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Cross sections of neutron
reactions in S-Cl-Ar region in the
s-process of nucleosynthesis
C. Oprea1, P. J. Szalanski2, A. Ioan1, P. M. Potlog3
1Frank Laboratory of Neutron Physics, JINR, Dubna 141980, Russia
2Dept. of Astrophysics, Faculty of Physics, Lodz University, Lodz,
Poland
3Institute of Space Sciences, 077125 Magurele, Romania
Corresponding author: [email protected]
1
Abstract
One of the main questions in astrophysics is the origin and the relative
abundance of 36Cl and 36S isotopes and their production during the sprocess of nucleosynthesis. A series of problems connecting with the
uncertainties in the (n,p), (n,a) and (n,g) reactions leading to the
decreasing or increasing of the concentration of 36Cl isotope were
analyzed. The cross sections of mentioned reactions at the astrophysical
relevant energies using Talys and Empire computer codes were
evaluated. The theoretical calculations of cross sections for determination
of isotopes astrophysical reaction rates were accomplished and the
results are compared with experimental results from literature. These data
are required for better understanding of the origin of the rare neutron rich
isotopes in the S-Cl-Ar region and for evaluation of the 40K/40Ar
chronometer.
2
Cl – Properties
- VII group of halogens, very electronegative
- yellow-green color in standard conditions (t = 250 C, patm = 1.01 bar)
- r = 2.898 g/l, melting point t= -101.50 C, boiling point t = 34.040 C
- after H2 and O2 it is the most abundant in sea water – 19.4 g/l
- very common in Earth crust (145 mg/kg)
- electronegativity – 3.612724 eV - > high reactiveness – it is found only in
chemical compounds – mostly salts NaCl, KCl etc
- Cl has two stable isotopes with the abundances – 35Cl (75.77%),
37Cl
(24.23%)
- 21 isotopes and 2 isomers are known
- 36Cl – produced in 35Cl neutron captures, Ar spallation, 40Ca muon capture
- 36Cl half life – t1/2 = 3.01 ∙ 105 y - > traces can be find in nature
3
Burning phases of 20-25 Mʘ star
4
Theoretical background
a  X  b  Y  ...
X – target nucleus, Y – produced nuclei (of interest)
NY =  ab N X  a
NY - Number of produced nuclei, ab = cross section,
dN
=  ab N X 
dt
Reaction rate,  = incident flux per area per time
a = fluence (number of particles per area)
r = na abva nX = wnX
n = particles density [m-3]
Cross Section – calculated in the frame of different nuclear reaction models

v =  v vdv
Averaged reaction rate: (n) = distribution (normalized
to 1; in our case MB distribution
0
5
Theoretical background
Cross Section Evaluation
- Compound Processes – Hauser Feshbach Formalism
- Preequilibrium Processes – Two Component Exciton Model
- Direct Processes – DWBA
Levels Density – Constant Temperature Fermi Gas Model
Neutron Energy – from 0.5 to 25 MeV
Nuclear Potentials - Wood – Saxon type with refinements
Astrophysical Rate (effective stellar rate) a -> b
- Calculated at temperature T taking into account various target excited states
 8 
N A v ab T  = 

