Beauty and Strangeness in Eigenvalues of Nuclear Shell Model Hamiltonian

Key words: 
• shell model /
• eigenvalues /
• Hamiltonian /
• truncation

Abstract: The eigenvalue problem is one of the fundamental issues of sciences. Many research fields have been challenged by diagonalizing huge matrices. The nuclear structure theorists face this problem in studies of medium-heavy
nuclei in terms of the nuclear shell model, in which the configuration space is too gigantic to handle. Thus one usually truncates the nuclear shell model configuration space based on various considerations. Another approach is to make use of super computers by various algorithms, and/or to obtain approximate eigenvalues. In this paper we review our recent efforts in obtaining approximate eigenvalues of the nuclear shell model Hamiltonian, with the focus on our semi-empirical approach and a number of extrapolation approaches towards predicting the lowest eigenvalue, as well as strong correlation between the sorted eigenvalues and the diagonal matrix elements, and so on.