We discuss in general some criteria and methods for constructing effective Hamiltonians. Then three different methods are compared for constructing an effective Hamiltonian to be used in nuclear shell-model calculations for A = 17-20, allowing (A-16) active nucleons in the d 5 2, s 1 2 vector space. For all three methods, the aim is to obtain a d 5 2, s 1 2 model which will simulate the results of a given full d 5 2, s 1 2, d 3 2 model. The three methods for finding the effective Hamiltonian are. 1. (a) conventional low-order perturbation theory; 2. (b) a projection technique, in which we construct a Hamiltonian whose eigenvalues excactly match a selected subset of d 5 2, s 1 2, d 3 2 eigenvalues, and whose eigenvectors excatly match the projections of d 5 2, s 1 2, d 3 2 eigenvectors on the d 5 2, s 1 2 space; and 3. (c) least-square fit to selected d 5 2, s 1 2, d 3 2 energies. For all three methods, we first restrict the effective Hamiltonian to a linear combination of 1-body and 2-body operators. Then for the perturbation and projection techniques, we also calculate the 3-body-operator terms in the effective Hamiltonian. When the effective Hamiltonians are limited to 1-body and 2-body terms, the leastsquare method yields the best overall fit to the low-lying spectrum of d 5 2, s 1 2, d 3 2.
ASJC Scopus subject areas
- Physics and Astronomy(all)