Nucleosynthesis

How did the various nuclides originate?

What determines their abundance?

When were the elements created?

Lecture outline: 1) The age of the universe 2) 3) The Big Bang Nucleosynthesis – initial + stellar 4) Abundance of elements

900s exposure from Palomar

8/21/12

The Age of the Universe

Four methods of determining age of universe: 1) 2) Cosmological models – H o (the Hubble constant in expansion of universe) T o – ratio of velocity to distance =13.7 billion years Isotope geochemistry – 187 Re  187 Os, t 1/2 =40 billion years T o =12-17 billion years 238 U decay, t 1/2 =4.5 billion years T o =12.5-16 billion years 3) 4) Age of oldest star clusters -- measure luminosity of brightest star, relies on stellar evolutionary model, T o =11-13 billion years Oldest white dwarfs -- measure luminosity of faint white dwarfs to determine how long they have been cooling, T o =12-13 billion years

The Big Bang

- 1920 ’ s: LeMaitre proposes on theoretical grounds that the universe is expanding - 1929: Hubble observed galaxies moving away from us with speeds proportional to distance - 1964: Penzias and Wilson detect ‘ primordial static ’ left over from Big Bang Time After Big Bang 5.39 x 10 -44 s 10 -43 10 -35 3 x 10 s s 10 -33 to 10 -32 1 x 10 -10 s -10 6 x 10 -6 s to 5 x 10 -6 10s 3.8 m 700,000 y s Temperature (K) - 10 31 10 28 10 27 10 15 ~10 13 1.4 x 10 12 3.9 x 10 9 9 x 10 8 3000 Event appearance of space, time, energy, and superforce gravity separates strong force and electro-weak force inflation electromagnetic and weak force stabilization of quarks, antiquarks formation of protons and neutrons stabilization of electrons and positrons formation of 2H, 3He, and 4He nuclei electrons captured by nuclei

1992 2005

WMAP:

Wilkinson Microwave Anisotropy Probe age of universe = 13.73 +/- 1% image microwave radiation from 379,000 years after Big Bang small temperature differences (10-6 K) signify heterogeneous distribution of matter

http://map.gsfc.nasa.gov/

Nucleosynthesis Schematic

Nucleosynthetic process Big bang

Main sequence stars:

Hydrogen burning Helium burning Carbon burning CNO cycle x-process (spallation) & supernova (?) a -process e-process s-process r-process Elements created 1 H, 4 He, 2 H, 3 H (Li, B?) 4 He 12 C, 4 He, 24 Mg, 16 O, 20 Ne 24 Mg, 23 Na, 20 Ne 4 He Li, Be, B 24 Mg, 28 Si, 32 S, 36 Ar, 40 Ca 56 Fe & other transition up to mass 209 up to mass 254

Nucleosynthesis during the Big Bang

- initially, protons ( 1 H) and neutrons combine to form 4 He, 2 H (D), and 3 He via exothermic fusion reactions.

- some uncertainty about whether some B, Be, and Li were created at this stage - H & He comprise 99% of mass of universe

Nucleosynthesis during small star evolution

For

‘

small

’

star, such as our Sun

- star must form from gravitational accretion of ‘ primordial ’ H and He - temperature ~ 10 7 after formation - H-burning creates 4 He from 1 H, longest stage of star (10 7 - 10 10 y) - He-burning begins with formation of Red Giant (T=10 8 K) 4 He + 4 He --> 8 Be 8 Be + 4 He --> 12 C 12 C + 4 He --> 16 O and so on to 24 Mg - core contracts as He consumed,  -process begins (T=10 9 K) 20 Ne --> 16 O + 4 He 20 Ne + 4 He --> 24 Mg and so on to 40 Ca

Nucleosynthesis during small star evolution (cont)

For

‘

small

’

star, such as our Sun

- odd # masses created by proton bombardment - slow neutron addition (s-process) during late Red Dwarf: 13 C + 4 He --> 16 O + n 21 Ne + 4 He --> 24 Mg + n follows Z/N stability up to mass 209

Nucleosynthesis during supernovae evolution

For massive stars

- same evolution as for small star, up to Red Giant stage - core contracts and heats at accelerating pace - when T~3x10 9 , several important element building processes occur: - energetic equilibrium reactions between n, p, and nuclei (e-process), builds up to 56 Fe - rapid addition of neutrons (r-process) builds up to mass 254

Heavy element formation - the

‘

s

’

and

‘

r

’

processes

Neutron # (N)

Chart of the Nuclides, low mass

Neutron #

Entire chart of the nuclides

The abundance of the elements - cosmic

- astronomers can detect different elements with spectroscopy (large telescopes equipped with high-resolution spectrometers)

The abundance of the elements - cosmic

- the models of nucleosynthesis are driven by the observed relative abundances of the elements in this and other galaxies Magic numbers: 2, 8, 20, 28, 50, 82,126 & even is always better than odd

The abundance of the elements - our solar system

Relative composition of heavy elements in sun very similar to “ primordial ” crust (the carbonaceous chondrite), so we assume that solar system was well-mixed prior to differentiation.

Unstable nuclides with half lives > 0.5Ma

Nuclear Physics & Radioactivity

What holds a nucleus together?

What drives radioactive decay?

What sets the timescale for radioactive decay?

What happens during radioactive decay?

