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 ground up by solving the non-relativistic [[Schrödinger equation]] infor termsall of the individualconstituent [[nucleon|nucleons]] and the [[nuclear force|interactionsforces between them]]. This is a more fundamental approach compared to e.g. the [[nuclear shell model]]. Previously limited to very light nuclei, recent 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}}</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-pertubative 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|pions]], as opposed to [[quark|quarks]] and [[gluon|gluons]] 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>

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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>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>