I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars.

Arthur Eddington

Betsy Beise, University of Maryland; Philippe Chomaz, GANIL; Alexandra Gade, Michigan State University; Bob McKeown, California Institute of Technology;

Frank Timmes, University of Arizona; Bill Zajc, Columbia University; John Hardy, Texas A&M University;Dave Morrissey, Michigan State University; Witek Nazarewicz, University of Tennessee; Derek Teaney,Stony Brook University; Michael Wiescher, University of Notre Dame; Sherry Yennello, Texas A&M University

National Science Foundation; US Department of Energy's Institute for Nuclear Theory;Michigan State University; National Superconducting Cyclotron Laboratory (NSCL)

June 28-July 10, 2009National Superconducting Cyclotron Laboratory (NSCL)Michigan State University | East Lansing, Michigan

http://meetings.nscl.msu.edu/NNPSS09

topics:invited lecturers:

sponsors:

Lectures, activities, and networking opportunities fornuclear physicists 1-2 years on either side of the PhD

2009 NATIONALNUCLEAR PHYSICSSUMMER SCHOOL

Hadron Physics, Nuclear Reactions, Nuclear Structure, QCD,Neutrinos, Nuclear Astrophysics, Fundamental Symmetries

organizers: nnpss@nscl.msu.eduHendrik Schatz (Chair), Wolfgang Bauer, Shari Conroy, Michael Thoennessen

Frank Timmes

Nuclear Astrophysics: Reaction Networks

Michigan State University 30Jun2009 - 02Jul2009

cococubed.asu.edu ftimmes@asu.edu

Outline for 01Jul2009

1. Three Vignettes

a. Energy Generation

b. Linear Algebra

c. Thermodynamic trajectories

2. Big Bang Nucleosynthesis

Stuff of the day

Synthesis of the elements in stars: forty years of progress cococubed.asu.edu/papers/wallerstein97.pdf

An answer to yesterday’s task

10 12 14 16 18 20 22

10-7

10-5

10-3

10-1

Mass F

raction

Time (s)

Cold CNO cycles, hydrostatic burn, T=15x106 K ρ=150 g cm

-3

H H H

H

H

H

α

α

α

αα α α α

C12

C12 C12 C12 C12C12C12 C12

C13

C13 C13 C13 C13C13C13 C13

N14

N14 N14 N14 N14N14N14 N14

N15

N15 N15 N15 N15N15N15 N15O16

O16

O16 O16O16O16 O16

O17

O17O17O17O17 O17

O18O18O18O18 O18

F19F19F19F19 F19

10-4

10-2

100

102

εnuc (e

rg g

-1 s-1)

ε

ε ε

ε

ε

ε

12C

13N

13C 14N

15O

15N

Cycle 1

(p, )

(p, )

(p, )(,e+ )

(,e+ )

(p, )

17O

17F

16O

18F

18O 19F

Cycle 2 Cycle 3

Cycle 4

(p, )

(p, )

(p, )

(p, )

(,e+ )

(,e+ )

(p, )

(p, )(p, )

14O 18Ne

(p, )

(p, )

(,e+ )(,e+ )

(p, )

( ,p)

19Ne( )

rp process

CNO: T9 < 0.2 Hot CNO: 0.2 < T9 < 0.5 rp process: T9 > 0.5

(,e+ )

An answer to yesterday’s task

10-11

10-7

10-3

101

105

109

1013

10-15

10-11

10-7

10-3

101

Mass F

raction

Time (s)

