Ab initio methods (nuclear physics): Difference between revisions

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{{Nuclear physics}}

In [[nuclear physics]], '''ab initio methods''' seek to describe the [[atomic nucleus]] from the groundbottom up by solving the non-relativistic [[Schrödinger equation]] for all constituent [[nucleon]]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]]. Previously limited to very light nuclei, recentRecent progress has enabled ab initio treatment of heavier nuclei such as [[isotopes of nickel|nickel]].<ref name=navratil2016>{{cite journal|first1=P.|last1=Navrátil|first2=S.|last2=Quaglioni|first3=G.|last3=Hupin|first4=C.|last4=Romero-Redondo|first5=A.|last5=Calci|title=Unified ab initio approaches to nuclear structure and reactions|journal=Physica Scripta|volume=91|issue=5|pages=053002|year=2016|url=http://stacks.iop.org/1402-4896/91/i=5/a=053002|doi=10.1088/0031-8949/91/5/053002|arxiv=1601.03765|bibcode=2016PhyS...91e3002N|s2cid=119280384}}</ref>

A significant challenge in the ab initio treatment stems from the complexities of the inter-nucleon interaction. The [[nuclear force|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 perturbation theory|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 [[pion]]s, as opposed to [[quark]]s and [[gluon]]s as in QCD. The effective theory contains parameters called low-energy constants, which can be determined from scattering data.<ref name=navratil2016 /><ref name=machleidt2011>

{{cite journal

|firstfirst1=R.

|lastlast1=Machleidt

|first2=D.R.

|last2=Entem

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|pages=1–75

|doi=10.1016/j.physrep.2011.02.001

|arxiv=1105.2919v12919

|bibcode = 2011PhR...503....1M |s2cid=118434586
}}</ref>

Chiral EFT implies the existence of [[many-body force]]s, most notably the three-nucleon interaction which is known to be an essential ingredient in the nuclear many-body problem.<ref name=navratil2016 /><ref name=machleidt2011 />

After arriving at a [[Hamiltonian (quantum mechanics)|Hamiltonian]] <math>H</math> (based on chiral EFT or other models) one must solve the Schrödinger equation

:<math display="block">H\vert{\Psi}\rangle = E \vert{\Psi}\rangle ,</math>,

where <math>\vert{\Psi}\rangle</math> is the many-body wavefunction of the [[mass number|''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)<ref name=pieper2001>

{{cite journal

|firstfirst1=S. C.

|lastlast1=Pieper

|first2=R. B.

|last2=Wiringa

|year=2001

|title=Quantum Monte Carlo calculations of light nuclei

|journal=[[Annual Review of Nuclear and Particle Science]]

|volume=51

|pages=53–90

|doi=10.1146/annurev.nucl.51.101701.132506|doi-access=free

|arxiv=nucl-th/0103005

}}</ref>

|bibcode=2001ARNPS..51...53P

|s2cid=18124819

}}</ref>

* No-core shell model (NCSM)<ref name=barrett2013>

{{cite journal

|firstfirst1=B.R.

|lastlast1=Barrett

|first2=P.

|last2=Navrátil

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|pages=131–181

|doi=10.1016/j.ppnp.2012.10.003

|bibcode=2013PrPNP..69..131B

}}</ref>

|url=https://digital.library.unt.edu/ark:/67531/metadc1415883/

* [[Coupled cluster]] (CC)<ref>{{cite journal | doi = 10.1088/0034-4885/77/9/096302 | title = Coupled-cluster computations of atomic nuclei | year = 2014 | last1 = Hagen | first1 = G. | last2 = Papenbrock | first2 = T. | last3 = Hjorth-Jensen | first3 = M. | last4 = Dean | first4 = D. J. | journal = Reports on Progress in Physics | volume = 77 | pages = 096302 | issue = 9 }}</ref>

}}</ref>

* [[Coupled cluster]] (CC)<ref>{{cite journal | doi = 10.1088/0034-4885/77/9/096302 | pmid = 25222372 | title = Coupled-cluster computations of atomic nuclei | year = 2014 | last1 = Hagen | first1 = G. | last2 = Papenbrock | first2 = T. | last3 = Hjorth-Jensen | first3 = M. | last4 = Dean | first4 = D. J. | journal = Reports on Progress in Physics | volume = 77 | pages = 096302 | issue = 9 | arxiv = 1312.7872 | bibcode = 2014RPPh...77i6302H | s2cid = 10626343 }}</ref>

* Self-consistent Green's function (SCGF)<ref name=cipollone2013>

{{cite journal

|firstfirst1=A.

|lastlast1=Cipollone

|first2=C.

|last2=Barbieri

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|year=2013

|title=Isotopic Chains Around Oxygen from Evolved Chiral Two- and Three-Nucleon Interactions

|journal=Phys.Physical Rev.Review Lett.Letters

|volume=111

|issue=6

|pages=062501

|doi=10.1103/PhysRevLett.111.062501

|pmid=23971568

}}</ref>

|arxiv=1303.4900

|bibcode=2013PhRvL.111f2501C

|s2cid=2198329

}}</ref>

* In-medium similarity renormalization group (IM-SRG)<ref name=hergert2013>

{{cite journal

|firstfirst1=H.

|lastlast1=Hergert

|first2=S.

|last2=Binder

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|year=2013

|title=Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two-Plus-Three-Nucleon Interactions

|journal=Phys.Physical Rev.Review Lett.Letters

|volume=110

|issue=24

|pages=242501

|doi=10.1103/PhysRevLett.110.242501

|pmid=25165916

}}</ref>

|arxiv=1302.7294

|bibcode=2013PhRvL.110x2501H

|s2cid=5501714

}}</ref>

==Further reading==

*{{cite magazine journal|last=Dean |first=D. |year=2007 |title=Beyond the nuclear shell model |doi=10.1063/1.2812123 |magazinejournal=Physics Today |volume=60 |issue=11 |page=48|bibcode=2007PhT....60k..48D |url=https://zenodo.org/record/1232029 }}

*{{cite magazinejournal |last=Zastrow |first=M. |year=2017 |title=In search for "magic" nuclei, theory catches up to experiments |doi=10.1073/pnas.1703620114 |magazinepmid=28512181 |pmc=5441833 |journal=Proc Natl Acad Sci U S A. |volume=114 |issue=20 |pages=5060–5062|bibcode=2017PNAS..114.5060Z |doi-access=free }}

{{cite magazine |last=Zastrow |first=M. |year=2017 |title=In search for "magic" nuclei, theory catches up to experiments |doi=10.1073/pnas.1703620114 |magazine=Proc Natl Acad Sci U S A. |volume=114 |issue=20 |pages=5060–5062}}

== References ==