Big-Bang Nucleosynthesis - Cyclotron Institute

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Dec 12, 2013 (3 years and 6 months ago)

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Primordial
Nucleosynthesis


S
tandard

B
ig
-
B
ang

N
ucleosynthesis

of
4
He
, D,
3
He,
7
Li

compared with
observations


The
SBBN “lithium problem”: nuclear aspects


(
6
Li,
9
Be

,
10,11
B)
and

CNO
in extended SBBN network


Conclusions

Alain Coc


(
C
entre de
S
pectrométrie
N
ucléaire et de
S
pectrométrie de
M
asse, Orsay)

Three observational evidences for the
Big
-
Bang Model

1.
The expansion of the
Universe

2.
The Cosmic Microwave Background radiation (CMB)

3.
Primordial
nucleosynthesis


Reproduces the light
-
elements
4
He, D,
3
He,
7
Li
primordial
abundances over a range of nine orders of magnitudes.


First determination of the baryonic density of the Universe,
(1
-
3)
×
10
-
31
g/
cm
3

[Wagoner 1973]
,
need for baryonic dark
matter


First determination of the number of light neutrino families,
N
ν

≤ 3
[Yang, Schramm,
Steigman
, Rood 1973]



Number of
neutrino families
N
ν

=
2.984
±
0.008
[
LEP
experiments]

D
etermination of the baryonic density of the
Universe



Baryonic density

B

4.5
×
10
-
31
g/cm
3

from the anisotropies
in the
C
osmic
M
icrowave
B
ackground
radiation,
....
,
WMAP
,
Planck (
2014?)


b
h
2
=
0.02249

0.00057

=(
6.16

0.16)
×
10
-
10

[WMAP: Komatsu et al. (
2011)
]




/

C

with


C

the critical density
T
he n
umber
of baryons per
photon,




n
b
/n


and


b
h
2
= 3.65

10
7


BBN: a probe of physics of the early Universe

Why BBN after WMAP?

Key questions in Cosmology:


Nature of dark matter


Nature of dark energy


Gravitation = General Relativity ?


Variation of constants

G→G(1+α
2
(t))

[Coc, Olive,
Uzan

&
Vangioni

2009]

(
Tensor
-
Scalar

gravity
)

The 12 reactions of standard BBN

Standard BBN


No convection


No diffusion


No mixing


Known physics


<12 reactions



Simple
nucleosynthesis

(?)





10 thermonuclear reaction rates deduced from experimental data


First 2 from theory: weak
n

p

rate and
p
(n,

)d


Additional 400 reactions up to CNO

T
>10GK

T
<
1GK

Sensitivity to thermonuclear reaction rates


Y
Y


l
n
Y



l
n
N
A

v





W
M
A
P
´

N
A

v
N
A

v


ln(
Y
) /


ln(
N
A
<

v>)

E
0
(

E
0
/2)

(MeV @ 1GK)

Reaction

4
He

D

3
He

7
Li


n
(n

p)

0.73

0.42

0.15

0.40

1
H(n,

)
2
H

0

-
0.20

0.08

1.33

0.025

2
H(p,

)
3
He

0

-
0.32

0.37

0.57

0.11(0.11)

2
H(d,n)
3
He

0

-
0.54

0.21

0.69

0.12(0.12)

2
H(d,p)
3
H

0

-
0.46

-
0.26

0.05

0.12(0.12)

3
H(d,n)
4
He

0

0

-
0.01

-
0.02

0.13(0.12)

3
H(

,

)
7
Li

0

0

0

0.03

0.23(0.17)

3
He(n,p)
3
H

0

0.02

-
0.17

-
0.27

3
He(d,p)
4
He

0

0.01

-
0.75

-
0.75

0.21(0.15)

3
He(

,

)
7
Be

0

0

0

0.97

0.37(0.21)

7
Li(p,

)
4
He

0

0

0

-
0.05

0.24(0.17)

7
Be(n,p)
7
Li

0

0

0

-
0.71

At WMAP baryonic density

[
Coc &
Vangioni

2010]


n

p


weak reaction
rates

The neutron lifetime is still a matter of debate (but not essential to BBN)


n
=
885.7

0.8 s
[PDG 2008]

or


n
=
878.5

0.7

0.3 s
[
Serebrov

et al. 2005]


