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Nucleosynthesis

Nucleosynthesis. University of Victoria Astr 501 Matt Penrice. Outline. Basics of nucleosynthesis Nucleosynthesis in stars Nuclesynthesis on earth Conclusion. Energy Production. Stars are powered by nuclear fusion Energy conservation Endothermic vs Exothermic. Cross Section.

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Nucleosynthesis

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  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

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