1 Introduction: From Bound States to the Continuum
3
closed quantum systems) to the weakly bound or unbound states (the open quantum
systems) while approaching the limit of nuclear stability with respect to the particle
emission. For this purpose, the approaches based on the equation of motions for the
reduced density of the combined system-plus-environment are not suitable and the
configuration-interaction approaches are preferred.
The shell structure and single-particle motion is a cornerstone of nuclear structure
[17]. The interacting shell model consists of the single-particle potential, characterized by a strong spin-orbit term [18, 19] and supplemented by a two-body residual
interaction [20, 21]. This successful model in describing low-energy excitations in
well-bound nuclei describes nucleus as a closed quantum system with nucleons
occupying bound levels isolated from the scattering states and decay channels. But is
this picture physically correct? Indeed, low-lying states of well-bound atomic nuclei
from the valley of beta-stability can be considered as the closed quantum systems.
However, in the vicinity of driplines and close to the lowest particle-emission
threshold in well-bound nuclei, the continuum coupling becomes gradually more
important, changing the nature of weakly bound states. Finally, in the particleunbound states, couplings to reaction channels and a continuum of scattering
states have a direct impact on their properties. In this regime, nuclear states in
neighboring nuclei form a network of interconnected states via the continuum, with
the clusters of correlated states in different domains of excitation energy, angular
momentum, and nucleon number (see Fig. 1.1). Depending on the network activity
caused by the coupling of states to reaction thresholds in different nuclei, different
phases of connectivity may exist in this network. Moreover, the divide between
the discrete resonant states and the nonresonant scattering continuum leads to the
artificial separation of nuclear structure from the nuclear reactions, and hinders a
deeper understanding of nuclear properties. Indeed, many structural properties of
the nucleus are determined indirectly and heavily depend on the nuclear reaction
theory, and vice versa, and this cries out for a unified theoretical framework.
Correlations among nucleons become crucial when the particle separation energy
is either small or negative. In this situation, the nucleon-nucleon correlations (e.g.,
the pairing field) and the single-particle field become equally important. Consequently, the configuration mixing, involving also continuum states, can no longer be
treated as a small perturbation [22]. On the contrary, it is an essential ingredient for
the existence and stability of these exotic systems. This has far going consequences
not only for the proprieties of weakly bound and resonance many-body states, but
also for the shell structure and the survival of magic numbers of nucleons. Away
from the beta-stability line toward the nucleon driplines, experimental data suggest
that standard magic numbers gradually disappear and new magic numbers appear
[23]. In the region of superheavy nuclei, the spin-orbit energy gaps diminish as
a result of the fast growth of the density of states and, consequently, the strong
shell effects at magic nucleon numbers weaken. Nuclear properties in this limit
are extremely sensitive both to the nucleon-nucleon interaction and the continuum
coupling [24].
Unbound states have significant impact on spectroscopic properties of nuclei,
especially those close to the particle driplines. The continuum of scattering states,
3
closed quantum systems) to the weakly bound or unbound states (the open quantum
systems) while approaching the limit of nuclear stability with respect to the particle
emission. For this purpose, the approaches based on the equation of motions for the
reduced density of the combined system-plus-environment are not suitable and the
configuration-interaction approaches are preferred.
The shell structure and single-particle motion is a cornerstone of nuclear structure
[17]. The interacting shell model consists of the single-particle potential, characterized by a strong spin-orbit term [18, 19] and supplemented by a two-body residual
interaction [20, 21]. This successful model in describing low-energy excitations in
well-bound nuclei describes nucleus as a closed quantum system with nucleons
occupying bound levels isolated from the scattering states and decay channels. But is
this picture physically correct? Indeed, low-lying states of well-bound atomic nuclei
from the valley of beta-stability can be considered as the closed quantum systems.
However, in the vicinity of driplines and close to the lowest particle-emission
threshold in well-bound nuclei, the continuum coupling becomes gradually more
important, changing the nature of weakly bound states. Finally, in the particleunbound states, couplings to reaction channels and a continuum of scattering
states have a direct impact on their properties. In this regime, nuclear states in
neighboring nuclei form a network of interconnected states via the continuum, with
the clusters of correlated states in different domains of excitation energy, angular
momentum, and nucleon number (see Fig. 1.1). Depending on the network activity
caused by the coupling of states to reaction thresholds in different nuclei, different
phases of connectivity may exist in this network. Moreover, the divide between
the discrete resonant states and the nonresonant scattering continuum leads to the
artificial separation of nuclear structure from the nuclear reactions, and hinders a
deeper understanding of nuclear properties. Indeed, many structural properties of
the nucleus are determined indirectly and heavily depend on the nuclear reaction
theory, and vice versa, and this cries out for a unified theoretical framework.
Correlations among nucleons become crucial when the particle separation energy
is either small or negative. In this situation, the nucleon-nucleon correlations (e.g.,
the pairing field) and the single-particle field become equally important. Consequently, the configuration mixing, involving also continuum states, can no longer be
treated as a small perturbation [22]. On the contrary, it is an essential ingredient for
the existence and stability of these exotic systems. This has far going consequences
not only for the proprieties of weakly bound and resonance many-body states, but
also for the shell structure and the survival of magic numbers of nucleons. Away
from the beta-stability line toward the nucleon driplines, experimental data suggest
that standard magic numbers gradually disappear and new magic numbers appear
[23]. In the region of superheavy nuclei, the spin-orbit energy gaps diminish as
a result of the fast growth of the density of states and, consequently, the strong
shell effects at magic nucleon numbers weaken. Nuclear properties in this limit
are extremely sensitive both to the nucleon-nucleon interaction and the continuum
coupling [24].
Unbound states have significant impact on spectroscopic properties of nuclei,
especially those close to the particle driplines. The continuum of scattering states,