881
.
5
±

1
.
5
s
[
PDG
2011]
;
880

884 s
[
Wietfeldt

&
Greene

2011]


n

p



n
-
1






(phase space)

(e distribution)

(

e

distribution)
dE

+
small
corrections



Weak rate change mostly affects n/p ratio at freeze out and hence
4
He
abundance



Change in expansion rate gives similar effect (n/p
freezeout

when weak rate


expansion rate)


p

e

®
n


p


e
®
n

e

p

e



e
®
n
n


e
®
p

e

n

e

®
p


e
n
®
p

e



e
1
H(n,

)D : theory versus experiments

Rate calculated from Effective Field theory with (theoretical)
uncertainties of 4%
[Chen & Savage (1999)]

or 1%
[
Rupak

(2000)]

compared to experiments
[
Arenhovel

&
Sanzone

(1991) review]

BBN energy
~ 25
keV

Additional check with
polarized beam
E1

and
M1
measurements
[
Tornow

et al. (2000)
]
,
e
-
scattering
[
Ryezaveva

et al. 2006
]

and new
(>1991) cross section
measurements
[Suzuki
et al. (1995),
Tomyo

et
al. (2003)]


Chen & Savage (1999)

Boltzmann


10 rates deduced from experimental data

Compilations and
evaluations

for/
including

BBN
thermonuclear

rates



Smith,
Kawano

&
Malaney

1999

(
with

uncertainties
)



NACRE,
Angulo

et al. 1999

(7/10,
tabulated

rates and
uncertainties
)



Nollett

&
Burles

2000

(no rates provided)



Cyburt
, Fields

&

Olive

2003
(
revaluation

of NACRE)



Serpico

et al.
2004

(rates and
uncertainties

provided
)



Descouvemont
,
Adahchour
,
Angulo
, Coc &
Vangioni
-
Flam

2004

[DAACV]



«

R
-
Matrix

» formalism: S
-
factors fits of data constrained by theory



Provide also
reaction rate uncertainties



Cyburt

2004

(rates
provided,
uncertainties calculated
but not provided)



Update

with
post 2004
experimental data yet to be done…

Systematic

uncertainties

:
prompt
versus
activation

measurements


The
3
He(

,

)
7
Be

reaction

Sensitivity = 0.97

E
0
(

E
0
/2
) = 0.37(0.21) MeV

[DAACV]

New precise measurements

:



Prompt
[Brown et al. 2007,
Confortola

et al. 2007,
Costantini

et
al. 2008]



Activation
[Nara Singh et al.
2005, Brown et al. 2007,
Confortola

et al. 2007,
Gyürky

et al. 2007
]



Recoil

[Di
Leva

et al. 2009]

Reanalysis of

3
He(

,

)
7
Be rate

[
Cyburt

&
Davids

2008
]
:

S(0)

= 0.580
±
0.043
keV.b

(13% higher than in DAACV04
)

S(0)

= 0.56
±
0.02
±
0.02
keV.b

[
Adelberger

et al.
2010]

Determination of primordial abundances

Primordial abundances :

1)
Observe a set of primitive objects born when the Universe
was young

2)
Extrapolate
to zero

metallicity
” (the heavy elements whose
abundance increase with time) e.g.
Fe/H, O/H, Si/H,….


0



4
He

in H II (ionized H) regions of blue compact
galaxies:
0.245
<
Y
p

<
0.262

[Aver, Olive &
Skillman

2011]


D

in remote cosmological clouds (i.e. at high redshift) on the line of
sight of quasars:
(2.84
±
0.26)
×

10
-
5

(1
-

)


[Fields &
Sarkar

2008]



3
He

in H II regions of
our

Galaxy
:

3
He/H ≤ (1.1
±
0.2)
×
10
-
5

[
Bania

et al. 2002
]


7
Li

at the surface of low
metallicity

stars in the halo of our Galaxy:
Li/H = (1.58
±
0.31)

10
-
10
[
Sbordone

et al. 2010
]

[
Izotov
,
Thuan

&
Stasinska

2007]

Burles

&
Tytler

1998a,b;

O’Meara et al. 2001;
D’Odorico

et al. 2001;
Pettini

& Bowen 2001
;
Kirkman

et al. 2003, Crighton et al. 2004,
Pettini

et al.
2008,
Fumagalli

et al. 2011,
Srianand

et al. 2010, Cooke et al.
2011,
Pettini

et al. 2012

4
He

D

[
Izotov
,
Thuan

&
Stasinska

2007]

4
He

©
Sbordone

in Lithium in
the Cosmos 2012

Observations

Beware of systematic uncertainties
(
4
He

and

Li
)


Li



Using most recent



Nuclear
data


Abund
an
ce determinations


At



given by WMAP


A
greement for
4
He, D
and

3
He



D
ifference
of a factor of

≈ 3
for Li !