 m 
*
1
2
2I
  2I
k T  GT 
NA
B
3
2

0 


 E  Ex
1 
 ab E E exp  
0
1
k BT



dE

 Ex 
2I   1

GT  =  0
exp  
2
I

1
k
T

 B 
6
Maxwell – Boltzmann Distribution
Relative neutrons abundance for different temperatures for 20-25 Mʘ stars
7
Cl – Importance
1. Astrophysical
- In later burning phases of massive stars the production of heavy elements above
iron strongly depends on neutron capture and radioactive decay
- 35Cl consum neutrons -> decreases the production of heavy elements
2. Nuclear waste management
- by nuclear technology the production of any kind of stabile and radioactive isotopes
(including 36Cl) is growing
- 35Cl is very common in water and due to the neutrons 36Cl is producing -> it is
necessary to know the reaction rates
3. Geology
- 36Cl/35Cl ratio is used to date water and geological samples exposed to neutrons
and cosmic rays
- cross sections are necessary to evaluate the production rate during the exposure
8
Results
In the interaction of fast neutrons (0.5 – 25 MeV) with 35Cl the following
isotopes are produced:
- 27Al13, 28Al13
- 29Si14, 30Si14, 31Si14
- 30P15, 31P15, 32P15, 33P15, 34P15
- 32S16, 33S16, 34S16, 35S16
- 34Cl17, 35Cl17, 36Cl17
Objectives
1) The cross sections of productions of the above mentioned isotopes were
calculated
2) Astrophysical rates of 35Cl(n,g)36Cl reaction
9
Results - Al isotopes production
27
0.007
Production of Al13
28
35
n+ Cl reaction
Production of Al13
6
35
n+ Cl reaction
5
0.005
Cross Section [mb]
Cross Section [mb]
0.006
0.004
0.003
0.002
0.001
4
3
2
1
0
0.000
24.30
24.45
24.60
24.75
24.90
Neutron Energy [MeV]
Q = -1.67 MeV
25.05
16
18
20
22
24
26
Neutron Energy [MeV]
Q = -8.94 MeV
10
Results - Si isotopes production
29
0.30
Production of Si14
35
35
n+ Cl reaction
30
Cross Section [mb]
0.20
0.15
0.10
0.05
Q = -1.64 MeV
0.00
35
n+ Cl reaction
25
20
15
10
5
Q = -1.2 MeV
0
21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5
Neutron Energy [MeV]
Cross Section [mb]
Cross Section [mb]
0.25
30
Production of Si14
16
18
20
22
24
26
Neutron Energy [MeV]
31
16
Production of Si14
14
n+ Cl reaction
35
12
10
8
6
4
2
Q = -7.7 MeV
0
12
14
16
18
20
22
Neutron Energy [MeV]
24
26
11
Results - P isotopes production (I)
31
30
Production of P15
0.035
35
n+ Cl reaction
n+ Cl reaction
Cross Section [mb]
0.030
0.025
0.020
0.015
0.010
200
150
100
50
Q = -1.93 MeV
0.005
Q = -6.94 MeV
0
0.000
8
23.7
24.0
24.3
24.6
24.9
10
12
25.2
14
16
18
20
22
24
26
Neutron Energy [MeV]
Neutron Energy [MeV]
150
Q = 9.37 MeV
100
50
Cross Section [mb]
200
Production of P15
35
n+ Cl reaction
6
35
n+ Cl reaction
250
33
7
32
Production of P15
300
Cross Section [mb]
Cross Section [mb]
Production of P15
250
35
5
4
3
2
1
Q = -9.54 MeV
0
0
-1
12
0
5
10
15
20
25
14
16
18
20
22
24
26
Neutron Energy [MeV]
Neutron Energy [MeV]
12
Results - P isotopes production (II)
34
Cross Section [mb]
2.0
Production of P15
35
n+ Cl reaction
1.5
1.0
0.5
0.0
14
16
18
20
22
24
26
Neutron Energy [MeV]
Q = -1.1 MeV
13
Results - S isotopes production
Cross Section [mb]
2.5
32
Production of S16
35
n+ Cl reaction
2.0
1.5
1.0
0.5
Q = -1.79 MeV
0.0
20
21
22
23
24
Cross Section [mb]
3.0
33
80
Production of S16
70
n+ Cl reaction
35
60
50
40
30
20
Q = -9.22 MeV
10
0
25
10
12
14
Neutron Energy [MeV]
16
18
20
22
24
26
Neutron Energy [MeV]
35
600
Production of S16
34
Production of S16
35
35
300
n+ Cl reaction
n+ Cl reaction
500
Cross Section [mb]
Cross Section [mb]
250
400
300
200
100
Q = -4.15 MeV
0
5
10
15
20
Neutron Energy [MeV]
25
200
150
Q = 0.62 MeV
100
50
0
0
5
10
15
20
Neutron Energy [MeV]
25
14
Results - Cl isotopes production
34
800
35
Production of Cl17
35
n+ Cl reaction
700
50
40
30
20
10
Q = -1.26 MeV
35
n+ Cl reaction
600
500
400
300
200
100
0
0
14
16
18
20
22
24
0
26
5
10
15
20
25
Neutron Energy [MeV]
Neutron Energy [MeV]
36
Production of Cl17
0.9
35
n+ Cl reaction
0.8
Cross Section [mb]
Cross Section [mb]
60
Production of Cl17
Cross Section [mb]
70
0.7
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
Neutron Energy [MeV]
25
15
Results - 36Cl Isotope Cross Section
36
1.4
Production of Cl17
0.9
5
35
35
n+ Cl reaction
1.2
0.8
10
15
20
25
30
1.4
36
Cl(n,g) Cl
Total
Discrete
Continuum
(n,gg)
1.2
0.7
1.0
0.6
0.8
0.8
0.6
0.6
0.4
0.4
0.4
0.3
0.2
0.2
ng [b]
Cross Section [mb]
0
0.5
0.2
0.0
0
5
10
15
20
25
Neutron Energy [MeV]
1.0
0.0
0
5
10
15
20
25
30
Neutron Energy [MeV]
Contribution to the cross section
Energy of emitted gamma= 8.79 MeV
- discrete and continuum states
- Total = discrete + continuum
different gg cascades were evaluated
16
Results – Cross Section Calculation Conditions
CS – evaluated with Talys (standard input)
Wood Saxon potential parameters
1) Incident channels
(n + 35Cl)
Real part
2.2 (d + 34S)
Imaginary part
U = 54 MeV
W = 0.32 MeV
r = 1.2 fm; a = 0.67 r = 1.2 fm; a = 0.67
U = 112 MeV
W = 0.4 MeV
r = 1.2 fm; a = 0.67 r =1.2 fm; a = 0.67
2) Emergent channels
2.3 (t + 33S)
U = 166 MeV
r = 1.2 fm; a = 0.67
2.1 (p + 35S)
W = 0.64 MeV
r = 1.2 fm; a = 0.67
2.4 (3He + 33P)
U = 172 MeV;
U = 59.6 MeV
W = 0.16 MeV
r = 1.2 fm; a = 0.67
r = 1.2 fm; a = 0.67
2.5 (a + 32P)
W = 0.57 MeV
r = 1.2 fm; a = 0.67 r = 1.2 fm; a = 0.67
U = 224 MeV
W = 0.8 MeV
r = 1.2 fm; a = 0.67
r = 1.2 fm; a = 0.67
17
Results - 36Cl Astrophysical Rate
10
8
35
36
36
Rate [ Cl]
Rate of Cl(n,g) Cl Reaction
10
7
3x10
6
0
2
4
6
9
8
10
0
T9 [X10 ] K
 8 
N A v ab T  = 

