### 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) |
---|---|

Pages (from-to) | 321-390 |

Number of pages | 70 |

Journal | Annals of Physics |

Volume | 90 |

Issue number | 2 |

DOIs | |

State | Published - 1975 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

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

**Hidden configurations and effective interactions : A comparison of three different ways to construct renormalized hamiltonians for truncated shell-model calculations.** / Barrett, Bruce R; Halbert, E. C.; McGrory, J. B.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 90, no. 2, pp. 321-390. https://doi.org/10.1016/0003-4916(75)90003-2

}

TY - JOUR

T1 - Hidden configurations and effective interactions

T2 - A comparison of three different ways to construct renormalized hamiltonians for truncated shell-model calculations

AU - Barrett, Bruce R

AU - Halbert, E. C.

AU - McGrory, J. B.

PY - 1975

Y1 - 1975

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26444441639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444441639&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(75)90003-2

DO - 10.1016/0003-4916(75)90003-2

M3 - Article

AN - SCOPUS:26444441639

VL - 90

SP - 321

EP - 390

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -