1. Reaction Rates Marialuisa Aliotta School of Physics
University of Edinburgh
principles of stellar structure and evolution
general features of thermonuclear reactions
experimental approach
Second European Summer School on Experimental Nuclear Astrophysics
St. Tecla, Sept. 28th – Oct. 5th 2003

2. The Macro-cosmos: some observables
Luminosity vs. surface temperature
Hertzsprung-Russel (HR) Diagram
Surprise!
SUPERGIANTS
No chaos, but order!
GIANTS
Stefan´s law: L = 4R2T4
Luminosity
sun
WHITE
DWARFS
MAIN
SEQUENCE
 Temperature [K]
~ 95% of all stars in MAIN SEQUENCE
highest probability of observing them in this stage
(cf. adulthood for human beings)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

3. The Macro-cosmos: some observables
Mass-Luminosity relationship
(for main sequence stars only)
L ~ M4 
more massive stars evolve more rapidly
mass (Msun) lifetime (years)
1 ~1010
5 ~108
10 ~107
L, T, M cannot take up ANY values
ORDER!
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

4. The Macro-cosmos: some observables
Abundance curve of the elements
Data sources:
Earth, Moon, meteorites,
stellar (Sun) spectra, cosmic rays...
Features:
distribution everywhere similar
12 orders-of-magnitude span
H ~ 75%
He ~ 23%
C  U ~ 2% (“metals”)
D, Li, Be, B under-abundant
exponential decrease up to Fe
peak near Fe
almost flat distribution beyond Fe
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

5. Experimental nuclear astrophysics
study energy generation processes in stars
study nucleosynthesis of the elements
What is the origin of the elements?
How do stars and galaxies form and evolve?
What powers the stars?
How old is the universe? …
MACRO-COSMOS
intimately related to
MICRO-COSMOS
NUCLEAR PHYSICS
KEY for understanding
Courtesy: M. Arnould
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

6. Quiescent stages of stellar evolution
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

7. Principles of stellar structure and evolution: quiescent evolution
Stellar structure and evolution controlled by:
Gravity  collapse
Internal pressure  expansion
Star composed of many particles (~1057 in the Sun)
Total energy: a) mutual gravitational energy of particles ()
b) internal (kinetic) energy of particles (including photons) (U)
For an ideal gas in hydrostatic equilibrium:
2U +  = virial theorem
Assume pressure imbalance
gravitational contraction sets in
amount of energy released -
internal energy change to restore equilibrium U = - ½ 
gas temperature increases
energy excess - ½  lost from star in form of radiation
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

8. Principles of stellar structure and evolution: quiescent evolution
gravitational contraction of gas (mainly H) increase of central temperature
if T high enough “nuclear burning” takes place
HYDROGEN BURNING (1st equilibrium)
4H  4He + 2b+ + 2n MeV
ash
of nuclear burning
energy source
gravitational collapse is halted  star undergoes phase of hydrostatic equilibrium
MAIN SEQUENCE STARS
Here:
T ~ 10 – 15 X106 K and r ~ 102 gcm-3 are required
M > 0.1 M
(Jupiter = failed star)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

9. (also depends on CNO abundance)
Principles of stellar structure and evolution: quiescent evolution
Hydrogen burning
Two main mechanisms: proton-proton chain and CNO cycle
Energy production rate
M < 1.5 M  T6 < 30 
p-p chain
M  1.5 M  T6 > 30 
CNO cycle
(also depends on CNO abundance)
(Fiorentini’s lecture)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

10. Principles of stellar structure and evolution: quiescent evolution
H exhausted in core
isothermal He core
contraction sets in
temperature
increases
H-burning shell
R ~ Ri  Ts ~ 3-4x103 K
Wien’s law: maxT = const.
RED GIANT STARS
contracting core
expanding envelope
when T ~ 108 K and r ~ 103 gcm-3 (minimum mass ~ 0.5 M)
HELIUM BURNING (2nd equilibrium)
3a  12C
12C(a,g)16O
+ 8 MeV
nuclear burning ashes
energy source
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

