<i>Ab initio</i>nuclear structure – the large sparse matrix eigenvalue problem

Abstract

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