Monte
-
Carlo BBN versus observations


Monte
-
Carlo (rate uncertainties)
BBN calculation
function of


or

b
h
2

compared with
observations

BBN calculations

Observations

Cyburt et al.
2008

Coc & Vangioni
2010

*

4
He

0.2486
±
0.000
2

0.2476
±
0.000
4

0.245
-
0.262


10
0

D/H

2.49
±
0.17

2.68
±
0.15

2.84
±
0.26


10
-
5

3
He/H

1.00
±
0.07

1.05
±
0.04

(0.9
-
1.3)


10
-
5

7
Li/H

5.24
+0.71
-
0.62

5.14
±
0.50

1.58
±
0.31


10
-
10

Monte
-
Carlo BBN versus
observations at
η
WMAP

*[
Aver, Olive &
Skillman

2011;
Fields
&
Sarkar

2008;
Bania

et al.
2002;

Sbordone

et al. 2010
]


Nuclear solution to the Li problem ?

Nuclear
solution to the Li problem
?


At
η
WMAP

7
Li

from
7
Be

decay


Need extra
7
Be
destruction
(normally trough
7
Be(
n,p
)
)

Tentatives proposed solutions


The
7
Be
(d,p)
8
Be*

2


reaction
[Coc et al.
2004
]


Unknown
Resonances in

7
Be + n, p, d, t,
3
He
and



?
[
Chakraborty
, Fields &
Olive
2011]


The

7
Be(n,

)
4
He
reaction

[M.
Gai
priv. comm.
]


Exotic neutron sources


Other solutions beyond the
Standard Model


New
7
Be (i.e.
7
Li) destruction channels


The
7
Be
(d,p)
8
Be*

2


reaction


Experiment at Louvain LN
[
Angulo

et al. 2005
]

: no
(integrated) cross
-
section enhancement


Hypothetical
resonance at
E
R

= 200
±
100
keV

with


40
keV

[
Cyburt

&
Pospelov

2009
];

corresponding to
≈16.7 MeV
9
B
level

?



No resonance observed at Oak Ridge in
D(
7
Be,d)
7
Be
scattering
[O’Malley et al. 2011]


Measured
E
x
=16.8 MeV
and


=81
keV

[Scholl
et al. 2011
]

primordial effect on
7
Li < 4%
[
Kirsebom

&
Davids

2011]


The

7
Be(n,

)
4
He
reaction

[M.
Gai
priv. comm.]


If

l
=
0
,

7
Be+n→2


(forbiden)

rate from
Wagoner 1969



I
f

l
=1
, could contribute to
7
Be
destruction
[
Serpico et al. 2004]


Experimental project with
n
beam from
Liquid Lithium Target
(LiLiT) at the Soreq Accelerator Facility (SARAF)
[M.
Gai
priv. comm.
]

Other resonances

?


Unknown Resonances in

7
Be + n, p, d, t,
3
He
and



?

[
Chakraborty
, Fields & Olive
2011]

4.00

10.00


15.04 (2
-
, 1
-
) ?

14.99 (2
-
, 1
-
) ?



7
Be+
3
He

15.00

9.000


6.580

(
2
+
)

5.220


3.353

2
+

10
C

16.50 (2+)



p
?

6
Be+


“Hoyle”
states ?

Poorly

known spectroscopy

9
B+
p

5.10



?

© F.
Hammache

Indirect study of
10
C
,
9
B

&
10
B

states via (
3
He,t), (
3
He,d) reactions

on
10
B
and
9
Be

targets

Recent
Orsay

Tandem Experiment

3
He

@

35MeV

t

or d

Position

gas chamber


E

proportional

counter


Plastic scintillator (E)

10
B,
9
Be targets 100

g/cm
2

DSSDs

ORSAY SPLIT
-
POLE
spectrometer

.

