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4.3.2 Theoretical Aspects
Ab Initio methods
The conceptual foundation of nuclear structure theory
is low-energy QCD, which describes the structure of
nucleons and their mutual interaction. Over the past
decade nuclear structure theory has started to exploit
the link to QCD in a quantitative way. Using the tools of
Effective Field Theory (EFT) based on the symmetries
and the relevant degrees of freedom of QCD in the
low-energy regime, consistent Hamiltonians for manynucleon
problems have been constructed (see “Hadron
Physics”, page 62).
The ab initio methods that are developed for nuclear
spectroscopy provide crucial information on the properties
of those interactions and allow for high precision
predictions of nuclear observables. Beyond the lightest
nuclei the No-Core Shell Model (NCSM) was successfully
employed for the study of ground and excited states
using two- plus three-nucleon interactions from EFT.
The agreement of these results with experimental data
has demonstrated the potential of EFT interactions for
precision studies of light nuclei. However, such calculations
pose an enormous computational challenge and
rely on supercomputer resources.
Powerful schemes have been proposed that allow for
a consistent transformation of the nuclear Hamiltonian
including three-body interactions, e.g., through renormalization
group techniques. The resulting soft interactions
form a universal starting point for QCD-based nuclear
structure studies in exact and approximate many-body
schemes.
The range of applications of ab initio many-body methods
is rapidly extending to heavier nuclei. Significant
progress has been made in the study of ground states
Box 1. Theory and experiment
Modern approaches in nuclear theory aim at an abinitio
understanding of nuclear structure and reactions.
Realistic effective interactions emerge from chiral interactions
with 2- and 3-body forces. Many-body methods
have lead to a consistent microscopic description of
light nuclei using nucleons as degrees of freedom.
These yield shell structure, clusters, halos, resonances,
capture and transfer reactions and scattering states
in a unified picture. The obtained understanding can
be tested by experiments, which probe excitation for
instance spectra, electromagnetic and weak transitions,
densities, form factors, spectroscopic amplitudes.
A recent example comes from isotope shift measurements
of drip-line nuclei using collinear laser
spectroscopy. Precise and model independent measurements
of charge radii, magnetic and quadrupole
moments provide important information of the wave
functions.
Sudden changes in the charge radii along an isotopic
change are related to changes in the nuclear structure.
The neon isotopes provide a particular interesting
example. The experimental charge radii measured at
ISOLDE are compared with microscopic structure calculations
using the Fermionic Molecular Dynamics
(FMD) approach. FMD uses a Gaussian wave-packet
basis and allows to describe nuclei with halos and
clustering. The two-proton separation energy in 17 Ne
is only 0.93 MeV and the structure is understood as
an 15 O core and two protons in s 2 or d 2 configurations.
The large charge radius in 17 Ne is caused by a large s 2
component of about 42%. In 18 Ne the charge radius is
smaller due to a smaller s 2 component in the wave function.
In 19 Ne and 20 Ne the charge radii increase again
due to clustering in the ground state wave function.
17 Ne 20 Ne 22 Ne
Distributions of dominant FMD configurations indicating an
extended two-proton wave function in 17 Ne and α-clustering
in 20 Ne.
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