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

€

T (K ) =1.5x1010

t(s)

€

νe + p ⇔ e+ + n

ν e + n ⇔ p+ e−

n/p = exp (- mc2/kT)

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

€

R = N xN y σ (v)vdv = N xN y σv0

∞

∫

€

R =N xN y σv

1+δ xy

€

P(v) =m

2πkT

⎛

⎝ ⎜

⎞

⎠ ⎟3 / 2

exp −mv2

2kT

⎛

⎝ ⎜

⎞

⎠ ⎟

€

σv =8

πμ

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 21

kT( )3 / 2 σ (E)E exp −

E

kT

⎛

⎝ ⎜

⎞

⎠ ⎟dE

0

∞

∫

But these are charged particle reactions!

•For p +p, CB ~ 550 keV.

•kT~ 1.3 keVbarrier penetration problem

€

P = exp(−2πZ1Z2e

2

hv) = exp(−31.29Z1Z2

μ

E

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

)

€

σ(E) =1

Eexp −31.29Z1Z2

μ

E

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟S(E)

€

σv =8

πμ

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 21

kT( )3 / 2 S(E)exp −

E

kT−

b

E1/ 2

⎡

⎣ ⎢ ⎤

⎦ ⎥dE0

∞

∫

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) Products

1H 5 x 107 0.002 4He

4He 2 x 108 0.02 12C, 16O, 20Ne

12C 8 x 108 0.07 16O, 20Ne, 24Mg

16O 2 x 109 0.2 20Ne, 28Si, 32S

20Ne 1.5 x 109 0.13 16O, 24Mg

28Si 3.5 x 109 0.3 A < 60

Hydrogen Burning

• First stage of a star; converts H into He.• First reaction(pp): p + p d + e+ +νe Q = 0.42 MeV

• Weak branch (pep) p + e- + p d + νe 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+ + 2νe Q = 26.7 MeV

Hydrogen Burning(ppI chain)

Side reaction

• 3He + 4He 7Be + νe

• e- + 7Be 7Li + νe 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+ + νe

• 8Be* 2 4He

• This sequence along with the p+p, d+p, etc is called the PPIII chain.

12C + p 13N + 13N 13C + e+ + νe13C + p 14N + 14N +p 15O +

15O 15N + e+ + νe15N + p 12C + 4He

CNO Cycle

Net effect is 4p 4He + 2e+ + 2νe

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 + 12C 20Ne + 4He12C + 12C 23Na + p12C + 12C 23Mg + n12C + 12C 24Mg +

16O + 16O 24Mg + 2 4He16O + 16O 28Si + 4He

16O + 16O 31P + p16O + 16O 31S + n16O + 16O 32S +

Synthesis of A > 60

• Use neutron capture• There are two types of n-capture

reactions. one on a slow time scale, the s-process 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) + - +

€

ν e

•Process terminates at 209Bi

€

209Bi(n,γ )210Bi β −

⏐ → ⏐ 210Po α ⏐ → ⏐ 206Pb 3(n,γ ) ⏐ → ⏐ ⏐ 209Pb β −

⏐ → ⏐ 209Bi

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

Table 12.3 Predicted solar neutrino fluxes (Bahcall and Pena-Garay)

Source Flux(particles/s/cm2)

pp 5.94 x 1010

pep 1.40 x 108

hep 7.88 x 103

7Be 4.86 x 107

8B 5.82 x 106

13N 5.71 x 108

15O 5.03 x 108

17F 5.91 x 106

Sun emits 1.8 x 1038 neutrinos/s with the flux hitting the Earth being 6.4 x 1010 neutrinos/s/cm2.

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:

€

ν e+37Cl→37Ar + e−

•Ar nuclei collected as gas, detect 2.8 keV e from Auger from ECProduce ~3 atoms/wk in volume of 1030 atoms.

Gallex detector

νe + 71Ga 71Ge + e-

• Collect Ge gas product• threshold = 0.232 MeV

Super K

• Detect Cerenkov radiation fromν + e- ν + e-

• threshold = 8 MeV

SNO

ν + e- ν + e-

νe + d 2p + e-

ν + d n + p + ν• Sensitive to all types of neutrinos

Results

• Davis : measured 2.1 +- 0.3 SNU expect 7.9 +- 2.4 SNU1 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