476
9 The Unification of Structure and Reaction Frameworks
orbital angular momentum ≤ 4 are taken into account. As the single-particle
states of 41 Ca and 41 Sc are built from fp shells, therefore only the = 1, 3 parts of
the Woods–Saxon potential can be fitted from the spectrum of A = 41 nuclei. The
= 0, 2, 4 parts of the Woods–Saxon potential are then fitted from the 40 Ca(p,p) and
40 Ca(n,n) scattering reactions, where all partial waves are involved. The parameters
of the Furutani–Horiuchi–Tamagaki interaction are fitted to the energies of lowlying states in the spectrum of 42 Sc.
Used reaction channels are built from the resonant target states of 41 Ca and
41 Sc, whose angular momentum is equal to 1/2 − , . . . , 7/2 − , and from the
first scattering target states of 41 Ca and 41 Sc of angular momentum equal to
1/2 ± , . . . , 7/2 ± , 9/2 + . The obtained energies of the nuclear eigenstates of 42 Sc
are shown in Fig. 9.9. In order to ponder out the importance of nonresonant targets
in the eigenstates of 42 Sc, no corrective factor has been used in the coupled-channel
Hamiltonian. It is clear from Fig.9.9 that the inclusion of nonresonant target states
in the basis of coupled channels is necessary in general. Discrepancies between the
energies calculated with Gamow shell model and Gamow shell model with coupled
channels, where nonresonant targets are neglected, can be as large as 600 keV, as
is the case for the 0 + ground state of 42 Sc. The effect of nonresonant target states
is relatively smaller for the excited states of 42 Sc. This is especially the case for
the 5 + and 7 + eigenstates, where energy difference is about 100 keV in all used
calculation schemes. In other excited states, the energy difference remains close to
200–300 keV. Clearly, these differences arise from the different nucleon–nucleon
Fig. 9.9 Low-lying spectrum of 42 Sc calculated in Gamow shell model (E GSM ) and coupledchannel Gamow shell model with channels built from resonant target states only (E GSM-CC ) or
from both resonant and nonresonant target states (E GSM-CC(NRC) ). Calculated energies are given
with respect to the 40 Ca core (from Ref. [104])
9 The Unification of Structure and Reaction Frameworks
orbital angular momentum ≤ 4 are taken into account. As the single-particle
states of 41 Ca and 41 Sc are built from fp shells, therefore only the = 1, 3 parts of
the Woods–Saxon potential can be fitted from the spectrum of A = 41 nuclei. The
= 0, 2, 4 parts of the Woods–Saxon potential are then fitted from the 40 Ca(p,p) and
40 Ca(n,n) scattering reactions, where all partial waves are involved. The parameters
of the Furutani–Horiuchi–Tamagaki interaction are fitted to the energies of lowlying states in the spectrum of 42 Sc.
Used reaction channels are built from the resonant target states of 41 Ca and
41 Sc, whose angular momentum is equal to 1/2 − , . . . , 7/2 − , and from the
first scattering target states of 41 Ca and 41 Sc of angular momentum equal to
1/2 ± , . . . , 7/2 ± , 9/2 + . The obtained energies of the nuclear eigenstates of 42 Sc
are shown in Fig. 9.9. In order to ponder out the importance of nonresonant targets
in the eigenstates of 42 Sc, no corrective factor has been used in the coupled-channel
Hamiltonian. It is clear from Fig.9.9 that the inclusion of nonresonant target states
in the basis of coupled channels is necessary in general. Discrepancies between the
energies calculated with Gamow shell model and Gamow shell model with coupled
channels, where nonresonant targets are neglected, can be as large as 600 keV, as
is the case for the 0 + ground state of 42 Sc. The effect of nonresonant target states
is relatively smaller for the excited states of 42 Sc. This is especially the case for
the 5 + and 7 + eigenstates, where energy difference is about 100 keV in all used
calculation schemes. In other excited states, the energy difference remains close to
200–300 keV. Clearly, these differences arise from the different nucleon–nucleon
Fig. 9.9 Low-lying spectrum of 42 Sc calculated in Gamow shell model (E GSM ) and coupledchannel Gamow shell model with channels built from resonant target states only (E GSM-CC ) or
from both resonant and nonresonant target states (E GSM-CC(NRC) ). Calculated energies are given
with respect to the 40 Ca core (from Ref. [104])