9
The Unification of Structure and Reaction
Frameworks
It has become customary to separate nuclear structure from nuclear reactions in the
development of theoretical models, even though both of them arise from the same
Hamiltonian [1–7]. In standard reaction frameworks [3, 4, 6], the structure aspects
of many-body nuclear states have been only indirectly included. For example, it
is customary to use coupled-channel equations and one-body optical potentials
to calculate reaction cross sections, whereby the parameters entering one-body
optical potentials are directly fitted from experimental data [8–11]. Consequently,
the correlations present in many-body nuclear states are considered only from an
effective point of view, as they only enter the fitted parameters of reaction potentials
[8–11]. It is also common to separate cross sections into two parts, one coming from
a calculation where the effect of nuclear structure degrees of freedom is averaged
within a mean-field potential, such as the distorted wave Born approximation, and
the other being a spectroscopic factor calculated in the standard shell model. In fact,
nuclear structure and reaction degrees of freedom are decoupled in this approach, so
there is no consistency between the Hamiltonians used for the calculation of nuclear
structure and nuclear reaction observables.
Cross sections can be usually written as the product of two factors, one containing
the kinetic dependence of the considered reaction and the other its correlation part
(see Sect. 7.4.1). However, even if the results obtained in this approach compare
well with experimental data in well-bound nuclei, they are not satisfactory when
considering weakly bound and resonance many-body states. Indeed, in a vicinity of
the driplines, nuclei exhibit halos or are unbound even in the ground state. Moreover,
many-body wave functions strongly depend on separation energies and on the partial
waves present in the model (see Sect. 7.4.2). Therefore, in the description of nuclear
reactions, aspects of the structure and the reaction can no longer be approximated
by the aforementioned factorization and are, on the opposite, intertwined. Hence,
it is necessary to devise a theoretical approach for nuclear reactions treating internucleon correlations and continuum degrees of freedom on the same footing.
© Springer International Publishing AG 2021
N. Michel, M. Płoszajczak, Gamow Shell Model, Lecture Notes in Physics 983,
https://doi.org/10.1007/978-3-030-69356-5_9
401
The Unification of Structure and Reaction
Frameworks
It has become customary to separate nuclear structure from nuclear reactions in the
development of theoretical models, even though both of them arise from the same
Hamiltonian [1–7]. In standard reaction frameworks [3, 4, 6], the structure aspects
of many-body nuclear states have been only indirectly included. For example, it
is customary to use coupled-channel equations and one-body optical potentials
to calculate reaction cross sections, whereby the parameters entering one-body
optical potentials are directly fitted from experimental data [8–11]. Consequently,
the correlations present in many-body nuclear states are considered only from an
effective point of view, as they only enter the fitted parameters of reaction potentials
[8–11]. It is also common to separate cross sections into two parts, one coming from
a calculation where the effect of nuclear structure degrees of freedom is averaged
within a mean-field potential, such as the distorted wave Born approximation, and
the other being a spectroscopic factor calculated in the standard shell model. In fact,
nuclear structure and reaction degrees of freedom are decoupled in this approach, so
there is no consistency between the Hamiltonians used for the calculation of nuclear
structure and nuclear reaction observables.
Cross sections can be usually written as the product of two factors, one containing
the kinetic dependence of the considered reaction and the other its correlation part
(see Sect. 7.4.1). However, even if the results obtained in this approach compare
well with experimental data in well-bound nuclei, they are not satisfactory when
considering weakly bound and resonance many-body states. Indeed, in a vicinity of
the driplines, nuclei exhibit halos or are unbound even in the ground state. Moreover,
many-body wave functions strongly depend on separation energies and on the partial
waves present in the model (see Sect. 7.4.2). Therefore, in the description of nuclear
reactions, aspects of the structure and the reaction can no longer be approximated
by the aforementioned factorization and are, on the opposite, intertwined. Hence,
it is necessary to devise a theoretical approach for nuclear reactions treating internucleon correlations and continuum degrees of freedom on the same footing.
© Springer International Publishing AG 2021
N. Michel, M. Płoszajczak, Gamow Shell Model, Lecture Notes in Physics 983,
https://doi.org/10.1007/978-3-030-69356-5_9
401