B

⡰猩


.

䔠† † † †
† † †
particle

. E

identification

© F.
Hammache

First results from Tandem experiment



No new
10
C

level


Broad levels?


U
nlikely

to contribute
(Coulomb barrier)
[
Broggini

et al.
ArXiv:
1202.523]


In
search

of new
10
C

levels
:
10
B
(
3
He,t)
10
C

BBN extended network up to CNO


Applications of extended network:




CNO
seeds for first
stars :
CNO/H
> 10
-
11

[
Cassisi

&
Castellani

1993]

:
CNO/H > 10
-
13

[
Ekström

et al. 2008]


Potential
neutron sources for
7
Be

destruction by
7
Be(
n,p
)
7
Li(p,

)
4
He
in BBN (the lithium problem
)?
Unexpected effect (e.g.
7
Li

sensitivity to
n(
p,γ
)d
)


Standard CNO primordial abundances versus exotic
production (e.g. “variation of fundamental constants”
)


Extended network predictions :
CNO/H ≈ 10
-
15

[
Iocco

et al. 2007
]

but reaction rates not given

CNO
nucleosynthesis

updated network

Z

A

n

1

H

1
-
3

He

3,4,6

Li

6
-
9

Be

7,9
-
12

B

8,10
-
15

C

9
-
16

N

12
-
17

O

13
-
20

F

17
-
20

Ne

18
-
23

Na

20
-
23



59 isotopes :


391
reaction rates
A
Z + n, p, d, t,
3
He
and


,
m
ostly unknown

hence possibly
high yield
uncertainty



Descouvemont

et al. 2004 (DAACV)



Angulo

et al. 1999 (NACRE I
)



Iliadis

et al. 2010



Talys

(271 rates
)

within 3 orders of
magnitude, at
T

1 GK
, compared with
experiments!



….
.


R
eaction rate variations by
0.001
,
0.01
,
0.1
,
10.
,
100.

&
1000.

factors


Reevaluation of selected rates


33 decay rates
[Audi et al. 2003
]

Reaction

Fractional change in CNO abundance

Test rate

reference

Rate factor

0.001

0.01

0.1

10.

100.

1000.

7
Li(d,

)
9
Be

1.00

1.00

1.00

1.01

1.11

2.10

TALYS
*

7
Li(
d,
n
)
2


1.66

1.65

1.55

0.28

0.06

0.02

Boy93
*

7
Li(
t
,n
)
9
Be

0.99

0.99

0.99

1.10

2.14

11.7

Bru90
*

7
Li(t
,2n
)
2


1.00

1.00

1.00

0.99

0.91

0.53

MF89

8
Li(n,

)
9
Li

1.00

1.00

1.00

1.01

1.06

1.62

Rau94

8
Li(

,

)
12
B

1.00

1.00

1.00

1.01

1.11

2.15

TALYS

8
Li(

,
n
)
11
B

0.89

0.89

0.90

1.97

11.2

78.1

Miz01
*

9
Li(

,
n
)
12
B

1.00

1.00

1.00

1.01

1.08

1.73

TALYS

10
Be(

,
n
)
13
C

1.00

1.00

1.00

1.00

1.03

1.28

TALYS

11
B(n,

)
12
B

0.91

0.91

0.92

1.81

9.91

87.7

Rau94
*

11
B(
d,n
)
12
C

0.70

0.71

0.73

3.67

30.2

280.

TALYS
*

11
B(
d,p
)
12
B

0.99

0.99

0.99

1.08

1.83

9.33

TALYS
*

11
B(
t,n
)
13
C

1.00

1.00

1.00

1.01

1.12

2.17

TALYS

11
C(n,

)
12
C

1.00

1.00

1.00

1.01

1.08

1.75

Rau94

11
C(
d,p
)
12
C

0.99

0.99

0.99

1.05

1.55

5.67

TALYS
*

12
C(t,

)
11
B

1.00

1.00

1.00

1.00

0.97

0.75

TALYS

13
C(d,

)
11
B

1.00

1.00

1.00

0.96

0.84

0.75

TALYS

Most important reactions for CNO
nucleosynthesis

*
Rate reevaluated in

Coc,
Goriely
,
Xu
,
Saimpert

&
Vangioni

2011

Main path
for:

