1. Introduction to Nuclear Astrophysics II
Richard H Cyburt

2. Solar System Abundances
Also called…
Cosmic abundances
Solar abundances
Standard abundances
Measured by 2 methods
Meteoritic abundances
Solar Photospheric abundances

3. Abundance Normalizations
Meteoritic abundances cited with a normalization such that N(Si) = 106 atoms
Photospheric abundances determined relative to Hydrogen

4. Abundance Measures Mass fraction: Xi = ri/rB (r = mass density)
Si Xi = 1
Mole fraction: Yi = ni/nB (n = number density)
Xi = Mi/MuYi = AiYi
El/H = ni/nH = Ni/NH (N = column density)
[El/H] = log10(El/H) – log10(El/H)solar

5. Nuclear Masses Z = proton number or atomic number N = neutron number
A = mass number = N+Z
M(A,Z) = Amu + D(A,Z)
D(A,Z) is the mass excess
M(A,Z) = ZmH + Nmn – B(A,Z)
B(A,Z) is the binding energy

6. Q-values REACTION: A+B -> C+D
Q-value is energy released in reaction
Q = MA + MB – MC – MD
For 3He(a,g)7Be Q = MeV

7. Why are Masses important?
Energy release powers stars & explosions
Gamma-rays can be seen…..
COMPTEL all-sky 26Al MeV map

8. Reaction cross section
Cross section is the effective area of interaction for a given reaction.
Gross Estimate: s = pa2
What is the typical interaction size?
Only 2 length-scales
Size of nuclide, R
de Broglie wavelength, k-1 ~ E-1/2
s = p(k-1+R)2

9. What’s a better estimate?
One that includes the probability for penetrating the nucleus…..
For n-induced: P ~ kR
For Z-induced: P ~ (2phkR)exp(-2ph)
h = Z1Z2a2c/v ~ E-1/2

10. S-factor s=E-1S(E)exp(-2ph) Combines de Broglie and penetration
Pulls out geometric terms, leaving only nuclear

11. Cross Section vs S-factor
From NNDC website:
Cyburt & Davids 2008

12. Resonances s ~ GiGf/[ (E-Er)2 + (Gtot/2)2 ]
Gi = 2g2P(E)
g2 = reduced width
Gg ~ Eg3 for E1 transitions
Basics of R-matrix…. (see Descouvemont & Baye 2010)

13. Reaction Rates
Rate = sv
Thermonuclear rate = thermal average

14. The JINA REACLIB Database http://groups.nscl.msu.edu/jina/reaclib/db/
MySQL database
PHP web-interface
Uptodate rxn rates
Continuously updated
Rate version tracking
Includes expt & thry
Cyburt et al. The Astrophysical Journal: Supplement Series 189 (2010) 240

15. NUCDATALIB http://groups.nscl.msu.edu/jina/nucldatalib/
MySQL database
PHP web-interface
Nuclide properties
Masses
Partition functions
Ground state spins
Store existing evaluations
Build libraries w/ evaluations
Includes expt & thry

16. The JINA Virtual Journals
Accessible online
~30 journals
Published weekly
Categorization
notification
JINA VJ
broad NA scope
SEGUE VJ
More obs-based
Cyburt et al. D-Lib Magazine January/February 2010 Volume 16, Number 1/2.

17. Other Online Tools Computational Astrophysics
Data Evaluation/Dissemination
National Nuclear Data Center [
Oak Ridge National Lab’s
NuGrid [
MESA [

18. Conclusions Nuclear Astrophysics is Diverse Field
It requires nuclear input for calculations
Masses
Structure
Reactions
Cross talk between fields is most important