 m 
*
1
2
2I
  2I
k T  GT 
NA
B
3
2

0 


 E  Ex
1 
 ab E E exp  
0
1
k BT



dE

18
Discussion and Conclusions
CS evaluation
- Talys standard input
- Necessary for astrophysical rate evaluations
– Improving the nuclear astrophysical data of 36Cl abundance, its origin and
production during the s – process
- Improving a series of problems connecting with the uncertainties in the (n,p), (n,a)
and (n,g) reactions leading to the decreasing or increasing of the concentration of 36Cl
- These data are required for better understanding of the origin of the rare neutron
rich isotopes in the S-Cl-Ar region and for a discussion of the 40K/40Ar chronometer.
CS Experimental Data
- Poor data for incident fast neutrons in comparison with thermal and resonance
region for all possible emergent channels
- Necessary new experimental data evaluation
- One possibility – IREN the LNF new Intense Resonance Neutron Source
19
References
[1]
P. E. Koehler, S. M. Graff, H. A. O'Brien, Yu. M. Gledenov, Yu. P.
Popov, Phys. Rev. C, 47, 5, 2107 (1993).
[2]
W. A. Fowler, G. R. Caughlan, B. A. Zimmerman, Annu. Rev.
Astron. Astrophys., 5, 525 (1967)
[3]
E. M. Burbidge, G. R. Burbidge, W. A. Fowler, F. Hoyle, Rev.
Modern Physics, 29, 4, 547, (1957)
[4]
K. Takahashi, K. Yokoi, Atomic Data and Nuclear Data Tables, 36,
375, (1987)
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