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

Understand

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.