1.64 -1.22
0.16 -0.10
0.70 -0.148
0.16 -0.10
Smir (Cmir/bs.p.)2
Physically meaningful values S ? (15/14)2
? 1.15
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With C2mir 1.89 ? 0.11 fm-1 sn?
(23.3keV) 5.3 ? 0.3 µb

sn? (23.3keV) Direct measurements at 23.3
keV (1992) 1.1 ?
0.28 µb Potential model calculations (1990)
5.1 µb Folding model
calculations (1999) (?s??/kT at 30 keV)
10.14 µb Microscopic cluster model (2000)
6.38 µb Coulomb
dissociation of 15C (MSU, 2002)
2.6 ? 0.9 µb Coulomb dissociation of 15C (GSI,
2002) 4.4 ? 0.6
µb Coulomb dissociation of 15C (RIKEN, 2002)
4.1 ? 0.4 µb Direct measurements at
23.3 keV (2005) 2.7 ?
0.22 µb
14
00
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• Summary and conclusion
• The 14C(n,?)15C cross sections are determined by
  the 15C ANC.
• The 15C(1/2) ANC is related to the proton width
  of 15F(1/2).
• Mirror symmetry between the 15C(1/2) and
  15F(1/2) isotopes offers a strong test for the
  low-energy 14C(n,?)15C cross sections.
• The 14C(n,?)15C cross sections predicted using
  mirror symmetry suggests that most of the cross
  sections, previously determined from experiments,
  are underestimated.

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• Why is it important to solve the 14C(n,?)15C
  puzzle?
• (n,?) reactions on short-lived radioactive
  nuclei are important for understanding various
  aspects of the nucleosynthesis
• no direct (n,?) experiments on short-lived
  radioactive targets are currently possible
• indirect methods are used
• validity of indirect methods must be
  investigated