Reactions studies in relation to
upcoming FRENA facility: Indirect
Method & RR-matrix
phenomenology
Sucheta Adhikari
Department of Physics
Techno India University, Kolkata
FRENA machine
High current low energy accelerator suitable for nuclear astrophysics experiments
Terminal Voltage - 0.2 to 3.0 MV
Typical DC Beam Currents at 3 MV after quadrupole triplet lens:
H+ - 3 mA
He2+- 70 µA
Heavier Ions - 20 - 60 µA
Reactions studies in relation to FRENA
Direct Reactions with higher Gamow Energy can be attempted e.g 12C+12C
(EG= 1.523 ± 0.296 MeV)
Reactions with low Gamow energy are difficult except without
underground facility
Extrapolation is required using R-matrix phenomenology
Reaction
Gamow
Energy EG
(keV)
Coulomb
Barrier VC
(keV)
EG /VC
15N(p,γ)
26.6
1711
0.016
3He(α,γ)
22.4
1112
0.02
12C(α,γ)
300
3100
0.08
12C+12C
1523
6660
0.23
ANC Method
σ capture =
[
∑ ε λ Γλ Γλγ
M int =
]
λ
( Eλ − E )1 − LR
I = ψ Aφaφb
I ∝ ψ ext = CW
φ = bW
I = Sϕ
C = Sb
Sα =
σ
σ
exp
transfer
theory
transfer
π
2J +1
M int + M ext
2
(
2
I
+
1
)(
2
I
+
1
)
k
1
2
1/ 2
M
ψ
ext
ext
k =
∝ψ
2
ext
= CW ( 2 kr ) ≈ Ce
− kr + η ln( 2 kr )
2µE B / h
Z 1Z 2e 2
η = −
h
µ
2EB
For weakly bound states EB, Mext is dominant
and ANC determines capture cross-section
Indirect methods can be used to constraint
the R-matrix fit through determination of
ANC
The ANC method uses transfer reactions
12C(α,γ
α,γ)
α,γ
problem
These reactions are important due to carbon and oxygen are the most
abundant elements in the world after burning helium and often heavier
elements are formed from these two elements. Then Our knowledge of
the reaction 12C(α,γ)16O helpful to better understand the evolution of
condense stars, such as neutron stars and black holes. The reason for this
interest lies in the potential of this reaction to determine important
astrophysical observables and unravel mysteries of nuclear reaction
mechanisms
Direct capture cross section measured upto 1MeV
Impossible to measure at Gamow peak
Indirect Measurements -α
α-transfer reactions
Earlier measurements - Above barrier measurements
S. Adhikari et al., Phys Rev. C 89, 044618 (2014)
S. Adhikari et al., Jour. Phys. G 44, 015102 (2016)
A. Belhout et al., Nucl. Phys. A 793, 178 (2007)
N. Keeley et al., Phys. Rev. C 67, 044604 (2003)
12C(6Li,d)16O∗
at 20 MeV
12C(7Li,t)16O∗
12C(6Li,d)16O∗
12C(6Li,d)16O∗
at 20 MeV
at 48 MeV
at 34 MeV
T. L. Drummer et al., Phys. Rev. C 59, 2574 (1999)
12C(6Li,d)16O∗
at 50 MeV
F. D. Bechetti et al., Nucl. Phys. A 344, 336 (1980)
12C(6Li,d)16O∗
at 90 MeV
M. Makowska-Rzeszutko et al., Phys. Lett. B 74, 187 (1978 )
12C(6Li,d)16O∗
MeV
K. Meier-Ewert, K. Bethge, and K. O. Pffeifer, Nucl. Phys. A 110, 142 (1968)
12C(6Li,d)16O∗
at 20 MeV
at 20
Brief overview and results of two
experiments by our group
6
Li (α ⊗ d )+12C → d +16O * (α ⊗12C ) at 20 MeV
S. Adhikari et al., Phys. Rev. C 89, 044618 (2014)
12C(6Li,d)
Breakup effects
on
transfer
mainly on the
ground state
Brief overview and results of two
experiments by our group
7
Li( α ⊗ t )+12C → t +16O * ( α ⊗12C ) at 20 MeV
S. Adhikari et al., Jour. Phys. G 44, 015102 (2016)
ANC extracted from above barrier measurements are model dependent !
Sub-Coulomb measurements
Only three measurements!
C. R. Brune, W. H. Geist, R. W. Kavanagh, and K. D. Veal Phys. Rev. Lett. 83, 4025 (1999)
Measured Excitation functions for the
12C(6Li,d)16O
and
12C(7Li,t)16O
reactions by
gamma
spectroscopy at 2.7-7.0 MeV energy range for 6Li projectile and 4.75-7.0 MeV for 7Li projectile
M.L. Avila et al, Phys. Rev. Lett. 114 (2015) 071101
Inverse kinematics Angular distribution for 12C(6Li,d) six backward angles at 5,7,9 MeV incident
energy of 12C
D. W. Heikkinen Phys. Rev. 141, 1007 (1966)
The 6Li +
12C
reaction has been studied for bombarding energies in the range 4.5 to 5.5 MeV.
Angular distributions and total cross sections were measured
Sub-Coulomb data analysis
C2=1.38 x 1010 fm-1
Sub-Coulomb data analysis
R-matrix analysis
12C(α,γ
α,γ)
α,γ
S.Adhikari and C. Basu
Proceedings of the DAE-BRNS
Symp. on Nucl. Phys. 60 (2015) 896
Suprita Chakraborty, Richard deBoer,
Avijit Mukherjee, and Subinit Roy
Phys. Rev. C 91, 045801 (2015)
S. Roy and his group at SINP has carried out
studies on the important CNO cycle reaction
13C(p,γ). The multichannel multilevel Rmatrix code AZURE2 has been used for this
calculations. The ANCs for all 14N states were
also extracted from capture data and they
corroborate with those extracted using
transfer reactions by Mukhamedzhanov et
al. The values of the S-factor at zero relative
energy was found to be consistent within
error bars for the two sets of capture data
used.
Scope of ANC studies with FRENA
machine
• Sub-Coulomb angular distributions over a wide angular range.
• The detection system will require position sensitive gas proportional
counter that will have to be fabricated.
• A small scattering chamber is being fabricated for this purpose.
Collaborators
C. Basu
I. J. Thompson
P. Sugathan
A. Jhinghan
B.R. Behera
S. Ray
K. S. Golda
A. Babu
N. Saneesh
G. Kaur
M. Thakur
R. Mahajan
R. Dubey
D. Singh
A. K. Mitra