Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson...

23
Behavior of Nuclear Reaction Networks Brad Meyer Clemson University

Transcript of Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson...

Page 1: Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson University. ... and d network p n d p ... . Y ...

Behavior of Nuclear Reaction NetworksBrad Meyer

Clemson University

Page 2: Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson University. ... and d network p n d p ... . Y ...

For the 238U decay chain

238238238238

238238238

238238234234238238234234

238238234234234

1

1

YYt

Ydt

dYand

YYYYt

YYdt

dY

λλ

λ

λλλλ

λλ

−=Δ⎟⎠⎞

⎜⎝⎛ +Δ

−=

+−=Δ−Δ⎟⎠⎞

⎜⎝⎛ +Δ

+−=

Page 3: Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson University. ... and d network p n d p ... . Y ...

Answer to Problem 2.1

⎥⎦

⎤⎢⎣

⎡Δ+

+−+

Δ

−=Δ

tYY

t

Y

and

t

YY

238

238238234234

234

234

238

238238238

111

1

λλλ

λ

λ

λ

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)()(

1)(

,/1

/1

238234

238234234234

238

238238238238

238

234

ttYYYttY

and

tYYYttY

then

tbut

tConsider

Δ+=Δ+=Δ+

Δ+=Δ+=Δ+

>>Δ

λλ

λ

λ

λ

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S Process

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Neutron Sources

• 13C(alpha,n)16O– 13C made from protons diffusing into 12C-rich

region• 22Ne(alpha,n)25Mg

– 22Ne made from 14N left over from CNO:– 14N(alpha,gamma)18F(beta+)18O(alpha,gamma)22Ne

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Sites of the s process

• Weak component: core helium burning in massive stars (production up to A=90)

• Main component: helium shell flashes in Asymptotic Giant Branch (AGB) stars (production up to A=209)

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Steady states in s process

73

72

72

73

7272737373 0

><><

=⇒

⇒><+><−=

vv

YY

YYvNYYvNdt

dY

Ge

Ge

nGeAnGeAGe

σσ

ρσρσ

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A simple helium burning + s-processexample

• Start with abundances after H burning + some extra 13C.

• T9=0.15, density = 1000 g/cc

• The FITS file:

http://www.ces.clemson.edu/~mbradle/JINA/

Choose sprocess.fits. Notice also the reactions file sprocess_reactions.html

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The steady state

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><=⇒

+−=

vNYYY

YYYvNdt

dY

Aeq

d

eqn

eqp

dnpAp

σλ

λρσ

γ

γ

Consider now equilibrium:p+n<->d

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More formally

=⇒

==

+−−=

iii

iii

dYdf

dVdT

Consider

dYPdVsdTdf

μ

μ

0

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For p,n, and d network

pdnp

npd

ddnnpp

dYdf

so

dYdYdY

but

dYdYdYdf

)( μμμ

μμμ

−+−=

−=−=

++=

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For equilibrium

dnp

so

df

μμμ =+

= 0

Page 15: Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson University. ... and d network p n d p ... . Y ...

General Nucleosynthesis Network

np ZAZAZ μμμ )(),( −+=

Page 16: Behavior of Nuclear Reaction Networks · Behavior of Nuclear Reaction Networks Brad Meyer Clemson University. ... and d network p n d p ... . Y ...

Nuclear Binding Energy

AAZBAB

and

AZZAZAZB

so

cAZMcmZAcZmAZB

MevAZAcAZM

np

np

/),(/

),()(),(

),()(),(

),(478.931),(

222

2

=

Δ−Δ−+Δ=

−−+=

Δ+=

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The Nuclear Data Tool

http://nucleo.ces.clemson.edu/home/online_tools/nuclear_data/0.1

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Ye

∑=i

iie YZY

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The NSE Calculator

http://nucleo.ces.clemson.edu/pages/nse/0.1

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An alpha-rich freezeout example

• Start with Ye=0.5 at T9=10 and density = 108 g/cc

• Volume expands on a 0.1 second timescale, density proportional to T9

3

• The FITS file:

http://www.ces.clemson.edu/~mbradle/JINA/

Choose alpha-rich.fits

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Tasks for today• S process (sprocess.fits)

– Plot the 4He abundance vs. time (in years: 1 year = 3.15e7 seconds)

– Plot neutron number density vs. time – Plot abundances vs. A for several time records– Investigate steady states

• Nuclear Data– Determine the nucleus with the highest B/A (hint: it is between

Z=20 and Z=30)– Determine the nucleus with the highest B/A but with Z=N (It also

lies between Z=20 and Z=30. Is that nucleus stable against beta decay?)

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Tasks for Today (cont.)

• NSE Calculator– Compute NSE for fixed T and varying density

or varying T and fixed density. Plot abundances vs. the varying quantity. Try this similarly for varying Ye.

• Alpha-rich freezeout (alpha-rich.fits)– Compare network abundances and NSE

abundances at various time records in the calculation.

• Investigate the Oracle (next)

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The Oracle of Bacon

http://oracleofbacon.org