Elsevier

Annals of Physics

Volume 90, Issue 2, April 1975, Pages 321-390
Annals of Physics

Hidden configurations and effective interactions: A comparison of three different ways to construct renormalized hamiltonians for truncated shell-model calculations

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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 d52, s12 vector space. For all three methods, the aim is to obtain a d52, s12 model which will simulate the results of a given full d52, s12, d32 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 d52, s12, d32 eigenvalues, and whose eigenvectors excatly match the projections of d52, s12, d32 eigenvectors on the d52, s12 space; and

  • 3.

    (c) least-square fit to selected d52, s12, d32 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 d52, s12, d32

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    Research jointly sponsored by the NSF (Grant GP-29250), and by the U.S. Atomic Energy Commission under contract with Union Carbide Corp.

    Alfred P. Sloan Foundation Research Fellow 1972–1974.

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