Lesson 13
Nuclear Astrophysics
Elemental and Isotopic
Abundances
Elemental and Isotopic
Abundances (cont.)
Elemental and Isotopic
Abundances
Overview of the Sun and the
Nucleosynthetic Processes
Involved
Primordial Nucleosynthesis
• Age of the universe 10-20 billion years
with best estimate being 14  1 x 109 y.
• Universe started with the Big Bang.
• Evidence for the Big Bang: 2.7 K
microwave radiation.
• Photon density ~ 400/cm3
Early history of the Universe
Evolution of the Universe
• 10-43 s Planck time 1032 K, vol=10-31
volcurrent
• kBT(eV)=8.5x10-5 T(K)
• Matter is QGP, all particle present.
• 10-6 s, T ~1013K, hadronic matter
condenses out.
• Matter is nucleons, mesons, neutrinos,
photons, electrons.
Evolution of the Universe
• 10-2 s. T~ 1011 K, ~ 4 x 106 kg/m3
1.5x1010
T (K ) 
t(s)
e  p  e  n



e  n  p  e

Evolution of the Universe
• At T=1012K, n/p ~ 1, at T=1011 K n/p ~ 0.86, etc. At T =
1011K, no complex nuclei were formed because the
temperature was too high to allow deuterons to form.
When the temperature fell to T= 1010K (t~ 1 s), the
creation of e+/e- pairs (pair production) ceased because kT
< 1.02 MeV and the neutron/proton ratio was ~ 17/83. At
a time of 225s, this ratio was 13/87, the temperature was T
~ 109K, then density was ~ 2 x 104kg/m3, and the first
nucleosynthetic reactions occurred.
First Nucleosynthesis
• Hydrogen burning
• n+pd+
• p + d  3He + 
• n + d  3H + 
• He formation
• 3H + p  4He + 
• 3He + n  4He + 
• 3H + d  4He + n
• d + d  4He + 
Big Bang Nucleosynthesis
After about 30 m, nucleosynthesis ceased. The temperature
was ~ 3 x 108K and the density was ~ 30 kg/m3. Nuclear matter
was 76% by mass protons, 24% alpha particles with traces of
deuterium, 3He and 7Li. The /n/p ratio is 109/13/87.
The relative ratio of p/4He/d/3He/7Li is a sensitive function
of the baryon density of the Universe. Chemistry began about
106 years later, when the temperature had fallen to 2000K and
the electrons and protons could combine to form atoms.
Further nucleosynthesis continues to occur in the interiors of stars.
Stellar Nucleosynthesis
• All elements beyond H and He
synthesized in stellar interiors
• Stellar nucleosynthesis continues to date
(2 x 105 y 99Tc lines in stars)
Stellar Evolution
• Population III stars (protostars)--H, He,
short lifetimes, now extinct
• Population II stars (H, He, 1% heavier
elements)
• Population I stars (H, He, 2-5% heavier
elements) Includes our sun.
Sun
•
•
•
•
•
•
•
Typical Population I star.
mass=2 x 1030 kg
radius=7 x 106 m
~1.41 x 103 kg/m3
surface T ~ 6000K
Luminosity ~ 3.83 x 1026 W
age ~ 4.5 x 109 y.
Herzsprung-Russell Diagrams
Stellar evolution and H-R
diagrams
Aside on our Sun
• ~ 7 x 109 more years on main sequence
• 1.1-1.5 x 109 years, luminosity will
increase by ~10%, making Earth
uninhabitable.
• Terrestrial life has used up about 3/4 of
its lifespan.
Supernovas
•
•
•
•
Massive stellar explosions
~1051 ergs released in a few seconds
2-3/century, last observation was 1987.
Some supernovas lead to the formation of
neutron stars.
Thermonuclear reaction rates

R  N x N y   (v)vdv  N x N y v
0

N x N y v
R
1 xy
 m 
P(v)  

 2kT 
3/ 2

 8 1/ 2 1
v   
3/ 2
  kT 
 mv2 
exp

 2kT 
 E 
 (E)E exp kT dE
0

But these are charged particle
reactions!
•For p +p, CB ~ 550 keV.
•kT~ 1.3 keVbarrier
penetration problem
P  exp(



