1 Introduction: From Bound States to the Continuum
11
Chapter 7 Nuclear halo states with one or more nucleons in the classically
inaccessible region are one of the most spectacular manifestations of the nuclear
open quantum system. Formation of halo depends on whether external nucleon is a
proton or neutron, and on its angular momentum. Structure of the halo depends also
on the deformation of a core and on the nucleon-nucleon correlations which in some
situations may prevent formation of an extended halo. Another salient features are
the properties of the asymptotic normalization coefficient and one-nucleon overlap
functions which are essential ingredients in understanding of the direct reactions
and the astrophysical factor in radiative capture reactions.
Near-threshold behavior of the wave functions has an influence on the reaction
cross sections and on the spectroscopic factors. In fact, as will be discussed in this
chapter, they are closely related. The relation between them is evident in the open
quantum system formulation of the shell model which assures a unitary description
of bound state and resonance wave functions in the vicinity of the particle emission
threshold.
The near-threshold effects depend on the nature of the nearby reaction channel. In
particular, it crucially depends on whether it is charged or neutral particle emission
channel. This has a direct consequence on the properties of mirror nuclei, their
spectra, and the isospin symmetry breaking in mirror states.
Chapter 8 Elimination of the core in the Gamow shell model opens a possibility
for the ab initio description of the resonances in light nuclei and multi-neutron
composites. Important issue in this case is the treatment of the problem of center-ofmass excitations. The no-core Gamow shell model with realistic chiral interactions
is benchmarked first against results of other many-body methods in bound nuclei
3 H, 3 He, 4 He, and then applied to study the unbound 5 He nucleus and the multineutron composites 3 n and 4 n. Using the renormalized interactions with a ˆ ¯
Q-box
method, the Gamow shell model in a core-plus-valence-particle approximation is
then also applied to study oxygen and fluorine isotopes.
Chapter 9 The Gamow shell model in Slater determinant representation does not
allow to describe entrance and final reaction channels. It is therefore a theory
adapted for studies of discrete bound states and resonances. To describe reaction
cross sections, one has to formulate the Gamow shell model in coupled-channel
representation. The resulting coupled-channel Hamiltonian can then be used not
only to describe reaction cross sections but, when diagonalized, can provide discrete
eigenvalues, i.e., can be used for studies of spectra and transition probabilities in
bound and unbound systems. In this representation, Gamow shell model becomes
the unified theory of nuclear structure and reactions, whereby using the same
Hamiltonian and the same coupled-channel equations, one describes all different
aspects of nuclear phenomena. Up to now, this unifying formalism has been
successfully applied to the simple direct reactions in light nuclei at low energies,
but this formalism is completely general and can be used to describe various
cross sections, spectra, transition probabilities, and decays also in heavy systems.
11
Chapter 7 Nuclear halo states with one or more nucleons in the classically
inaccessible region are one of the most spectacular manifestations of the nuclear
open quantum system. Formation of halo depends on whether external nucleon is a
proton or neutron, and on its angular momentum. Structure of the halo depends also
on the deformation of a core and on the nucleon-nucleon correlations which in some
situations may prevent formation of an extended halo. Another salient features are
the properties of the asymptotic normalization coefficient and one-nucleon overlap
functions which are essential ingredients in understanding of the direct reactions
and the astrophysical factor in radiative capture reactions.
Near-threshold behavior of the wave functions has an influence on the reaction
cross sections and on the spectroscopic factors. In fact, as will be discussed in this
chapter, they are closely related. The relation between them is evident in the open
quantum system formulation of the shell model which assures a unitary description
of bound state and resonance wave functions in the vicinity of the particle emission
threshold.
The near-threshold effects depend on the nature of the nearby reaction channel. In
particular, it crucially depends on whether it is charged or neutral particle emission
channel. This has a direct consequence on the properties of mirror nuclei, their
spectra, and the isospin symmetry breaking in mirror states.
Chapter 8 Elimination of the core in the Gamow shell model opens a possibility
for the ab initio description of the resonances in light nuclei and multi-neutron
composites. Important issue in this case is the treatment of the problem of center-ofmass excitations. The no-core Gamow shell model with realistic chiral interactions
is benchmarked first against results of other many-body methods in bound nuclei
3 H, 3 He, 4 He, and then applied to study the unbound 5 He nucleus and the multineutron composites 3 n and 4 n. Using the renormalized interactions with a ˆ ¯
Q-box
method, the Gamow shell model in a core-plus-valence-particle approximation is
then also applied to study oxygen and fluorine isotopes.
Chapter 9 The Gamow shell model in Slater determinant representation does not
allow to describe entrance and final reaction channels. It is therefore a theory
adapted for studies of discrete bound states and resonances. To describe reaction
cross sections, one has to formulate the Gamow shell model in coupled-channel
representation. The resulting coupled-channel Hamiltonian can then be used not
only to describe reaction cross sections but, when diagonalized, can provide discrete
eigenvalues, i.e., can be used for studies of spectra and transition probabilities in
bound and unbound systems. In this representation, Gamow shell model becomes
the unified theory of nuclear structure and reactions, whereby using the same
Hamiltonian and the same coupled-channel equations, one describes all different
aspects of nuclear phenomena. Up to now, this unifying formalism has been
successfully applied to the simple direct reactions in light nuclei at low energies,
but this formalism is completely general and can be used to describe various
cross sections, spectra, transition probabilities, and decays also in heavy systems.