### Abstract

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}.

Original language | English (US) |
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Pages (from-to) | 321-390 |

Number of pages | 70 |

Journal | Annals of Physics |

Volume | 90 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1975 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*90*(2), 321-390. https://doi.org/10.1016/0003-4916(75)90003-2