Nuclear Signatures & Nuclear Physics

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Nuclear Signatures & Nuclear Physics

Topics in Nuclear Astrophysics

Michael Wiescher

University of Notre Dame

Hydrogen burning in Sun

Explosive reactions

in the SN shock front

Helium burning in Red Giants

Notre Dame JINA lectures, Fall 2003

rp-process on accreting

white dwarfs (Nova) or

neutron stars (X-ray burst)


Out-Line

• General concept and definitions

• Hydrogen burning sequences

• Nucleosynthesis in late stellar evolution

• Nucleosynthesis in explosive burning in supernova

• Explosive burning in cataclysmic binary systems

• Nucleosynthesis in Big Bang and Cosmic Rays


Topics in Nuclear Astrophysics I

Nuclear Signatures & Nuclear Physics

Observational Signatures

Abundances

Light-curves & radioactivity

Nuclear energy production rate

Nuclear reaction cross sections

Nuclear reaction mechanisms

Techniques for determining cross sections


Signatures of

Nucleosynthesis

galactic abundance distribution

• nucleosynthesis processes

• nucleosynthesis history

of our universe

• cosmic chemical evolution

Abundance

10 10

10 5

10 0

10 -5

stellar H-, He, C, O, Si-burning

cosmic rays

stars, supernovae

s-process

He-burning in AGB stars,

massive stars

p-process

site disputed

r-process

type II supernovae,

merging neutron stars

0 50 100 150 200

A


References

Chemical Evolution of Galaxies

J Audouze, B M Tinsley

Annual Review of Astronomy and Astrophysics. Volume 14, Page 43-79, Sep 1976

Element Production in the Early Universe

D N Schramm, R V Wagoner

Annual Review of Nuclear Science. Volume 27, Page 37-74, Dec 1977

Elemental and Isotopic Composition of the Galactic Cosmic Rays

J A Simpson

Annual Review of Nuclear and Particle Science. Volume 33, Page 323-382, Dec 1983

Nucleosynthesis

J W Truran

Annual Review of Nuclear and Particle Science. Volume 34, Page 53-97, Dec 1984

NUCLEOSYNTHESIS IN ASYMPTOTIC GIANT BRANCH STARS:

Relevance for Galactic Enrichment and Solar System Formation

M. Busso, R. Gallino, G. J. Wasserburg

Annual Review of Astronomy and Astrophysics. Volume 37, Page 239-309, Sep 1999


Site-Specific

Specific

Nucleosynthesis Pattern

Nova (Chandra)

Metal-Poor Halo Star (HST)

Mg

Ne

O

On-line observation of nucleosynthesis products!


Meteorites

Chondrites: Chondrules - small

~1mm size spherical inclusions in matrix

Meteoritic inclusions are

early condensates of

nucleosynthesis ejecta –

supernovae, novae,

stellar winds AGB stars

STELLAR NUCLEOSYNTHESIS AND THE ISOTOPIC COMPOSITION OF PRESOLAR GRAINS

FROM PRIMITIVE METEORITES

Ernst Zinner, Annual Review of Earth and Planetary Sciences. Volume 26, Page 147-188, May 1998


Cosmo-Chemistry Chemistry of Meteorites

Chondrule

AGB-Stars

Supernovae

Novae


Light and Light-Curves

Light intensity correlates with energy-output

Light curve follows the radioactive decay law 56 Ni, 56 Co, 44 Ti


Galactic Radioactivity - γ-Radiation

Gamma-Ray Astronomy; R Ramaty, R E Lingenfelter,

Annual Review of Nuclear and Particle Science. Volume 32, Page 235-269, Dec 1982

1 MeV-30 MeV

γ-Radiation in Galactic Survey

44

Ti in Supernova Cas-A Location

1.157 MeV γ-radiation

(Half life: 60 years)


Nuclear Reactions in Stars

• generate energy

• create new isotopes and elements

γ

12

C(p,γ) 13 N

reaction probability ⇒ σ: reaction cross section

11


Cross Section – a reminder!

cross section =area!

