1. University of Victoria Astr 501 Matt Penrice
Nucleosynthesis
University of Victoria
Astr 501
Matt Penrice

2. Outline Basics of nucleosynthesis Nucleosynthesis in stars
Nuclesynthesis on earth
Conclusion

3. Energy Production Stars are powered by nuclear fusion
Energy conservation
Endothermic vs Exothermic

4. Cross Section
Classically the cross section depends on the geometric area of the nuclei
Quantum mechanically the cross section depends on the de Broglie wavelength

5. Reaction Rate
Nuclear reaction rates depend on the number density of projectile and target particles as well as the velocity and cross section
Nuclei in the star will have a velocity distribution therefore
Taking the velocity distribution and identical particles into account we arrive at

6. Mean Lifetime
We also need to know the mean lifetime of nuclei in the star
Therefore we can define the mean lifetime as

7. Maxwell-Boltzmann Distribution
Assume the stellar gas is in thermodynamic equilibrium and nondegenerate and nonrelativistic
Reaction rate per particle revisited
After some hand waving (RM,CMV,CME)

8. Coulomb Barrier
Positively charged nuclei repel each other which forms an energy barrier
Cauldrons in the Cosmos, Rolfs, Rodney

9. Classical Problem
Classically for the p+p reaction to occur the energy of the protons must exceed 550 keV which corresponds to a central stellar temperature of 6.4 GK
This temperature is much higher then what is expected for stellar interiors as well as raising the issue of the fusion causing an explosion rather than a controlled burn
We know that stars burn so how can we resolve this issue?

10. Q&M To The Rescue
Classically a particle with energy E< Ec cannot penetrate the Coulomb barrier. However quantum mechanically it has a finite possibility to “tunnel” through the Coulomb barrier

11. Some Numbers
For a temperature of 0.01 GK if we only consider the high energy wing of the M-B distribution the probability of overcoming the barrier is P=3*10^-375
For a temperature of 0.01 GK the tunneling probability is P=9*10^-10

12. S-Factor
The cross section for charged particle reactions drops sharply for energies below the Coulomb barrier
S(E) is known as the astrophysical S-factor which is slowly varying for nonresonant reactions
Cauldrons in the Cosmos, Rolfs, Rodney

13. Gamow Peak Reaction rate per particle pair again
Cauldrons in the Cosmos, Rolfs, Rodney

14. Narrow Resonance
If the particles in the entrance channel form an excited state decay can occur
This decay can only occur for unique energies and is defined as a resonant phenomenon
Breit-Wigner formula (single-level resonance)

15. Narrow Resonance II
Narrow resonance reaction rate per particle pair

16. Nuclesynthesis On Earth
Hydrogen Bombs
National Ignition Facility

17. Conclusion
Nucleosynthesis in stars requires quantum tunneling to overcome the Coulomb barrier
This allows for controlled nuclear burning giving rise to the long lived low mass stars we see today
Narrow resonance becomes important in lower mass stars where the temperature is lower