Nucleosynthesis

1. 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