* hydrostatic: btemp= 3.000E+09 bden= 1.000E+09

he4 he4he4

he4he4

he4

he4

he4 he4

he4he4

he4

he4he4

he4 he4he4

he4he4 he4

c12

c12c12c12

c12

c12c12

c12

c12

c12

c12c12 c12 c12c12

c12

c12

c12

o16

o16o16o16

o16

o16o16 o16

o16

o16 o16o16o16

o16

o16

o16

o16

o16

o16

o16

ne20

ne20ne20ne20

ne20

ne20ne20

ne20

ne20

ne20

ne20

ne20

ne20 ne20ne20

ne20

ne20

ne20

mg24

mg24mg24mg24

mg24

mg24mg24

mg24

mg24

mg24

mg24

mg24

mg24mg24

mg24

mg24

mg24

mg24

mg24

mg24

si28

si28si28si28

si28

si28si28si28

si28 si28

si28

si28si28 si28 si28

si28

si28

si28

si28

si28

s32

s32s32s32

s32

s32s32 s32 s32

s32

s32s32s32

s32 s32

s32

s32

s32

s32

s32ar36

ar36ar36ar36

ar36

ar36ar36ar36

ar36

ar36ar36

ar36

ar36

ar36ar36

ar36

ar36

ar36

ar36

ar36

ca40

ca40ca40ca40

ca40

ca40ca40ca40

ca40ca40

ca40

ca40

ca40

ca40

ca40ca40

ca40

ca40

ca40

ca40

ti44

ti44

ti44ti44ti44ti44ti44 ti44 ti44

ti44

ti44

ti44

ti44 ti44

ti44ti44

ti44

ti44

ti44ti44

cr48

cr48

cr48cr48cr48cr48cr48cr48 cr48 cr48 cr48

cr48cr48

cr48

cr48 cr48cr48

cr48cr48

cr48

fe52

fe52

fe52

fe52fe52

fe52fe52fe52 fe52 fe52 fe52fe52fe52

fe52fe52 fe52fe52

fe52fe52 fe52

ni56

ni56

ni56

ni56ni56ni56 ni56 ni56 ni56 ni56ni56ni56

ni56 ni56 ni56ni56ni56 ni56 ni56

1013

1017

1021

1025

εnuc (e

rg g

-1 s-1)

ε εεεεεεε

ε

ε

ε

ε

ε

ε

εεεε

εε

4He 12C 16O

27Al 31P 35Cl 39K 43Sc 47V 51Mn 55Co

20Ne 24Mg 28Si 32S 36Ar 40Ca 44Ti 48Cr 52Fe 56Ni

(α,γ)(αα,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ) (α,γ)

(p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p) (p,γ)(α,p)

Alpha-chain Network

Energy Generation

εnuc = −

∑

i

NAMic2Yi − εν (erg g−1 s−1)

An important consequence of changing the composition is the release (or absorption) of energy. The energy generation rate is

where Mi c2 is the rest mass energy of species i. Using

Mi = Aimµ + Mex,i

εnuc =∑

i

NAEbind,iYi −

∑

i

NA(ZiMex,p + NiMex,n)Yi − εν

Mex,i = ZiMex,p + NiMex,n −Bi/c2

the energy generation rate is sometimes written as

The energy lost to the freely streaming neutrinos has two parts: weak reactions and neutrino thermal processes.

For weak reactions, average energy losses are calculated for each nucleus by considering the excited state distribution, Gamow-Teller distribution, etc.

εν =

∑

i

⟨Eν⟩Yi,weak

The results are tabulated; see for example Langanke & Martinez-Pinedo (2000).

3 6 9

T9

10−80

10−60

10−40

10−20

ρYe= 10

7

ρYe= 10

8

ρYe= 10

9

ρYe= 10

10

10−4

10−2

100

102

104

3 6 9

T9

10−80

10−60

10−40

10−20

10−6

10−5

10−4

10−3

10−2

10−1

56Co e

− capture

56Co β

+

decay

56Fe e

+

capture56

Fe β− decay

λ (

s−1)

Thermal neutrinos processes include

pair neutrino:

photoneutrino:

plasma neutrino:

bremsstrahlung:

recombination:

Results are typically expressed in tables or fitting formulas, for example, Itoh et al. 1996.

e+

+ e−

→ ν + ν

e+

+ γ → e−

+ ν + ν

γplasmon → ν + ν

e−

continuum→ e

−

bound+ ν + ν

e− + N(Z, A)→ e− + N(Z, A) + ν + ν

100

103

106

109

1012

10-4

10-2

100

102

104

106

108

Density (g/cm3)

Energ

y L

oss R

ate

(erg

/g/s

)

T=5e8 K X(12

C)=X(16

O)=0.5

Pair neutrino

Photoneutrino

Plasma neutrino

Bremsstrahlung

Recombination

Total

Interlude

Kamiokande neutrinos SN1987A

÷x = b

Within our implicit integrations we’re solving (large) systems of linear equations. As the linear algebra generally dominates the time to obtain a solution, we’ll want to use efficient solvers.

