Ab initio methods (nuclear physics)

In <a href="/facts/Nuclear_physics/fzQbt1aF">nuclear physics</a>, ab initio methods seek to describe the <a href="/facts/Atomic_nucleus/orpIm5Xl">atomic nucleus</a> from the bottom up by solving the non-relativistic <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> for all constituent <a href="/facts/Nucleon/6fguU9Xk">nucleons</a> 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 <a href="/facts/Nuclear_shell_model/1Qgep495">nuclear shell model</a>. Recent progress has enabled ab initio treatment of heavier nuclei such as <a href="/facts/Isotopes_of_nickel/3jPqldnR">nickel</a>.
A significant challenge in the ab initio treatment stems from the complexities of the inter-nucleon interaction. The <a href="/facts/Nuclear_force/A2MyJoWE">strong nuclear force</a> is believed to emerge from the <a href="/facts/Strong_interaction/JjRsKcLg">strong interaction</a> described by <a href="/facts/Quantum_chromodynamics/3cA2ctyb">quantum chromodynamics</a> (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 <a href="/facts/Lattice_QCD/XTlwL4Am">lattice QCD</a>), and a model must be used instead. The most sophisticated models available are based on <a href="/facts/Chiral_perturbation_theory/7E04FlDu">chiral effective field theory</a>. This <a href="/facts/Effective_field_theory/oQ2nWoko">effective field theory</a> (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 <a href="/facts/Pion/x5HamzG3">pions</a>, as opposed to <a href="/facts/Quark/hwuuVkV5">quarks</a> and <a href="/facts/Gluon/t6YH8I21">gluons</a> 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 <a href="/facts/Many-body_force/YkgC4uG4">many-body forces</a>, most notably the three-nucleon interaction which is known to be an essential ingredient in the nuclear many-body problem.
After arriving at a <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonian</a> 
 
 
 
 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 href="/facts/Mass_number/VyBbJ1oI">A</a> nucleons in the nucleus. Various ab initio methods have been devised to numerically find solutions to this equation:

<ul><li>Green's function Monte Carlo (GFMC)</li>
<li>No-core shell model (NCSM)</li>
<li><a href="/facts/Coupled_cluster/VAdquKSJ">Coupled cluster</a> (CC)</li>
<li>Self-consistent Green's function (SCGF)</li>
<li>In-medium similarity renormalization group (IM-SRG)</li></ul>

Ab initio methods (nuclear physics) open-in-new

Ab initio methods (nuclear physics)