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Neutron burning in Stars

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Structure and evolution

of AGB stars

M bol

T eff


The main s-process s

in AGB stars

H

12

C(p,γ) 13 N(β + υ) 13 C

13

C(α,n)

He-flash

neutron source 13 C(α,n)

16

dY

13

dt

dYn

dt

C

= −Y

= −


x

13

Y

C

X

⋅Y

4

⋅Y

n

He

⋅ ρ ⋅ N

⋅ ρ ⋅ N

A

A

συ

συ

13

16 O

C ( α , n)

X ( n,

γ )

+ Y

+ Y

13

C

12

C

⋅Y

⋅Y

4

He

1

H

⋅ ρ ⋅ N

⋅ ρ ⋅ N

A

A

συ

συ

13

12

C(

p,

γ )

C ( α , n)


Present status on 13 C(α,n) 16 O

σ(E) =

1

E

exp( 2πη)S(E)

Previous experiments

Indicate large uncertainty

In low energy range!


Low-energy, low-background

Experiment with 4π4

BaF 2 γ-array

α-beam


Experimental Set-Up@FZ-Karlsruhe

Active shielding

techniques;

Pulse shape

analysis;


Low energy reaction yield of

13 C(α,n)

16 O

Yield

Yield

/

/

mC

mC

10

10 6 6

10

10 5 5

10

10 4 4

10

10 3 3

10

10 2 2

10

10 1 1

10

10 0 0

10

10 -1 -1

Cosmic Ray &

Beam induced

background

0.3

0.3

0.4

0.4

0.5

0.5

0.6

0.6

0.7

0.7

0.8

0.8

0.9

0.9

1

E 1

E lab in

lab in

MeV

MeV

S-Faktor

S-Faktor

in

in

10

10 6 6 MeV

MeV

barn

barn

6

6

5

5

4

4

3

3

2

2

1

1

Kellogg

Kellogg

Bair

Bair

Brune

Brune

Davids

Davids

Drotleff

Drotleff

diese Arbeit

diese Arbeit

0

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1

1.2

E 1.2

E cm in

cm in

MeV

MeV

1 order of magnitude improvement in background reduction necessary!


proton number

Ni

Co

Fe

The s-Process

(n,γ)

(β − )

(β + )

Zn

Cu

80

Br, t 1/2 =17 min, 92 % (β − ), 8 % (β + )

p-process

p-only

Ge

Ga

Se

As

Kr

Br

Sr

Rb

s-only

r-only

Zr

Y

85

Kr, t 1/2 =11 a

79

Se, t 1/2 =65 ka

r-process

64

Cu, t 1/2 =12 h, 40 % (β − ), 60 % (β + )

63

Ni, neutron t number

1/2 =100 a

finished, press left mouse button to continue


s-process studies in lab

Neutron production by 7 Li(p,n) reaction at

1.98 MeV: Neutron spectrum resembles a

kT=30keV Maxwell Boltzmann spectrum!


Activation Method

MB neutron spectrum bombardment of natural sample (mg)

e.g. Krypton gas.

80

Kr(n,γ) 81 Kr(β--γ)

84

Kr(n,γ) 85 Kr(β - -γ)

86

Kr(n,γ) 87 Kr(β - -γ)

85

Kr(4.48h)

81

Kr(13.3s)

Measurement of resulting

γ-activity yields

cross section & reaction rate.


Cross section determination by

activation method

( ) (

−λ⋅t

P e )

irr

= ⋅ 1−

A t

irr

P = N ⋅ f

( ) = A( t )

A t

w

⋅φ

⋅σ

n

irr

⋅e

( n,

γ )

−λ⋅t

w

σ

( n,

γ )

1

η

n

( t )

λ ⋅e

λ⋅t

c

= ⋅


λ

N


f

I

⋅φ


(

−λ⋅t

) ( )

irr

− ⋅tc

1−

e 1−

e

w

I

t

−λ⋅t

( ) ( )

( )

c

c

−λ⋅tc

t = η ⋅ A t ⋅e

⋅ dt = η ⋅ ⋅ A( t )

c


0

w

1−

e

λ

N: number of target atoms/cm 2

t irr : irradiation time

t w : waiting (transport) time

t c : counting time

η: efficiency of detection system

f: neutron absorption factor

w

σ (n, γ) : energy averaged cross section

φ n : time integrated neutron flux

I(t c ): yield


Neutron sources VdG

In-beam γ-measurement for A X(n,γ) A+1 X


In beam cross section

I

γ

= φ ⋅σ ⋅ N ⋅b

⋅η

( )

n n,

γ

I γ : gamma yield

σ (n, γ) : energy averaged cross section

φ n : time integrated neutron flux

N: number of target atoms/cm 2

η: detector efficiency

b: gamma branching

Through summing effects

~90% efficiency

In large detectors


In-Beam γ-Spectra


Neutron induced nucleosynthesis

dN

A,

Z

dt

() t

( + λ ⋅ N )

= −nn

⋅ N

A,

Z

συ − λA,

Z

⋅ N

A,

Z

+ nn

⋅ N

A−1,

Z

συ

A

A−1,

Z A,

Z −1

A,

Z −1

Approximation for s-process network for A neglecting branching points

dN

A

dt

() t

= −nn

⋅ N

A

συ + nn

⋅ N

A

A−1 συ

A−1


Cross section and abundance

dN

A

dt

() t

= −nn

⋅ N συ

A

+ nn

⋅ N συ

A

A−1 A−1

For time integrated neutron exposure

τ ≡ ∫

n n


υ ⋅dt

And relation for s-wave neutron capture συ = σ ⋅ υ

dN

A


For equilibrium:

( t)

= −N


A

+ N

A−1σ

A−1

( t)

dN

A = 0;

N


A

= N

A A

d

=

−1σ

−1

τ

const


s-process results

Low neutron capture

cross section at

closed shell nuclei,

N=50, 82, 126

⇒ enrichment of

closed shell nuclei,

⇒ s-process peaks!