H
, D,
3
He,
4
He,
7
Li,

6
Li,

9
Be
,
10,11
B
and
CNO (
12
C
), out of the
>400 reactions


6
LiBe
11
B and CNO
nucleosynthesis

Monte
-
Carlo BBN versus observations

*
Hammache

et al.
2010,
Ω
b
from

Spergel

et al. 2007


or
Komatsu et al. 2011



Number of atoms

[
Iocco

et al. 2007]

[Coc et al. 2012]

(
12
C+
13
C)/H (

10
-
16
)

5.5

6.75

(
14
C+
14
N)/H (

10
-
17
)

5.0

6.76

16
O/H (

10
-
20
)

2.7

9.13

CNO/H (

10
-
16
)

6.0

7.43

Number of
atoms

13
reactions

Monte
-
Carlo

[CV 2010]

424
reactions

Network
††

[Coc et
al. 2012]

4
He (
Y
p
)

0.2476
±
0.0004

0.2476

D/
H
(

10
-
5
)

2.68
±
0.15

2.59

3
He/
H
(

10
-
5
)

1.05
±
0.04

1.04

7
Li/
H
(

10
-
10
)

5.14
±
0.50

5.24

6
Li/
H
(

10
-
14
)

1.3
*

1.2


Estimated uncertainty:

CNO
/
H =(0.5
-
3
)
×
10
-
15

Counter intuitive
effects in BBN


The
1
H
(n,

)
D

reaction
affects mostly
7
Li

n(p,

)d


0.7


The
7
Li(
d,n
)2
4
He

reaction
affects
strongly the
CNO
but leaves
7
Li

(and other
isotopes) unchanged!


Systematic sensitivity
studies are
important

1.
Neutron injection at
constant rate

2.
Neutron injection from
decay with
τ
χ

= 40
mn


3.
Neutron injection from
annihilation with
T
C
= 0.3 GK

Alleviates the
7
Li

problem
at the expense of
D


Representative
results








[
Albornoz

Vásquez
,
Belikov
, Coc,
Silk &
Vangioni
, submitted]

Main collaborators

Elisabeth
Vangioni
,
Jean
-
Philippe
Uzan

(
I
nstitut d

A
strophysique de
P
aris
)


Keith Olive


(
U
. of
M
innesota
)


Pierre
Descouvemont
, Stéphane
Goriely

(
U
niversité
L
ibre de
B
ruxelles)



SBBN
+

WMAP in good agreement with
D
and
4
He
observations



However disagreement (factor of 3
-
4) with
Li

observations


Nuclear
:
most
probably no
but important to quantify needed depletion


Stellar depletion (
diffusion+turbulence
)
[
Korn

et al. 2006, Richard et al.
2005; http://
www.iap.fr
/
lithiuminthecosmos2012]
?


Cosmology and particle physics ?



Using extended network: minute amounts of
6
Li
,
9
Be
,
10,11
B

and
CNO

produced


Systematic sensitivity studies are important


SBBN is now a parameter free model !


When looking back in time,
Standard
BBN is the last milestone of
know physics
:
probe of the physics of the early Universe

Conclusions

Backup

Reaction

Fractional

change in
6
Li
abundance

Test rate

reference

Rate factor

0.001

0.01

0.1

10.

100.

1000.

3
He(t,

)
6
Li

1.00

1.00

1.00

1.03

1.31

4.11

FK90

4
He(d,

)
6
Li

0.004

0.013

0.010

9.97

99.7

995.

Ham10

Reaction

Fractional

change in
11
B
abundance

Test rate

reference

Rate factor

0.001

0.01

0.1

10.

100.

1000.

3
He(
t,
np
)
4
He

1.00

1.00

1.00

1.00

0.97

0.79

CF88

7
Be(
d,p
)
2


1.01

1.01

1.01

0.93

0.55

0.11

CF88

11
C(n,


)
2


1.16

1.16

1.15

0.40

0.01

0.0001

Rau94
*

Most important reactions for
6
LiBe
11
B
nucleosynthesis

Reaction

Fractional

change in
9
Be
abundance

Test rate

reference

Rate factor

0.001

0.01

0.1

10.

100.

1000.

7
Li(d,

)
9
Be

0.83

0.83

0.85

2.52

17.7

170.

TALYS
*

7
Li(
t
,n
)
9
Be

0.52

0.53

0.57

5.29

48.2

477.