11. Principles of stellar structure and evolution: quiescent evolution
12C/16O BURNING
… 12C ashes = Ne, Na, Mg
… 16O ashes = Al, … Si
major ash = 28Si
SUPER RED-GIANT STARS
28Si MELTING
… A = 40-65
major ash = 56Fe
PRE-SUPERNOVA STARS
further reactions
become endothermic
final gravitational collapse
SUPERNOVA EXPLOSION (type II)
T, r
M  8 M
remnant: neutron star or black hole
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

12. Principles of stellar structure and evolution: summary
Stellar mass (M)
Stage reached
< 0.08
no thermonuclear fusion
H burning
He burning
8 - 11
C burning
> 11
all stages
Evolution stages of a 25 M star
Stage reached
Timescale
Tcore (109 K)
Density (g cm-3)
H burning
7x106 y
0.06 5
He burning
5x105 y
0.23
7x102
C/O burning
600 y / 6 months
0.93 – 2.3
2x105 – 1x107
Si melting
1 d
4.1
3x107
Explosive burning
0.1 – 1 s
varies
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

13. Principles of stellar structure and evolution: quiescent evolution
Main parameters: 1) initial mass (  central temperature)
2) initial chemical composition (  nuclear processes)
Energy generation rate
 ~ Tn
n ~ 4 (H-burning)
n ~ 30 (C-burning)
Quiescent burning
Main
Sequence
~ 1010 y
Red Giant
~ 3x108 y
Super Giant
~ 3x104 y
Pre-Supernova
Gravitational
Contraction H He C
O, Ne …
innermost regions only
contribute to nuclear burning
e.g. 1/10 M for H-burning
less for subsequent stages
H-burning  MAIN SEQUENCE
longest stage of star’s lifetime
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

14. Explosive stages of stellar evolution
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

15. Principles of stellar structure and evolution: explosive evolution
NOVAE
= sudden increase in star’s luminosity
(L ~ 104 – 106 Li and t ~ 1 h – 1 d)
semi-detached binary system:
White Dwarf + less evolved star (e.g. Red Giant)
H-rich mass transfer
from RG to WD
degenerate matter  P and T uncoupled
thermonuclear runaway  cataclysmic explosion
temperature and density
increase on WD’s surface
(p,) and (,p) reactions on proton-rich nuclei
T > 108 K
 > 103 g cm-3
determine nature of nova phenomenon
nucleosynthesis up to A ~ 60 mass region
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

16. “seed” nuclei in Fe region
Principles of stellar structure and evolution: explosive evolution
X-RAY BURSTERS & X-RAY PULSARS
semi-detached binary system: Neutron star + less evolved star
T ~ 109 K
 ~ 106 g cm-3
(,p) and (p,) reactions on proton-rich nuclei
nucleosynthesis up to A ~ mass region
intense X-ray fluxes
CORE-COLLAPSE SUPERNOVAE
end stage of M ~ 8-30 M stars
core collapse & rebound
shock wave
outer layers blown off
Neutron Star or Black Hole remnants
T > 109 K
n > 1020 g cm-3
“seed” nuclei in Fe region
(n,) reactions on neutron-rich nuclei followed by  decays
nucleosynthesis of n-rich elements through r-process
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

17. gravitational contraction
Stellar life cycle
BIRTH
gravitational contraction
Interstellar gas
Stars
mixing of
interstellar gas
thermonuclear
reactions
energy production
stability against collapse
synthesis of “metals”
abundance distribution
explosion
DEATH
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

18. Thermonuclear reactions in stars
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

19. Thermonuclear reactions in stars: properties of nuclei
Aston:
measurements of atomic masses
E = Mnc2
Mnucl < mp + mn
enormous energy stored in nuclei!
Rutherford (1919):
discovery of nuclear reactions
liberate nuclear energy source
complex nuclides formed through reactions
amount of energy liberated in nuclear reaction:
Q =[(m1+m2)-(m3+m4)]c2 > 0
Binding energy curve
spontaneous nuclear processes:
Q > 0
Q < 0
Q > 0
fusion up to Fe region
fission of heavy nuclei
H most abundant element in the Universe
FUSION reactions most effective in stars
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

20. Thermonuclear reactions in stars: general features & definitions
Consider reaction:  Q12 > 0
(  known from
atomic mass tables)
Reaction cross section   probability for a reaction to occur
Dimension: area Unit: barn (b) = cm2
In general: not possible to determine reaction cross section from first principles
However:
cross sections depend on nature of force involved
cross sections are energy (i.e. velocity) dependent
Reaction
Force
 (barn)
Eproj (MeV)
15N(p,)12C
strong
0.5
2.0
3He(,)7Be
electromagnetic
10-6
p(p,e+)d
weak
10-20
Reaction rate:
r =
N1N2
v(v)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