 1/ 2
2Z1Z2 e 2
)  exp(31.29Z1Z2   )
E 
v

 1/ 2 
1
 (E)  exp
 S(E)
31.29Z1Z2
E  
E


 8 1/ 2 1
v   
3/ 2
  kT 

 E
b 
dE
1/ 2 

 S(E)exp kT  E
0
Stellar Nucleosynthesis--A
Scorecard
• Big Bang 75% H, 25% He, trace 7Li
• From ~ 106 years after the Big Bang to
present, get nuclear fusion reactions in
stars that synthesize the elements up to A
~ 60.
Fuel
T(K)
kT(MeV)
H
5 x 107
0.002
He
2 x 108
0.02
12
C
8 x 108
0.07
16
O
2 x 109
0.2
Ne
1.5 x 10 9
0.13
3.5 x 10 9
0.3
1
4
20
28
Si
Products
4
He
12
C, 16O, 20Ne
16
O, 20Ne, 24Mg
20
Ne, 28Si, 32S
16
O, 24Mg
A < 60
Hydrogen Burning
•
•
•
•
•
First stage of a star; converts H into He.
First reaction(pp): p + p  d + e+ +e Q = 0.42 MeV
Weak branch (pep) p + e- + p  d + e Q = 1.42 MeV
Next Reaction d + p 3He +  Q = 5.49 MeV.
86% Branch 3He + 3He  4He + 2p Q = 12.96 MeV
• Net reaction
• 4p  4He + 2e+ + 2e
Q = 26.7 MeV
Hydrogen Burning(ppI chain)
Side reaction
• 3He + 4He  7Be + e
• e- + 7Be  7Li + e Q = 0.86 MeV
• p + 7Li  2 4He
• This side branch along with the p+p, d+p
is called the ppII process
Another side branch
• 7Be + p  8B + 
• 8B  8Be* + e+ + e
• 8Be*  2 4He
• This sequence along with the p+p, d+p,
etc is called the PPIII chain.
CNO Cycle
+ p  13N + 
13N 13C + e+ + 
e
13C + p  14N + 
14N +p  15O + 
15O  15N + e+ + 
e
15N + p  12C + 4He
12C
Net effect is 4p  4He + 2e+ + 2e
CNO Cycle
He burning
• Eventually the H fuel will be exhausted,
get gravitational collapse, further heating
and red giant formation. Then He
burning will commence. The reaction is
the 3 process.
3 4He  12C Q = 7.37 MeV
+ 12C  20Ne + 4He
12C + 12C  23Na + p
12C + 12C  23Mg + n
12C + 12C  24Mg + 
16O + 16O  24Mg + 2 4He
16O + 16O  28Si + 4He
16O + 16O  31P + p
16O + 16O  31S + n
16O + 16O  32S + 
12C
Reaction
Time
H burning
6 x 109 years
He burning
0.5 x 10 6 years
C burning
200 years
Ne burning
1 year
O burning
Few months
Si burning
days
Synthesis of A > 60
• Use neutron capture
• There are two types of n-capture
reactions. one on a slow time scale, the sprocess and one on a rapid time scale, the
r process.
• In s process reactions, - decay
intervenes between n captures while in
the r process, it does not.
s-Process
• Example
• 56Fe + n  57Fe (stable) + 
• 57Fe + n  58Fe (stable) + 
• 58Fe + n  59Fe (t1/2 = 44.5 d) + 
• 59Fe  59Co (stable) + - +  e
•Process terminates at 209Bi



3(n, )


Bi(n, ) Bi  Po

Pb 
 Pb 209Bi
209
210
210
206

209
r-process ( in supernovas)
p process
• makes proton-rich nuclei
• most reactions are photonuclear reactions
like (,p), (, n), (, )
• probably occurs in supernovas.
rp process
Solar Neutrinos
Sun emits 1.8 x 1038 neutrinos/s with the flux hitting
the Earth being 6.4 x 1010 neutrinos/s/cm2.
Table 12.3 Predicted solar neutrino fluxes (Bahcall and Pena-Garay)
Source
Flux(particles/s/cm2)
pp
5.94 x 10 10
pep
1.40 x 10 8
hep
7.88 x 10 3
7
Be
4.86 x 10 7
8
5.82 x 10 6
B
13
5.71 x 10 8
15
5.03 x 10 8
N
O
17
F
5.91 x 10 6
Fluxes and Detectors
Solar Neutrino Detectors
• The most famous detector is the Chlorine
detector of Ray Davis.
• Contained 100,000 gal C2Cl4 in a cavern
1600 m below the earth’s surface in the
Homestake kine.
• Reaction used:   Cl Ar  e
37
37

e
•Ar nuclei collected as gas, detect 2.8 keV e from
Auger from EC
Produce ~3 atoms/wk in volume of 1030 atoms.
Gallex detector
• e + 71Ga  71Ge + e• Collect Ge gas product
• threshold = 0.232 MeV
Super K
• Detect Cerenkov radiation from
•  + e-   + e• threshold = 8 MeV
SNO
•  + e-   + e• e + d  2p + e• +dn+p+
• Sensitive to all types of neutrinos
Results
• Davis : measured 2.1 +- 0.3 SNU
expect 7.9 +- 2.4 SNU
1 SNU = 10-36 neutrino captures/s/target
atom
• Gallex: measured 77 +- 10 SNU
expect 127 SNU
Solution
• neutrino oscillations
• imply neutrino has mass
Synthesis of Li, Be, B