6.3 Effective Nucleon–Nucleon Interactions for Gamow Shell Model. . .
253
even though they are quantitatively different (see Tables 6.1, 6.2, and 6.3)). This
could be expected as one has no Coulomb interaction in the Hamiltonian.
Effective nuclear matrix elements can then be expected to be different for
well-bound, weakly bound, and unbound many-body states. Differences can be
particularly large when p and d waves are occupied, and even for f waves they
remain of the order of a few hundreds of keV, which should still be possible to
observe experimentally.
Obviously, the pure two-particle configuration is an idealization of the realistic
situation. Nevertheless, these effects should be seen not only in the spectra of nuclei
with two nucleons outside the closed (sub)shell but also in more complicate spectra
of states when single-particle levels with low angular momenta are significantly
occupied. The emission widths are sizable with p and d waves, as they are typically
close to 500 keV, but become of the order of a few tens of keV when f waves are
occupied.
As a consequence, the derivation of effective nuclear matrix elements for nuclei
close to driplines demands to include the continuum coupling. This is true for p
partial waves, but also when = 2, 3, which is rather unexpected as these partial
waves cannot give rise to halo configurations, for example, (see Sect. 7.2.1.1). In
fact, only a model including both continuum coupling and inter-nucleon correlations, such as the Gamow shell model, can provide with definite conclusions for
that matter. The inter-nucleon correlations in the continuum can generate a complex
nuclear structure which is impossible to predict from an independent-particle model
or from a shell model based on harmonic oscillator basis states.
6.3
Effective Nucleon–Nucleon Interactions for Gamow Shell
Model Calculations in Light Nuclei
Traditionally, light nuclei have provided an excellent testing ground for microscopic
nuclear structure models. The seminal work in the p-shell nuclei, effected in
Refs. [24, 25], initiated the interacting shell model. This model became a pillar of
nuclear structure theory and provided guidance to understand the data on energy
levels, electromagnetic transitions, nuclear moments, and various particle decays.
The identification of basic features and symmetries of the bare nucleon–nucleon
interaction, and the continuous development of effective interactions in finite model
spaces enabled this impressive progress in the description of nuclear spectra.
Because of the harmonic oscillator basis used, only well-bound nuclear states can
be reliably considered in the standard shell model. Continuum degrees of freedom,
crucial in the proximity of particle-emission threshold in weakly bound and in
resonance states, are neglected in this model. In fact, coupling to the scattering
continuum and the decay channels is prominent close to driplines and in nuclear
reactions [26–28].
Estimating the uncertainties of theoretical predictions is a prerequisite in physical
models. Indeed, in the absence of the uncertainty quantification of theoretical
results, it is impossible to assess the quality of predictions, thus precluding reliable
253
even though they are quantitatively different (see Tables 6.1, 6.2, and 6.3)). This
could be expected as one has no Coulomb interaction in the Hamiltonian.
Effective nuclear matrix elements can then be expected to be different for
well-bound, weakly bound, and unbound many-body states. Differences can be
particularly large when p and d waves are occupied, and even for f waves they
remain of the order of a few hundreds of keV, which should still be possible to
observe experimentally.
Obviously, the pure two-particle configuration is an idealization of the realistic
situation. Nevertheless, these effects should be seen not only in the spectra of nuclei
with two nucleons outside the closed (sub)shell but also in more complicate spectra
of states when single-particle levels with low angular momenta are significantly
occupied. The emission widths are sizable with p and d waves, as they are typically
close to 500 keV, but become of the order of a few tens of keV when f waves are
occupied.
As a consequence, the derivation of effective nuclear matrix elements for nuclei
close to driplines demands to include the continuum coupling. This is true for p
partial waves, but also when = 2, 3, which is rather unexpected as these partial
waves cannot give rise to halo configurations, for example, (see Sect. 7.2.1.1). In
fact, only a model including both continuum coupling and inter-nucleon correlations, such as the Gamow shell model, can provide with definite conclusions for
that matter. The inter-nucleon correlations in the continuum can generate a complex
nuclear structure which is impossible to predict from an independent-particle model
or from a shell model based on harmonic oscillator basis states.
6.3
Effective Nucleon–Nucleon Interactions for Gamow Shell
Model Calculations in Light Nuclei
Traditionally, light nuclei have provided an excellent testing ground for microscopic
nuclear structure models. The seminal work in the p-shell nuclei, effected in
Refs. [24, 25], initiated the interacting shell model. This model became a pillar of
nuclear structure theory and provided guidance to understand the data on energy
levels, electromagnetic transitions, nuclear moments, and various particle decays.
The identification of basic features and symmetries of the bare nucleon–nucleon
interaction, and the continuous development of effective interactions in finite model
spaces enabled this impressive progress in the description of nuclear spectra.
Because of the harmonic oscillator basis used, only well-bound nuclear states can
be reliably considered in the standard shell model. Continuum degrees of freedom,
crucial in the proximity of particle-emission threshold in weakly bound and in
resonance states, are neglected in this model. In fact, coupling to the scattering
continuum and the decay channels is prominent close to driplines and in nuclear
reactions [26–28].
Estimating the uncertainties of theoretical predictions is a prerequisite in physical
models. Indeed, in the absence of the uncertainty quantification of theoretical
results, it is impossible to assess the quality of predictions, thus precluding reliable