21. Maxwell-Boltzmann distribution
Thermonuclear reactions in stars: general features & definitions
In stellar plasma: velocity of particles varies over wide range
(v) velocity distribution
<v>12 =
Reaction rate per particle pair:
v(v)(v)dv
Quiescent stellar burning:
non-relativistic, non-degenerate gas in thermodynamic equilibrium at temperature T
Maxwell-Boltzmann distribution
(v)  exp = exp
Probability (E)
(E)  exp(-E/kT)
= reduced mass
v = relative velocity
(E)  E kT
Energy
<v>12 =
(E) exp E dE
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

22. Thermonuclear reactions in stars: general features & definitions
Ni = number density
Total reaction rate: R12 = (1+12)-1 N1N2 <v> reactions cm-3 s-1
Energy production rate: 12 = R12 Q12
Mean lifetime of nuclei X
against destruction by nuclei a =
energy production
as star evolves
change in abundance
of nuclei X
<v> = KEY quantity
to be determined from experiments and/or theoretical considerations
as star evolves, T changes  evaluate <sv> for each temperature
NEED ANAYLITICAL EXPRESSION FOR !
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

23. Non-resonant process Resonant process
Thermonuclear reactions in stars: reaction mechanisms
Consider reaction: a + X  b + Y
(b = particle or photon)
Non-resonant process
One-step process leading to final nucleus Y
  |<b+Y lHl a+X>|2
single matrix element
occurs at all interaction energies
cross section has WEAK energy dependence
Resonant process
Two-step process: 1) compound nucleus formation a + X  C*
2) decay of compound nucleus C*  b + Y V r r0 E
incident nucleus Er
Er+1 E1 E2 
  |<b+Y lH’l C*>|2 |<C* lHl a+X>|2
two matrix elements
occurs at specific energies
cross section has STRONG energy dependence
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

24. Reactions between charged particles
nucleosynthesis up to Fe
typically quiescent stages
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

25. determines exponential drop in abundance curve!
Thermonuclear reactions in stars: charged particles
charged particles
Coulomb barrier V
Coulomb potential
energy available: from thermal motion
Ekin ~ kT (keV)
Ecoul ~ Z1Z2 (MeV)
kT ~ 8.6 x 10-8 T[K] keV
tunnel
effect r0 r
nuclear well
T ~ 15x106 K (e.g. our Sun)  kT ~ 1 keV
T ~ 1010 K (Big Bang)  kT ~ 2 MeV
reactions occur through TUNNEL EFFECT
tunneling probability P  exp(-2)
during quiescent burnings: kT << Ec
in numerical units:
2ph = Z1Z2(m/E)½
m in amu and Ecm in keV
2ph = GAMOW factor
determines exponential drop in abundance curve!
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

26. Thermonuclear reactions in stars: non-resonant reactions
geometrical factor (particle’s
de Broglie wavelength)
interaction
matrix element
penetrability probability depends on projectile’s angular momentum  and energy E
 (E) = exp(-2) S(E)
(for s-waves only!)
non-nuclear origin
STRONG energy
dependence
nuclear origin
WEAK energy
dependence
Above relation defines ASTROPHYSICAL S(E)-FACTOR
N.B.
If angular momentum is non zero
 centrifugal barrier must also be taken into account
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

27. Thermonuclear reactions in stars: Gamow peak
With above definition of cross section:
<v>12 =
S(E) exp dE
f(E)
varies smoothly
with energy
governs energy dependence
MAXIMUM reaction rate:
Gamow peak
tunnelling through
Coulomb barrier
 exp( )
Maxwell-Boltzmann
distribution
 exp(-E/kT)
relative probability
energy kT E0
E0
E0 < E0
only small energy range contributes
to reaction rate 
OK to set S(E) ~ S(E0) = const.
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

