In
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies th ...
, ab initio methods seek to describe the
atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester ...
from the bottom up by solving the non-relativistic
Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
for all constituent
nucleon
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number.
Until the 1960s, nucleons were thought to be ele ...
s 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
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model utilizes the Pauli exclusion principle to model the structure of atomic nuclei in terms of energy levels. The first shell model was proposed by Dmitri Ivanenk ...
. Recent progress has enabled ab initio treatment of heavier nuclei such as
nickel
Nickel is a chemical element; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive, but large pieces are slo ...
.
A significant challenge in the ab initio treatment stems from the complexities of the inter-nucleon interaction. The
strong nuclear force
In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interactions. It confines quarks into protons, neutrons, and other hadron particles, an ...
is believed to emerge from the
strong interaction
In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...
described by
quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of ...
(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
Lattice QCD is a well-established non- perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the ...
), and a model must be used instead. The most sophisticated models available are based on
chiral effective field theory. This
effective field theory
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees ...
(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
pion
In particle physics, a pion (, ) or pi meson, denoted with the Greek alphabet, Greek letter pi (letter), pi (), is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the ...
s, as opposed to
quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s and
gluon
A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s 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 force
A three-body force is a force that does not exist in a system of two objects but appears in a three-body system. In general, if the behaviour of a system of more than two objects cannot be described by the two-body interactions between all possib ...
s, 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
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
(based on chiral EFT or other models) one must solve the Schrödinger equation
where
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
Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used ...
(CC)
* Self-consistent Green's function (SCGF)
[
]
* In-medium similarity renormalization group (IM-SRG)
[
]
Further reading
*
*
References
{{Reflist
Nuclear physics