VARIATIONAL BUILDUP ON NUCLEAR SHELL MODEL BASES

A method is proposed for accurately calculating a few of the low-lying states belonging to each nuclear spin within the shell model. A properly chosen initial vector is operated upon iteratively, generating a basis in which the Hamiltonian matrix is tridiagonal. The process may be halted when low-lying eigenvalues, up to a preset number, have been determined to a required accuracy, implying a truncation of the complete vector space. Simple formulae are given for the errors induced by this truncation, both for eigenvalues and eigenfunctions. Illustrative calculations are shown for the 0+ (T = 0), 2+ (T = 0), 4+ (T = 0), 2+ (T = 1) and+ (T = 1) states of 20Ne. By taking the leading SU3 states as initial vectors, quite accurate low-lying eigenvalues and eigenfunctions are obtained with a small-sized truncation space. The T = 0 states mentioned allow a three dimensional truncation to yield lowest eigenvalues with an error of less than 0.05 MeV as well as corresponding eigenfunctions having an overlap of greater than 99.5% with the exact ones. Special eigenvalue-problem techniques are discussed in the appendix. © 1969.