28. Thermonuclear reactions in stars: Gamow peak
most effective energy region for thermonuclear reactions
E0 ± E0/2
energy window of astrophysical interest
E0 = f(Z1, Z2, T)
varies depending on reaction and/or temperature
Examples: T ~ 15x106 K (T6 = 15)
reaction
Coulomb
barrier (MeV) E0
(keV)
exp(-3E0/kT) E0
p + p
0.55
5.9
7.0x10-6
 + 12C
3.43 56
5.9x10-56
16O + 16O
14.07
237
2.5x10-237
area of Gamow peak
(height x width) ~ <v>
STRONG sensitivity
to Coulomb barrier
separate stages: H-burning
He-burning
C/O-burning …
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

29. insert in expression for reaction rate,
Thermonuclear reactions in stars: resonant reactions
Resonant reactions
1. Narrow resonances
 << ER
Breit-Wigner formula
(E)BW = π2(1+12)
a b
(E-Er)2 + (/2)2
insert in expression for reaction rate,
integrate and get:
<v>12 =
exp
(for single resonance)
resonance strength
(integrated cross section over resonant region)
low-energy resonances (ER  kT) dominate reaction rate
Experiment: determine
and ER
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

30. energy dependence of partial a(E), b(E) and total (E) widths
Thermonuclear reactions in stars: resonant reactions
2. Broad resonances
 ~ ER
Breit-Wigner formula +
energy dependence of partial a(E), b(E) and total (E) widths
N.B. Overlapping broad resonances of same Jπ  interference effects
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

31. Thermonuclear reactions in stars: resonant reactions
3. Sub-threshold resonances
any exited state has a finite width
 ~ h/
high energy wing can extend
above particle threshold
cross section can be entirely dominated
by contribution of sub-threshold state(s)
Example: 12C(,)16O
(Gialanella’s lecture & Schürmann’s talk)
TOTAL REACTION RATE
vtot = vr + vnr
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

32. Reactions with neutrons
nucleosynthesis beyond Fe
typically explosive stages
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

33. Thermonuclear reactions in stars: neutron captures
NO Coulomb barrier
neutrons produced in stars are quickly thermalised
E0 ~ kT = relevant energy (e.g. T ~ 1-6x108 K  E0 ~ 30 keV)
accounts for almost flat abundance
distribution beyond iron peak
Typically:
<sv> ~ const = <sTvT>
neutron-capture cross sections can be measured DIRECTLY at relevant energies
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

34. Experimental approach & laboratory requirements
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

35. Quiescent burning stages of stellar evolution
Experimental approach: general features
Quiescent burning stages of stellar evolution
FEATURES
T ~ K  E0 ~ 100 keV << Ecoul  tunnel effect
 barn <  < 10-9 barn
 average interaction time  ~ <v>-1 ~ 109 y
unstable species DO NOT play significant role
PROBLEMS
10-18 b <  < 10-9 b  poor signal-to-noise ratio
 major experimental challenge
 extrapolation procedure required
REQUIREMENTS
poor signal-to-noise ratio  long measurements
 ultra pure targets
 high beam intensities
 high detection efficiency
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

36. Experimental procedure
Experimental approach: extrapolation
Experimental procedure
measure (E) over as wide a range as possible,
then EXTRAPOLATE down to Gamow energy region around E0!
CROSS SECTION
LOG
SCALE 
direct measurements E0
Ecoul
Coulomb barrier
(E)
non-resonant
resonance
extrapolation needed !
many orders
of magnitude
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

37. Thermonuclear reactions in stars: non resonant reactions
Example:
cross section
S-factor
Data EXTRAPOLATION down to astrophysical energies REQUIRED!
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

38. Experimental approach: extrapolation
S(E)-FACTOR
S(E)
extrapolation
LINEAR
SCALE
direct measurement
low-energy tail
of broad
resonance Er
non resonant
process
sub-threshold
resonance
-Er
interaction energy E
DANGER OF EXTRAPOLATION !
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

39. Experimental approach: extrapolation
ALTERNATIVE SOLUTIONS
Go UNDERGROUND  reduce (cosmic) background
example: LUNA facility  (Junker’s lecture)
Use INDIRECT methods  (Figuera’s lecture)
INTRINSIC LIMITATION
At lower and lower energies
ELECTRON SCREENING EFFECT sets in
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