Bru90
*

7
Li(
3
He,
p
)
9
Be

1.00

1.00

1.00

1.04

1.45

5.49

TALYS

7
Be(
d,p
)
2


1.01

1.01

1.01

0.95

0.67

0.38

CF88

7
Be(
t,p
)
9
Be

0.65

0.65

0.69

4.15

35.6

345.

TALYS
*

*
Rate reevaluated in

Coc,
Goriely
,
Xu
,
Saimpert

&
Vangioni

2011

Origin of CMB, SBBN and Li observations discrepancies


Stellar/Galactic ?




Observational bias: 1D/3D, LTE/NLTE model atmospheres, effective
temperature scale



Li stellar destruction
[
Korn

et al. (2006)]



Pregalactic

6
Li production
[Suzuki & Inoue (2002);
Rollinde

et al. 2005]



6
Li production by solar
-
like flares
[
Tatischeff

&
Thibaud

2007]


Non Standard Model(s) ?



Affecting expansion rate during BBN : Quintessence, Tensor
-
Scalar gravity,
ν
-
degeneracy,….


Variation of fundamental couplings :

em

[
Ichikawa & Kawasaki 2004]
, or
all

[Landau et al.
2005, Coc et al. 2007]


Massive particle decay

: could produce
6
Li and destroy
7
Li
[
Jedamzik

(2004,2006), Kawasaki et al. (2005), Ellis et al. (2005)]

n

p

weak reaction rate




n
=
885.7

0.8 s
[PDG 2004]





n
=
878.5

0.7

0.3

[
Serebrov

et al. 2005,
Mathews
,
Kajino

&
Shima

2004]



n

p
=

n
-
1






(phase space)

(e distribution)

(

e

distribution
)
dE

+
small corrections

[
Dicus

et al. (1982),
Brown & Sawyer (2001)
]

The
2
H(
d,n)
3
He

reaction

Sensitivity = 0.61

E
0
(

E
0
/2
) = 0.12(0.12) MeV

New precise measurements

of
2
H(d,n)
3
He (and
2
H(d,p)
3
H) reaction
at TUNL
[Leonard et al. 2006]

Excellent agreement with

DAACV
2004
fit within Gamow window



No change in central Li/H value



Reduced uncertainty



R
-
matrix fit reliability


The
2
H(
d,n)
3
He

reaction

New “Trojan Horse Method”
measurement
[
Tumino

et al.
2011]


~15%
difference with DAACV


~10%
change in
7
Li


~
8
%
change in
D


3
%
“theoretical uncertainty” (?)



Inhomogeneous BBN
[Thomas et al. 1993, 1994]



Primordial CNO BBN

[Iocco et al. 2007]

CNO nucleosynthesis

©Fields & Olive 2006



Origin of the rates ???



Data bases of nuclear level properties



Estimates following
Fowler & Hoyle
1964;
Wagoner

1967
prescriptions

Comparison between
Talys

and experiments

[
Iliadis

et al. 2010
]

Comparison between
Talys

and experiments

[NACRE
1999]

[Thomas
et al. 1993;
1994]

Comparison between
Talys

and
estimates

Rates based on
Fowler &
Hoyle 1964

and
Wagoner
1967

prescriptions

Reevaluated reaction rates

Stability of results with re
-
evaluated reaction rates

Independent re
-
evaluation of
8
Li(α,n)
11
B
by
La
Cognata

& Del
Zoppo

2011

Changes in
11
B(
d,n
)
by
11
B(
d
,p
)
cancel
each other

Changes
CNO
by
1.5%

CNO nucleosynthesis

Number of atoms

[Iocco et al.
2007]

Initial
Network

Updated
Network

(
12
C+
13
C)/H (

10
-
16
)

5.5

4.43

6.75

(
14
C+
14
N)/H (

10
-
17
)

5.0

3.98

6.76

16
O/H (

10
-
20
)

2.7

5.18

9.13

CNO/H (

10
-
16
)

6.0

4.83

7.43

CNO nucleosynthesis

Stability of results:

Nuclear uncertainties?


Need a Monte
-
Carlo and statistically defined uncertainties: TBD


Estimate from
i
) rate factor uncertainties
<10
at
T
=1 GK
,
ii) sensitivity study


CNO factor uncertainty

4