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

Bruce R Barrett, E. C. Halbert, J. B. McGrory

Research output: Contribution to journalArticle

27 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)321-390
Number of pages70
JournalAnnals of Physics
Volume90
Issue number2
DOIs
StatePublished - 1975

Fingerprint

configurations
projection
interactions
eigenvectors
eigenvalues
operators
vector spaces
nucleons
set theory
perturbation theory
perturbation
energy

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

@article{881a0a095b174db6acb237e8abf281a3,
title = "Hidden configurations and effective interactions: A comparison of three different ways to construct renormalized hamiltonians for truncated shell-model calculations",
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.",
author = "Barrett, {Bruce R} and Halbert, {E. C.} and McGrory, {J. B.}",
year = "1975",
doi = "10.1016/0003-4916(75)90003-2",
language = "English (US)",
volume = "90",
pages = "321--390",
journal = "Annals of Physics",
issn = "0003-4916",
publisher = "Academic Press Inc.",
number = "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 -