{\it Ab initio} nuclear structure - the large sparse matrix eigenvalue problem

Abstract

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several {\it ab initio} methods have now emerged that provide nearly exact solutions for some nuclear properties. The {\it ab initio} no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds $10^{10}$ and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. W also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these {\it ab initio} approaches.

SciDAC2009 invited paper; 10 pages and 10 figures

References in corpus (4)

• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Ab initio no-core full configuration calculations of light nuclei
• Convergence in the no-core shell model with low-momentum two-nucleon interactions
• Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei

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