We’ll briefly look at dense, direct sparse, and iterative sparse solvers.

Matrix à is reduced to upper triangular form in tandem with a right-hand side b by Gaussian elimination, and backsubstitution on the upper triangular matrix yields the solution to ÷x = b.

This is the method you probably first learned.

If the arithmetic is exact, then the answer computed in this manner will be exact, if no zeros appear on the diagonal.

2 −1 1

−2 2 −3

2 −4 3

x1

x2

x3

=

3

−7

3

1 −1/2 1/2

−2 2 −3

2 −4 3

x1

x2

x3

=

3/2

−7

3

1 −1/2 1/2

0 1 −2

0 −3 2

x1

x2

x3

=

3/2

−4

0

1 −1/2 1/2

0 1 −2

0 0 −4

x1

x2

x3

=

3/2

−4

−12

1 −1/2 1/2

0 1 −2

0 0 1

x1

x2

x3

=

3/2

−4

3

x3 = 3 x2 = 2 x1 = 1

But computer arithmetic is not exact, so there will always be some truncation and rounding error in the answer.

If a “small” number appears on the diagonal, then its use as the pivot may lead to computing differences between big numbers and little numbers with a subsequent loss of precision.

A way around this problem is to ensure small pivots are not used by swapping rows (partial pivoting) or rows and columns (full pivoting), so as to use a particularly desirable pivot element.

What is a desirable pivot? It is not completely known theoretically. It is known, both theoretically and in practice, that simply picking the largest available element as the pivot is a very good choice.

Fact: Gauss elimination with no pivoting is numerically unstable in the presence of any roundoff error, even when a small pivot is not encountered. Never do Gauss elimination without pivoting!

LEQS is a dense matrix, Gaussian elimination routine.

The maximum element in each row serves as the pivot element, but no row or column interchanges are performed, so LEQS may be unstable on matrices that are not diagonally dominant.

A small amount of effort is expended to minimize calculations with matrix elements that are zero.

All Gaussian elimination routines have the disadvantage that for a sequence of right-hand sides, the entire matrix must be decomposed for each right-hand side.

The origin of LEQS is somewhat obscure, but circa 1962. It may be the most common linear algebra solver used for evolving nuclear reaction networks.

Ford-Seattle

1962

A · x =

(

L · U

)

· x = L ·

(

U · x

)

= b

A frequently used form of Gauss Elimination is LU decomposition.

The basic idea is to find two matrices L and U such that LU = Ã, where L is a lower triangular matrix (zero above the diagonal) and U is an upper triangular matrix (zero below the diagonal).

Once we have computed L and U we the solve L·y=b then U·x=y,a process that takes O(n2) operations.

While the factorization stage still requires O(n3) operations, it need be done only once. We can solve with as many right-hand sides as we care to, one at a time. This is a superior advantage.

A linear system is called sparse if only a relatively small number of its matrix elements aij are nonzero.

It is wasteful to use general methods on such problems, because most of storage the O(n3) operations involve zero operands.

Direct methods for sparse matrices are not that different from dense LU decomposition methods; they are just cleverly applied with due attention to the bookkeeping of zero elements.

The basic approach that all solvers use are 1) Symbolic decomposition 2) Numerical decomposition 3) Backsubstitution 4) Iterative polishing

MA28 is the Coke classic of sparse matrix solvers. hsl.rl.ac.uk/archive/hslarchive.html

UMFPACK is a modern, direct sparse matrix solver. www.cise.ufl.edu/research/sparse/umfpack

Iterative methods for sparse systems only reference the matrix à only through multiplication of a vector. “Matrix free” methods.