40. The electron screening
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

41. penetration through Coulomb barrier between BARE nuclei
Experimental approach: electron screening
(E) = S(E) exp(-2)
penetration through Coulomb barrier between BARE nuclei
in stellar plasmas: ions in sea of free electrons Ec
bare
Coulomb potential
Debye-Hückel radius
RD ~ (kT/)½
E + Ue
screened E Rn RD Rt
Ue = electron screening potential
Similarly:
in terrestrial laboratories:
interaction between ions (projectiles) and atoms or molecules (target)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

42. Experimental approach: electron screening
cross-section enhancement factor:
fplasma(E) =  exp(Ue/E)  1
plasma(E)
bare(E)
 (E)
screened
bare E E
bare S(E)
S(E)
high-energy data
extrapolation
screened S(E)
fit to measured
low-energy data
 Ue
BUT: electron screening in lab DIFFERENT from electron screening in plasma
need to understand flab(E)
improve calculation of fplasma(E)
PROBLEM: experimental Ue >> theoretical Ue
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

43. Explosive burning stages of stellar evolution
Experimental approach: general features
Explosive burning stages of stellar evolution
FEATURES
T > 108 K  E0 ~ 1 MeV ~ Ecoul
 barn <  < 10-3 barn
 NO extrapolation needed
 average interaction time  ~ <v>-1 ~ seconds
unstable species DO GOVERN nuclear processes
PROBLEMS
 ~ <v>-1 ~ seconds  unknown nuclear properties
 low beam intensities
(5-10 o.d.m. lower than for stable beams)
 beam-induced background
REQUIREMENTS
unstable species  RIBs production and acceleration
 large area detectors
 high detection efficiency
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

44. Experimental approach: data needs
NUCLEAR DATA NEEDS
reactions
involving:
A < 30
A > 30
cross-section
dependence:
individual resonances
nuclear properties
statistical properties
Hauser-Feshbach calculations
knowledge
required:
excitation energies
spin-parity & widths
decay modes
masses
level densities
part. separation energy
experimental constraints wherever possible
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

45. Experimental approach: explosive nucleosynthesis
EXAMPLES
rp-process
r-process
rapid proton captures X(p,)Y
rapid neutron captures X(n,)Y
synthesis of neutron-rich nuclei
A > 60
synthesis of proton-rich nuclei
A ~ 100
proton
capture
neutron
capture
- decay
+ decay Z
stable N
unstable
(Shotter’s lecture)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

46. Overview of main astrophysical processes
M.S. Smith and K.E. Rehm, Ann. Rev. Nucl. Part. Sci, 51 (2001)
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

47. stellar reactions take place through TUNNEL effect
Thermonuclear reactions in stars: overview
Hydrostatic equilibrium T ~ K  average interaction time  ~ <v>-1 ~ 109 y
unstable species do not play significant role
stellar reactions take place through TUNNEL effect
Gamow peak
tunnelling through
Coulomb barrier
 exp( )
Maxwell-Boltzmann
distribution
 exp(-E/kT)
relative probability
energy kT E0
E0
kT << E0 << Ecoul
10-18 barn <  < 10-9 barn
Extrapolation NEEDED
Solutions: underground measurements
indirect approaches
BUT! Electron screening problem
Explosive phenomena T > 108 K  average interaction time  ~ <v>-1 ~ seconds
unstable nuclei govern nuclear reaction processes
Sophisticated techniques for
RIBs production and acceleration
Ad-hoc detection systems required
E0 ~ Ecoul
10-6 barn <  < 10-3 barn
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003

48. Further reading W.D. Arnett and J.W. Truran Nucleosynthesis
The University of Chicago Press, 1968
J. Audouze and S. Vauclair An introduction to Nuclear Astrophysics
D. Reidel Publishing Company, Dordrecth, 1980
E. Böhm-Vitense Introduction to Stellar Astrophysics, vol. 3
Cambridge University Press, 1992
D.D. Clayton Principles of stellar evolution and nucleosynthesis
The University of Chicago Press, 1983
H. Reeves Stellar evolution and Nucleosynthesis
Gordon and Breach Sci. Publ., New York, 1968
C.E. Rolfs and W.S. Rodney Cauldrons in the Cosmos
The University of Chicago Press, (…the “Bible”)
Copies of this lecture at:
Second European Summer School on Experimental Nuclear Astrophysics - St. Tecla, Sept. 28th – Oct. 5th 2003