2

2 3

σ ≅ π ⋅ r nucleus

≈ 1.26⋅π

⋅ A

[ fm]

projectile orbital momentum l

h

p = hk

= ;

D

L = hl ⇒


L = b×

p

b = D ⋅l



b


p

= b ⋅hk

= b ⋅

h

D

orbital momentum l in σ

2l

+ 1

σ

l

( E)


E

2 2

2 2

( r − r ) = π ⋅( b − b )

σ

l

≅ π ⋅ Fl

= π ⋅

l

+

σ ≅ π ⋅

l

l+

1

l 1

2 2 2

( l + 1)

− l ) ⋅D

= π ⋅( 2l

+ 1)

l

⋅D

2


Transmission through the barrier


⎢−


2

h d


dr

⎪⎧

V ( r)

= ⎨

⎪⎩

2

2

2

Z1Z2e

r

Z1Z2e

r

l(

l + 1) h

+

2


r

2

+ V

nucl

r≥R

0

r<

R

2

0


+ V ( r)

− E⎥ϕl

( r)

= 0


ϕ ( r)

=

l

A⋅

F

l

( r)

+

B ⋅G

l

( r)

r

R 0

P

l

2

ϕl

( r = ∞)

1

= ⇒ Pl

( E,

R0

) =

ϕ

2

2

( r = R0 )

F ( E,

R ) + G ( E,

R

l

F l , G l are the Coulomb wave functions

l

0

l

0

)


Cross section for charged particles

Exponential decline towards lower energy due to Coulomb barrier


Resonant Reaction Mechanism

resonance capture: population of unbound state in compound nucleus

E r

2

S in

E x

E r

S out

Γ

i

Γ

Γ

Γ

in

out

γ




P


l

P

E

l

P


l


ψ


2L+

1

γ

ψ

f

C

ψ


H

out

ψ

H

gs

int

s

ψ

ψ

+ ψ

H

i

T

R

em

2

+ ψ

H

ψ

s

C

in

ψ

C

2

2

2 Γin

⋅Γout

σ( E)

= π D ω⋅

2

ω =

2J

+ 1

( 2j

+ 1) ⋅( 2j

+ 1)

p

( )

2

E−E

+ ( Γ 2)

T

r


Direct Capture Mechanism

one-step reaction mechanism through e-m interaction

σ ( E)

= P ⋅ ψ H ψ + ψ

l f em p T

2

E r

P l is the penetrability through the Coulomb

S in

and orbital momentum barrier

γ energy changes with particle energy


cross section for neutron capture


⎢−


2

h d


dr

2

2

+

l(

l + 1) h

2


r

2



E⎥ϕl

( r)


no Coulomb barrier, just orbital momentum term!

=

0

P

l

=

ϕl(

r = ∞)

ϕ ( r = R )

l

0

2


P

P

P

l=

0

l=

1

l=

2

=

=

=

r

=

λ

k ⋅ r

3

( k ⋅ r)

2

( k ⋅r)

5

( k ⋅r)

2

+ 3( k ⋅r) + ( k ⋅ r)

( 1+

)

( 9

4

)


Cross section for neutral particles

l=0

l=1

l=0, s-wave follows 1/v law,

l=1, p-wave experiences orbital momentum barrier


Hauser Feshbach Approach

assumption of many resonances!

(high level density ρ in particle

unbound region of compound nucleus)

i

+

j


o +

m

σ ( E)

i

= π ⋅D

2

j


1+

δ

i,

j

( )


2 j + 1 ⋅( 2 j + 1)

i

j

J , π

( 2J

+ 1)

T

j

( E,

J,

π ) ⋅To

( E,

J,

π )

T ( E,

J,

π )

tot

T

:

transition probability

Smooth Coulomb barrier determined energy dependence!


inverse reactions

A + a ⇒ B + b

or

B + b ⇒ A + a


detailed balance theorem I

A + a

B + b

ϕ H ϕ =

Bb

Aa

2

ϕ

Aa

H

ϕ

Bb

2

C J

2

identical matrix elements for transition

through same compound configuration

σ

σ

Aa

Bb

= π D

= π D

2

Aa

2

Bb


(2


(2

j

j

A

B

(2J

+ 1)

+ 1) ⋅(2

j

(2J

+ 1)

+ 1) ⋅(2

j

a

b

+ 1)



+ 1)

ϕ

ϕ

Bb

Aa

H

H

ϕ

ϕ

Aa

Bb

2


detailed balance theorem II

A + a

C J

B + b

theorem allows to calculate

reaction cross section from

known cross section of the

inverse reaction process!

λ

2

Aa


µ

Aa

1

⋅ E

Aa

;

µ

Aa

=

m

m

A

A

⋅m

+ m

a

a

E

Aa

=

E

cm

σ

σ

Aa

Bb

=

(2

(2

j

j

B

A

+ 1)(2

+ 1)(2

j

j

b

a

+ 1)

+ 1)


m

m

B

A

⋅m

⋅m

b

a



E

E

Bb

Ab


Conclusion

• observational indication for nuclear processes

in the past and present universe!

• low energy reaction processes through

resonant and non-resonant reaction channels

• cross section determination through

single resonance formalism

direct capture or transfer formalism

statistical model formalism

detailed balance approach

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