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

Selection rules:

Nuclear Astrophysics: transferDWBA angular cross section

Nuclear Astrophysics: transfer

Angular momentum selection

Nuclear Astrophysics: neutron induced

No Coulomb means:

12C(n, γ) 13C

Nuclear Astrophysics: screeningDWBA angular cross section

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

Nuclear Astrophysics: indirect methodsCoulomb Dissociation

ANC method

Nuclear Astrophysics: indirect methodsSub-threshold state

Above threshold the width relates to the ANC

Nuclear Astrophysics:Testing the ANC method