Iterative methods can be slow to converge and the number of iterations to reach a given level of accuracy is not known a priori.

A popular method, generalized minimum residuals, seeks a minimization of the function

One way to generate a good “guess” is to solve some portion of Ã, call it matrix Z, that is easy to solve. Z is called the preconditioner.

⇤f(x) = AT

·

�

A · x � b

⇥

f(x) =1

2r · r =

1

2

�

�

�A · x− b

�

�

�

2

BiCG is described by Barret et al in “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods”. netlib2.cs.utk.edu/linalg/html_templates/Templates.html

SPARSKIT is a modern, iterative sparse matrix solver. www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html

Interlude

We’ve been holding the temperature and density constant;

Such conditions are called “hydrostatic” burning, since the local energy release doesn’t change the temperature or density, as during the hydrostatic phases of a star’s evolution.

dT

dt= 0

dρ

dt= 0

We will now relax these assumptions, andconsider any thermodynamic profile.

Density

Temperature

t=0

t=1

t=2

t=3

t=4

We could evolve temperature and density ODEs separately and then evolve the reaction network, or we can evolve the temperature and density ODEs simultaneously with the network.

The first is “operator splitting” and assumes a loose coupling between physical processes. Operator splitting is easy to implement and, by far, the most common choice.

An example when the assumption of loose coupling breaks down.

Time Step

Tem

pera

ture

n n+1 n+2

TooCool

TooHot

JustRight

• Photodisintegration dominates• Negative energy generation rate• Material cools

• Electron capture dominates• Positive energy generation rate• Material heats

What thetemperatureshould do

A Hydrodynamic-Burning Instability

The second is “unsplit”. It avoids the coupling issues, but is more difficult to implement, particularly for implicit integrations.

Our networks uses the unsplit method. Energy, temperature and density burning ODEs are appended to the reaction network.

T

T

ρ

ρ

These entries from the

temperature and density

derivatives of the reaction

rates

enuc

enuc

These entries from the

abundance derivatives

As an example, during the Big Bang the photon temperature of the expanding universe obeys the ODE:

dT

dt=

√

8πGaf(x)

3c2T 3

[

xdg/dT

3g− 1

]

−1

f(x) = 1 +45

2π4

∫

∞

0

[

√

x2 + y2 +y2

3√

x2 + y2

]

exp[

√

x2 + y2 + 1]

−1

y2dy

g(x) = 1 + Nν

7

8

[

4

11f(x)

]4/3

+

∫

∞

0

√

x2 + y2

[

exp(

√

x2 + y2

)

+ 1]

−1

y2dy

x =

mec2

kT

where

We can know the temperature at any given time because the dominant constituents are either massless or relativistic.

What we don’t know a priori is the density ρb of ordinary matter in the expanding universe. How shall we parameterize our ignorance?

A common way to express the baryon density is in terms of a baryon-to-photon ratio; the number of photons for every particle.

Mass density and number density

Number density of photons

Baryon density in terms of the photon temperature and the free parameter nb/nγ

ρb =

nb

NA

nγ =30ζ(3)

π4

aT3

γ

k

ρb =nb

nγ

=30ζ(3)

π4kNA

T3

γ

How our universe cools and gets less dense, for a given nb/nγ ratio.

Expansion factor R/R0

10-12 10-10 10-8 10-6 10-4 10-2

1

102

104

106

108

1010

1012T

em

pera

ture

(K

)

1010

1

10-10

10-20

10-30

10-40

All C

onst

itue

nts

in E

quilib

rium

PairsAnnihilate

RadiationUniverse

MatterUniverse

1 104 108 1012 1016

Time (sec)

Dens

ity

(g/c

m3)

Normalized to ρ0 = 2x10-29 g/cm3 and T

0 = 3 K

T=Tν

Tγ

Tν

ρν

ρb

ργ

ρe

ρν=ρe

Now

A typical Big Bang reaction network.

