6
Physical Applications of the Gamow Shell
Model
6.1
Effective Interaction in the Vicinity
of the Particle-Emission Threshold
Structure of weakly bound/unbound nuclei close to particle driplines is different
from that around the valley of beta-stability. There are many unique features of
exotic nuclei that give prospects for entirely new phenomena likely to be different
from anything we have observed to date. These phenomena can be described using
the Gamow shell model. Certain specific features of interactions in weakly bound
systems have been recently identified. In general terms, these interactions depend
explicitly on the location of various emission thresholds and on the structure of Smatrix poles which dominate the corresponding decays.
For bound states appears a virtual scattering involving intermediate scattering
states. Continuum coupling of this kind affects also the effective nucleon–nucleon
interaction. For unbound states, the continuum structure appears explicitly in the
properties of those states. In the mean-field picture, when approaching the onenucleon dripline (S n,p → 0), the magnitude of the chemical potential approaches
the pairing gap: −λ n,p − Δ n,p → 0, i.e. the pairing correlations become as
important as the mean-field effects. Generalizing this observation, one expects that
the dependence of weakly bound systems on effective nucleon–nucleon interaction
is stronger than in “normal” nuclei.
One may ask how the effective nucleon–nucleon interaction is modified by the
virtual scattering into the particle continuum. In shell model embedded in the
continuum studies of binding energy systematics in sd shell nuclei, it was found
that in the nuclei close to the neutron dripline the neutron-proton T =0 interaction
is significantly reduced with respect to the neutron-neutron T =1 interaction [1, 2].
Later, this observation has been confirmed in the study of lifetime of 16 F [3]. The
reduction of neutron-proton T =0 interaction in neutron-rich nuclei is a consequence
of a decrease in the one neutron emission threshold when approaching the neutron
dripline, i.e. it is a genuine continuum coupling effect which cannot be mimicked
© 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_6
239
Physical Applications of the Gamow Shell
Model
6.1
Effective Interaction in the Vicinity
of the Particle-Emission Threshold
Structure of weakly bound/unbound nuclei close to particle driplines is different
from that around the valley of beta-stability. There are many unique features of
exotic nuclei that give prospects for entirely new phenomena likely to be different
from anything we have observed to date. These phenomena can be described using
the Gamow shell model. Certain specific features of interactions in weakly bound
systems have been recently identified. In general terms, these interactions depend
explicitly on the location of various emission thresholds and on the structure of Smatrix poles which dominate the corresponding decays.
For bound states appears a virtual scattering involving intermediate scattering
states. Continuum coupling of this kind affects also the effective nucleon–nucleon
interaction. For unbound states, the continuum structure appears explicitly in the
properties of those states. In the mean-field picture, when approaching the onenucleon dripline (S n,p → 0), the magnitude of the chemical potential approaches
the pairing gap: −λ n,p − Δ n,p → 0, i.e. the pairing correlations become as
important as the mean-field effects. Generalizing this observation, one expects that
the dependence of weakly bound systems on effective nucleon–nucleon interaction
is stronger than in “normal” nuclei.
One may ask how the effective nucleon–nucleon interaction is modified by the
virtual scattering into the particle continuum. In shell model embedded in the
continuum studies of binding energy systematics in sd shell nuclei, it was found
that in the nuclei close to the neutron dripline the neutron-proton T =0 interaction
is significantly reduced with respect to the neutron-neutron T =1 interaction [1, 2].
Later, this observation has been confirmed in the study of lifetime of 16 F [3]. The
reduction of neutron-proton T =0 interaction in neutron-rich nuclei is a consequence
of a decrease in the one neutron emission threshold when approaching the neutron
dripline, i.e. it is a genuine continuum coupling effect which cannot be mimicked
© 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_6
239