Lecture outline: 1) nuclear physics 2) radioactive decay 3) secular equilibrium 4) counting statistics a

particles in a cloud chamber

8/21/12

The Four Forces of Nature

Force Strong nuclear Electromagnetic Weak nuclear Strength 1 10 -2 10 -13 Range <<1/r 2 (finite, v. short) 1/r 2 (infinite, but shielded <<1/r 2 (finite, v. short) Gravity 10 -39 1/r 2 (infinite) Occurrence inter-nucleon nucleus, atom B-decay, neutrinos everywhere

Four Tenets of Nuclear Physics

1) mass-energy equivalence (E=mc 2 ) 2) wave-particle duality (particles are waves, and waves are particles) 3) conservation of energy, mass, momentum 4) symmetry

Binding energy

Let ’ s revisit the fusion of four protons to form a 4 He nucleus: 4( 1 1

H

)  1( 2 4

He

 4(1.007277)

e

  2 

e



E

 1(4.00150)  

m *these masses come from the table of nuclides

0.02761

amu

We have calculated the

mass deficit

--> i.e. the whole is less than sum of the parts The mass deficit is represented by a HUGE energy release, which can be calculated using Einstein ’ s famous equation, E=mc 2 , and is usually expressed in Mev

Contributions to Binding Energy

E B = strong nuclear force binding -surface tension binding + spin pairing +shell binding-Coulomb repulsion 1) strong nuclear force -- the more nucleons the better 2) surface tension -- the less surface/volume the better (U better than He) 3) spin pairing -- neutrons and protons have + and - spins, paired spins better 4) shell binding -- nucleus has quantized shells which prefer to be filled (magic numbers) 5) Coulomb repulsion -- packing more protons into nucleus comes at a cost (although neutron addition will stabilize high Z nuclei)

Radioactive Decay

- a radioactive

parent

nuclide decays to a

daughter

nuclide - the probability that a decay will occur in a unit time is defined as the

decay constant

 is time independent; the

mean life

  (units of y -1 is defined as  =1/λ ) N 0

dN dt

  

N N



N e

0  

t

  ln(2)

t

1/ 2 1000000 900000 800000 700000 600000 t 1/2 = 5730y

N

0

t

¾

N

0 / 2

t

¾

N

0 / 4

t

¾ 500000 400000 300000

N

0 / 8 200000 100000 0 0 5730 10000 20000 30000 40000 50000

Years

Activity calculations

Activity

 

N

- usually reported in dpm (disintegrations per minute), example: 14 C activity = 13.56 dpm / gram C

A



A e

0  

t

- because activity is linerarly proportional to number N, then A can be substituted for N in the equation

N

  

t

Example calculation: How many 14 C disintegrations have occurred in a 1g wood sample formed in 1804AD?

T=208y t 1/2 = 5730y so  = 0.693/5730y = 1.209e

-4 y -1 N 0 =A 0 /λ so N 0 =(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e

-4 = 5.90e

10 atoms N( 14 C)=N( 14 C) 0 *e -(1.209e-4/y)*208y = 5.75e

10 atoms # decays = N 0 -N = 1.46e

9 decays

Four types of radioactive decay

1) alpha (  ) decay 4 He nucleus (2p + 2n) ejected 2) beta (  ) decay - change of nucleus charge, conserves mass 3) gamma (  ) decay - photon emission, no change in A or Z 4) spontaneous fission - for Z=92 and above, generates two smaller nuclei



decay

241

Am

95 237

Np

93  2 4

He

- involves strong and coloumbic forces - alpha particle and daughter nucleus have equal and opposite momentums (i.e. daughter experiences “ recoil ” )



decay - three types

1) β- decay 2) β+ decay 3) Electron capture 1 3

H

b ¾ 2 3

He

+

e

+ u

e

- converts one neutron into a proton and electron - no change of A, but different element - release of anti-neutrino (no charge, no mass) 11

C

6 b ¾ + 11 5

B

+

e

+ + u

e

- converts one proton into a neutron and electron - no change of A, but different element - release of neutrino 4 7

Be

+

e

7 3

B

+ u converts one proton into a neutron

e

no change of A, but different element release of neutrino



decay

256 100

Spontaneous fission

Fm sf

¾ 140 54

Xe

+ 112

Pd

46 + 4

n

- heavy nuclides split into two daughters and neutrons - U most common (fission-track dating) 2 3

He

* g ¾ 2 3

He

+ g - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay

Fission tracks from 238 U fission in old zircon

Decay chains and secular equilibrium

- three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached 238 U --> radioactive daughters --> 206 Pb Also 235 U (t 1/2 )= 700My And 232 Th (t 1/2 )=10By 234 Th 24d After ~10 half-lives, all nuclides in a decay chain will be in

secular equilibrium,

where  ( 1 )  ( 2 )  ...

Decay chains and secular equilibrium (cont)

Ex:

N

1  1 l ¾ >>  2 2 1

N

2 N 3 l ¾

N

3 0.1

0.01

N 1 N 2  1 /  2 =0.1

N 2 o =0  secula 1 N 1 =  r equilib 2 N 2 rium N 2 o =N 1 o 0.001

0 5  2 1 2 t/  1 3 4 5 The approach to secular equilibrium is dictated by the intermediary, because the parent is always decaying, and the stable daughter is always accumulating.

Counting Statistics

Radioactive decay process behave according to binomial statistics.

For large number of decays, binomial statistics approach a perfect Gaussian.

Ex: 100 students measure 14 C disintegrations in 1g of modern coral (A=13.56dpm) with perfect geiger counters, for 10 minutes 1  =68.3% 2  =95% 3  =99%

124.0

135.6

147.2

Observed # disintegrations Since the students only counted 135.6 disintegrations, they will only achieve a 1  accuracy of ± sqrt(135.6)= ± 11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5% In other words, your 1 

relative

error (in %) will be equal to (1/(sqrt(total counts)))*100