(n,γ)

(d,γ)

(n,γ)

(n,γ)

(p,γ)(p,γ)

(p,γ)

(ν,e-)(e+,ν)

free decay

(d,p)

(n,p)

(d,n)

To Be

7

From

Be7

From

Be8

From

Li7

To Li7

Exoergic Direction

(d,p)(t,pn)

(He3,2p)

(He4 ,γ)

(d,n)

(He3,pn)

(t,2n)

(n,H

e4 )

(γ,H

e4 )

(p,H

e4 )

(He4 ,γ)

p d

He3 He4

t

n

For times < 15 s the temperature > 3 billion K, and our universe is still a soup of protons, neutrons, electrons and more exotic matter. Anything more complex is blasted apart by high energy photons.

101

102

103

104

105

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

101

Mass F

raction

Time (s)

* big bang: eta= 6.140E-10 Nnu= 3.000E+00 H0= 7.100E+01 Tcmb= 2.730E+00

nnnnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

n

n

n

n

nn

n

n

n

pppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp p p p p p p p

dddddddd

dddd

dddd

ddddd

ddddddddd

dddddddddddddddddddddddddddd

dd

dd d d d d d

t

ttttttttt

tt

t tt t

ttttt

ttt t

ttttttttttttttttttttttttttttttttt

tt

tt

t t t t t

he3

he3he3he3he3he3he3he3he3he3

he3he3

he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3 he3 he3 he3 he3 he3

he4he4he4

he4he4he4he4he4he4he4

he4he4

he4he4

he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4 he4 he4 he4 he4 he4

li6li6li6li6li6

li6li6li6li6li6li6li6li6li6li6li6li6li6li6li6

li6li6

li6li6

li6 li6 li6 li6 li6

li7

li7li7

li7li7li7li7li7

li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7

li7li7

li7li7 li7 li7 li7 li7 li7

be7be7be7be7be7be7be7be7be7be7be7be7be7be7be7

be7

be7

be7be7 be7 be7 be7 be7 be7

b11b11b11b11b11b11b11b11b11b11b11b11b11

b11b11

b11

By 3 min deuterium survives after it is fused and is quickly turned into helium. Without deuterium all the neutrons would decay and our universe would be pure hydrogen.

101

102

103

104

105

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

101

Mass F

raction

Time (s)

* big bang: eta= 6.140E-10 Nnu= 3.000E+00 H0= 7.100E+01 Tcmb= 2.730E+00

nnnnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

n

n

n

n

nn

n

n

n

pppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp p p p p p p p

dddddddd

dddd

dddd

ddddd

ddddddddd

dddddddddddddddddddddddddddd

dd

dd d d d d d

t

ttttttttt

tt

t tt t

ttttt

ttt t

ttttttttttttttttttttttttttttttttt

tt

tt

t t t t t

he3

he3he3he3he3he3he3he3he3he3

he3he3

he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3 he3 he3 he3 he3 he3

he4he4he4

he4he4he4he4he4he4he4

he4he4

he4he4

he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4 he4 he4 he4 he4 he4

li6li6li6li6li6

li6li6li6li6li6li6li6li6li6li6li6li6li6li6li6

li6li6

li6li6

li6 li6 li6 li6 li6

li7

li7li7

li7li7li7li7li7

li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7

li7li7

li7li7 li7 li7 li7 li7 li7

be7be7be7be7be7be7be7be7be7be7be7be7be7be7be7

be7

be7

be7be7 be7 be7 be7 be7 be7

b11b11b11b11b11b11b11b11b11b11b11b11b11

b11b11

b11

Carbon and oxygen are not produced since: (1) there are no stable isotopes with 5 or 8 nucleons, (2) the Coulomb barrier starts to be significant, (3) the low density suppresses the fusion of helium to carbon.

By 35 min nucleosynthesis is essentially complete.

