Transcript of F. Nunes (Universidade Fernando Pessoa, Porto)
Nuclear Astrophysics
Nuclear Astrophysics:Schematics: direct capture
Nuclear Astrophysics:Schematics: resonant capture
Nuclear Astrophysics:Schematics: subthreshold state
Nuclear Astrophysics:Schematics
Nuclear Astrophysics
Gamow window
Reaction rate at a temperature T
Astrophysical S-factor
E0 and ΔE0
Nuclear Astrophysics: resonant vs direct
If lR=lmin
Reaction cross section:
Resonant part -> R-matrix
otherwise
Direct part -> next
Nuclear Astrophysics
Asymptotic behaviour of the solutions:
A(a, γ)B
Final state
Initial state
Nuclear Astrophysics
Shift factor and penetration factor
At low energies
•For negative energies, the penetration factor has no meaning, but shift factor can still be defined•For neutron induces (no charge) the penetration factor goes as k2l+1.
Nuclear Astrophysics
Nuclear Astrophysics: radiative processes
Multipole decomposition of the E.M. field
The photon emission hamiltonian is weak compared to the nuclear, thus we use first order perturbation:
Long wave-length approximation
Nuclear Astrophysics: radiative processes
Radiative capture cross section in terms of the multipoles
Nuclear Astrophysics: low energy S-factorElements that determine the low energy dependence
• κ – bound state pole• Li Initial centrifugal barrier• ηi Remnant of the initial Coulomb barrier• Lf Final centrifugal barrier• ηf Final Coulomb barrier
Nuclear Astrophysics: low energy S-factorBound state pole
Nuclear Astrophysics: low energy S-factorBound state pole
Nuclear Astrophysics: low energy S-factorBound state pole
Nuclear Astrophysics: low energy S-factorEffect of the remnant of the initial Coulomb barrier
Nuclear Astrophysics: low energy S-factorEffect of the remnant of the initial Coulomb barrier
Nuclear Astrophysics: low energy S-factorExamples:
Nuclear Astrophysics: low energy S-factorExamples:
Nuclear Astrophysics: low energy S-factorTaylor expansions: of S(E) for charged particle
of (σ v) for neutrons
Nuclear Astrophysics: low energy S-factorTaylor expansions