464
9 The Unification of Structure and Reaction Frameworks
The 12 C core is mimicked by a Woods–Saxon potential, while the residual
nuclear interaction between valence nucleons is effective and of Furutani–
Horiuchi–Tamagaki type.
Explain why this model space is appropriate to calculate the resonance
spectrum of 15 F as well as the excitation function of the reaction 14 O(p,p). For
the latter point, use the fact that proton projectile energies are smaller than
6 MeV (see Ref.[73]).
B. Using physical arguments, show that the 1/2 + and 5/2 + resonance states have
a single-particle character.
The experimental width of the 1/2 − resonance is small, of about 40 keV.
Its experimental energy, of about 4.8 MeV with respect to proton emission
threshold, is well above the Coulomb barrier, situated at 1.2 MeV above proton
emission threshold. Consequently, explain why the 1/2 − resonance state must
have a complicated structure.
C. Run the Gamow shell model code to obtain the resonance spectrum of 15 F.
From the configuration mixing associated to the 1/2 + and 5/2 + , and 1/2 −
many-body states, show that the 1/2 + and 5/2 + resonance states are singleparticle states.
Explain the relative stability of the 1/2 − resonance state from its configuration mixing.
D. Run the Gamow shell model coupled-channel code to obtain the resonance
spectrum of 15 F.
Explain why the latter spectrum and that calculated in C slightly differ.
E. Run the Gamow shell model coupled-channel code to generate the excitation
function of the reaction 14 O(p,p).
From the plot of the 14 O(p,p) excitation function, indicate the energy zones
where the influence of the resonance states of 15 F on the cross section is the
most important.
Explain the form of the cross section therein.
9.4.2 Radiative Capture Cross Sections in the Mass Region A = 6–8
Nuclei in the mass region A = 6–8 of nuclear chart are of great importance in
nuclear astrophysics. The 7 Be(p, γ ) reaction is responsible of the most energetic
solar neutrinos [77]. It occurs at the end of the proton–proton chain and is apparently
responsible for most of solar energy release [78]. It is also directly linked to the socalled solar neutrino problem, where the neutrino flux arising from 8 B in the sun,
measured experimentally, is twice smaller than the prediction of the standard model
[79]. This problem was solved recently with the discovery of nonzero masses of
neutrinos, responsible for neutrino flavor oscillations [80]. In the standard model,
the neutrino had always been considered as massless [79].
9 The Unification of Structure and Reaction Frameworks
The 12 C core is mimicked by a Woods–Saxon potential, while the residual
nuclear interaction between valence nucleons is effective and of Furutani–
Horiuchi–Tamagaki type.
Explain why this model space is appropriate to calculate the resonance
spectrum of 15 F as well as the excitation function of the reaction 14 O(p,p). For
the latter point, use the fact that proton projectile energies are smaller than
6 MeV (see Ref.[73]).
B. Using physical arguments, show that the 1/2 + and 5/2 + resonance states have
a single-particle character.
The experimental width of the 1/2 − resonance is small, of about 40 keV.
Its experimental energy, of about 4.8 MeV with respect to proton emission
threshold, is well above the Coulomb barrier, situated at 1.2 MeV above proton
emission threshold. Consequently, explain why the 1/2 − resonance state must
have a complicated structure.
C. Run the Gamow shell model code to obtain the resonance spectrum of 15 F.
From the configuration mixing associated to the 1/2 + and 5/2 + , and 1/2 −
many-body states, show that the 1/2 + and 5/2 + resonance states are singleparticle states.
Explain the relative stability of the 1/2 − resonance state from its configuration mixing.
D. Run the Gamow shell model coupled-channel code to obtain the resonance
spectrum of 15 F.
Explain why the latter spectrum and that calculated in C slightly differ.
E. Run the Gamow shell model coupled-channel code to generate the excitation
function of the reaction 14 O(p,p).
From the plot of the 14 O(p,p) excitation function, indicate the energy zones
where the influence of the resonance states of 15 F on the cross section is the
most important.
Explain the form of the cross section therein.
9.4.2 Radiative Capture Cross Sections in the Mass Region A = 6–8
Nuclei in the mass region A = 6–8 of nuclear chart are of great importance in
nuclear astrophysics. The 7 Be(p, γ ) reaction is responsible of the most energetic
solar neutrinos [77]. It occurs at the end of the proton–proton chain and is apparently
responsible for most of solar energy release [78]. It is also directly linked to the socalled solar neutrino problem, where the neutrino flux arising from 8 B in the sun,
measured experimentally, is twice smaller than the prediction of the standard model
[79]. This problem was solved recently with the discovery of nonzero masses of
neutrinos, responsible for neutrino flavor oscillations [80]. In the standard model,
the neutrino had always been considered as massless [79].