8
No-Core Gamow Shell Model
The most fundamental approach to describe nuclear states is to use a fully
microscopic Hamiltonian where all nucleons are active. It is the subject of ab
initio methods, where the only input is the nucleon–nucleon interaction and nuclear
states arise from an exact solution of the many-body Schrödinger equation. Indeed,
the nucleon–nucleon interaction is now well understood and several two-body
versions of the nuclear interaction exist, which reproduce the deuteron binding
energy and radius, as well as cross sections of nucleon–nucleon scattering. One
can cite the Argonne υ 18 interaction [1], defined in coordinate space with several
combinations of spin and isospin operators and fitted in two-nucleon properties, the
CD Bonn interaction [2], following the same approach in momentum space, as well
as chiral interactions, which possess the same symmetries as the chiral Lagrangian
of quantum chromodynamics while using nucleons as degrees of freedom.
While theoretically sound and intuitive, the ab initio approaches are nevertheless
very difficult to apply in practice. Its first caveat is the hard core repulsion
of nucleons at short distance. Indeed, the latter generates very important high
momentum components, preventing the simple picture of independent particles to be
used even as a starting point. In order to avoid this problem, equivalent low-energy
interactions have been devised, which do not bear repulsion at low energy, but are
built to reproduce the physical properties of two-nucleon systems for all physical
energies of interest, typically up to 300 MeV [1, 2].
A widely used method to devise low-energy interactions is based on the renormalization group method and is deemed V low-k . It relies on a Feshbach separation of
the model space, in which the components of high momentum in the interaction are
renormalized by a standard decoupling method between low and high momentum
space. The latter method has been successfully applied to the phenomenological
Argonne υ 18 and CD Bonn interactions. When considered with chiral interactions,
it leads to the most fundamental approach to treat nucleons starting from quantum
chromodynamics, called the effective field theory [3]. It is based on the perturbative
expansion of the nucleon–nucleon interaction in powers of m π /Λ, where m π is the
© 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_8
365
No-Core Gamow Shell Model
The most fundamental approach to describe nuclear states is to use a fully
microscopic Hamiltonian where all nucleons are active. It is the subject of ab
initio methods, where the only input is the nucleon–nucleon interaction and nuclear
states arise from an exact solution of the many-body Schrödinger equation. Indeed,
the nucleon–nucleon interaction is now well understood and several two-body
versions of the nuclear interaction exist, which reproduce the deuteron binding
energy and radius, as well as cross sections of nucleon–nucleon scattering. One
can cite the Argonne υ 18 interaction [1], defined in coordinate space with several
combinations of spin and isospin operators and fitted in two-nucleon properties, the
CD Bonn interaction [2], following the same approach in momentum space, as well
as chiral interactions, which possess the same symmetries as the chiral Lagrangian
of quantum chromodynamics while using nucleons as degrees of freedom.
While theoretically sound and intuitive, the ab initio approaches are nevertheless
very difficult to apply in practice. Its first caveat is the hard core repulsion
of nucleons at short distance. Indeed, the latter generates very important high
momentum components, preventing the simple picture of independent particles to be
used even as a starting point. In order to avoid this problem, equivalent low-energy
interactions have been devised, which do not bear repulsion at low energy, but are
built to reproduce the physical properties of two-nucleon systems for all physical
energies of interest, typically up to 300 MeV [1, 2].
A widely used method to devise low-energy interactions is based on the renormalization group method and is deemed V low-k . It relies on a Feshbach separation of
the model space, in which the components of high momentum in the interaction are
renormalized by a standard decoupling method between low and high momentum
space. The latter method has been successfully applied to the phenomenological
Argonne υ 18 and CD Bonn interactions. When considered with chiral interactions,
it leads to the most fundamental approach to treat nucleons starting from quantum
chromodynamics, called the effective field theory [3]. It is based on the perturbative
expansion of the nucleon–nucleon interaction in powers of m π /Λ, where m π is the
© 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_8
365