In nuclear physics, ab initio methods seek
to describe the atomic nucleus from the ground
up by solving the non-relativistic Schrödinger
equation for all constituent nucleons and
the forces between them. This is done either
exactly for very light nuclei (up to four
nucleons) or by employing certain well-controlled
approximations for heavier nuclei. Ab initio
methods constitute a more fundamental approach
compared to e.g. the nuclear shell model.
Recent progress has enabled ab initio treatment
of heavier nuclei such as nickel.A significant
challenge in the ab initio treatment stems
from the complexities of the inter-nucleon
interaction. The strong nuclear force is believed
to emerge from the strong interaction described
by quantum chromodynamics (QCD), but QCD is
non-perturbative in the low-energy regime
relevant to nuclear physics. This makes the
direct use of QCD for the description of the
inter-nucleon interactions very difficult
(see lattice QCD), and a model must be used
instead. The most sophisticated models available
are based on chiral effective field theory.
This effective field theory (EFT) includes
all interactions compatible with the symmetries
of QCD, ordered by the size of their contributions.
The degrees of freedom in this theory are
nucleons and pions, as opposed to quarks and
gluons as in QCD. The effective theory contains
parameters called low-energy constants, which
can be determined from scattering data.Chiral
EFT implies the existence of many-body forces,
most notably the three-nucleon interaction
which is known to be an essential ingredient
in the nuclear many-body problem.After arriving
at a Hamiltonian
H
{\displaystyle H}
(based on chiral EFT or other models) one
must solve the Schrödinger equation
H
|
Ψ
⟩
=
E
|
Ψ
⟩
{\displaystyle H\vert {\Psi }\rangle =E\vert
{\Psi }\rangle }
,where
|
Ψ
⟩
{\displaystyle \vert {\Psi }\rangle }
is the many-body wavefunction of the A nucleons
in the nucleus. Various ab initio methods
have been devised to numerically find solutions
to this equation:
Green's function Monte Carlo (GFMC)
No-core shell model (NCSM)
Coupled cluster (CC)
Self-consistent Green's function (SCGF)
In-medium similarity renormalization group
(IM-SRG)
== Further reading ==
Dean, D. (2007). "Beyond the nuclear shell
model". Physics Today. Vol. 60 no. 11. p.
48. Bibcode:2007PhT....60k..48D. doi:10.1063/1.2812123.Zastrow,
M. (2017). "In search for "magic" nuclei,
theory catches up to experiments". Proc Natl
Acad Sci U S A. Vol. 114 no. 20. pp. 5060–5062.
Bibcode:2017PNAS..114.5060Z. doi:10.1073/pnas.1703620114