101

102

103

104

105

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

101

Mass F

raction

Time (s)

* big bang: eta= 6.140E-10 Nnu= 3.000E+00 H0= 7.100E+01 Tcmb= 2.730E+00

nnnnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

n

n

n

n

nn

n

n

n

pppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp p p p p p p p

dddddddd

dddd

dddd

ddddd

ddddddddd

dddddddddddddddddddddddddddd

dd

dd d d d d d

t

ttttttttt

tt

t tt t

ttttt

ttt t

ttttttttttttttttttttttttttttttttt

tt

tt

t t t t t

he3

he3he3he3he3he3he3he3he3he3

he3he3

he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3he3 he3 he3 he3 he3 he3

he4he4he4

he4he4he4he4he4he4he4

he4he4

he4he4

he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4

he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4he4 he4 he4 he4 he4 he4

li6li6li6li6li6

li6li6li6li6li6li6li6li6li6li6li6li6li6li6li6

li6li6

li6li6

li6 li6 li6 li6 li6

li7

li7li7

li7li7li7li7li7

li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7li7

li7li7

li7li7 li7 li7 li7 li7 li7

be7be7be7be7be7be7be7be7be7be7be7be7be7be7be7

be7

be7

be7be7 be7 be7 be7 be7 be7

b11b11b11b11b11b11b11b11b11b11b11b11b11

b11b11

b11

A key unknown in big bang nucleosynthesis had been the density of ordinary matter ρb. The cosmic microwave background provides by far the most precise determination.

WMAP

10-33

10-32

10-31

10-30

10-29

10-28

10-11

10-9

10-7

10-5

10-3

10-1

Baryon mass density (g/cm3)

Mass fra

ction

H0=70.5 km/s/Mpc T

cmb=2.725 K N

ν=3.0 τ

neutron=885.7 s

d d d dd

dd

dd

d

d

d

d

he3he3he3he3he3he3

he3he3he3he3he3he3he3he3he3he3he3he3he3

αα

αα α α α α α α α α α α α α α α α

li6li6 li6 li6

li7

li7

li7li7 li7

li7

li7li7

li7li7

li7 li7 li7 li7 li7 li7 li7 li7 li7

c11c11

c11c11

c11c11

c11c11

c11

ρcrit

The observed light element abundances is consistent with a WMAP determined baryon density, with the possible exception of 7Li.

Several independent measurements lead to a consistent constraint.

WMAP.22

.23

.24

.25

.26

H0=70.5 km/s/Mpc T

cmb=2.725 K N

ν=3.0 τ

neutron=885.7 s

~ ~

4He

10-5

10-4

Mass F

raction

~ ~

2H

3He

2×10-31

4×10-31

6×10-31

10-9

10-8

Baryon mass density

7Li

Download, compile, and run the Big Bang nucleosynthesis code from cococubed.asu.edu/code_pages/burn.shtml Plot the evolution of the abundances.

Download, compile, and run the Big Bang thermodynamics code from cococubed.asu.edu/code_pages/burn.shtml Plot the evolution of the photon and neutrino temperatures.

Tasks for the day

Questions and Discussion

Betsy Beise, University of Maryland; Philippe Chomaz, GANIL; Alexandra Gade, Michigan State University; Bob McKeown, California Institute of Technology;

Frank Timmes, University of Arizona; Bill Zajc, Columbia University; John Hardy, Texas A&M University;Dave Morrissey, Michigan State University; Witek Nazarewicz, University of Tennessee; Derek Teaney,Stony Brook University; Michael Wiescher, University of Notre Dame; Sherry Yennello, Texas A&M University

National Science Foundation; US Department of Energy's Institute for Nuclear Theory;Michigan State University; National Superconducting Cyclotron Laboratory (NSCL)

June 28-July 10, 2009National Superconducting Cyclotron Laboratory (NSCL)Michigan State University | East Lansing, Michigan

http://meetings.nscl.msu.edu/NNPSS09

topics:invited lecturers:

sponsors:

Lectures, activities, and networking opportunities fornuclear physicists 1-2 years on either side of the PhD

2009 NATIONALNUCLEAR PHYSICSSUMMER SCHOOL

Hadron Physics, Nuclear Reactions, Nuclear Structure, QCD,Neutrinos, Nuclear Astrophysics, Fundamental Symmetries

organizers: nnpss@nscl.msu.eduHendrik Schatz (Chair), Wolfgang Bauer, Shari Conroy, Michael Thoennessen