The classical s-process model

Correlation between observed and calculated

σ·N A vs A curve reflects two neutron exposure

events with different neutron flux exposure:

weak s-process: τ w =4mb -1 ,

main s-process: τ m =0.3mb -1

Indication for s-process branchings


s-process branching points

Branching point analysis

provides important information

on s-process conditions

n-flux, density, temperature

r-process shielded

branching point

148

Pm branching point is reflected in the observed

abundances of the s-isotopes 148 Sm and 150 Sm.

β-unstable

f

β

=

λ

β

+

λ

n

β

n

συ


σ

σ

148

150

Sm

Sm

N

N

148

150

Sm

Sm


0.9


Accurate analysis of the neutron density depends on:

• accuracy In the cross section measurements (20%)

• stellar decay rate of 148 Pm

(not necessarily identical with laboratory decay rates

– e-capture, thermally induced decays …

Neutron flux: ~(4.1±0.6)·10 8 cm -3

f

β

=

λ

β

+

n

λ

n

β

συ

148

Pm


σ

σ

148

150

Sm

Sm

N

N

148

150

Sm

Sm


0.9

n

n

=

1−

f

β

f

β


λ

συ

β

148

Pm

=

1−

f

β

f

β


υ ⋅

σ

1

148

Pm


t

1/ 2

ln 2

(

148

Pm)


Additional s-process parameters

deduced from branching point analysis

Temperature dependent t 1/2

Density dependent (e-capture) t 1/2

Temperature dependent t 1/2

through isomer population


End-points of s-process Pb

First tests at n-ToF neutron source

204,206,207,208

Pb(n,γ) 205,207,208,209 Pb, 209 Bi(n,γ) 210 Bi

Po

84

Bi

83

Pb

82

Tl

81

Hg

80

s-process

feeding

204

203

205 206 207 208 209

β- β- β- β-

204

EC

205

β- β-

206

202 203 203 204 205

α

α

210 211

209

207

β-

β-

210m

210 g.s.

α

β-

211

r-process contributions

Old star abundance distribution

points to r-process origin of Pb

Z

N

122 123 124 125 126 127 128

n-capture on stable

Pb isotopes needed!


CERN accelerator Complex

n_TOF

Linac(s): up to 50 MeV PSB: up to 1 GeV PS: up to 24 GeV

alberto.mengoni@cern.ch


CERN accelerator Complex: n_TOF

1 pulse/2.5 s

alberto.mengoni@cern.ch


alberto.mengoni@cern.ch

CERN n_TOF Facility

• Design: the n_TOF Target

• The Tunnel

movie by V Vlachoudis

Pb target 80x80x60 cm 3

In water (3cm) filled Al container

Production 300 n/p

Shielding required for γ,µ,π absorption


Neutron flux distribution @ n-Tof


Neutron energy

E

n

∆E

E

n

= 0.5⋅m

n

=

2


L

Time of flight technique

2

−10

⎛ L ⎞ 0.5⋅

mn

0.5⋅939.59MeV

7.23⋅10

[ s] ⋅ L[ cm]

⋅⎜

⎟ t = ⋅ L =

⋅ L =

2

⎝ t ⎠ En

En[ MeV ] ⋅c

En[ MeV ]

( ∆L) 2 + ( υ ⋅ ∆t) 2

n

Energy resolution

n

For 180 m flight path

a 10keV neutron has

a flight time of t=41µs

∆E n /E n ≈10 -3

180 m flight path


Conversion example

Conversion of time of flight

spectrum into the neutron

energy spectrum for the

n capture reaction 151 Sm(n,γ)


counts

n-capture on Pb - first results

208

Pb(n,γ) 209 Pb ToF

spectrum simulation

204

Pb(n,γ) 205 Pb

1/v lav

resonances

neutron-energy [MeV]

neutron-energy [MeV]


Pb analysis with r-Matrix

204

Pb

In general, good agreement with previous parameters. But,

only 4 resonances below 7 keV have complete

resonance parameters in literature


Detail of Pb analysis

204

Pb

Analysis still underway… but results indicate that previously

adopted resonance parameters need improvement!


Conversion example

Conversion of time of flight

spectrum into the neutron

energy spectrum for the

n capture reaction 151 Sm(n,γ)


Multitude of open questions!

• impact of threshold cluster states in He burning

• low energy contributions to neutron sources

• neutron capture on light nuclei – neutron poison

• neutron capture on long-lived radioactive nuclei

for branching point analysis

• end-point of s-process (n-capture on Pb, Bi isotopes)

The accuracy of stellar s-process abundance distribution

limits the accuracy of the predicted r-process abundance

distribution and the identification of the r-process site!

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