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Title: Effective Interactions and Operators in Nuclei within the No-Core Shell Model

Abstract

We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short-range operators, such as the nucleon-nucleon potential, the unitary-transformation method works extremely well at the two-body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A {<=} 16). However, for long-range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two-body cluster level does not include the higher-order correlations needed to renormalize these long-range operators adequately. Usually, such correlations can be obtained either by increasing the order of the cluster approximation or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher-order correlations in small model spaces.

Authors:
;  [1];  [2];  [2];  [3];  [3]
  1. Department of Physics, University of Arizona, P.O. Box 210081, Tucson, Arizona 85721 (United States)
  2. Lawrence Livermore National Laboratory, Livermore, P.O. Box 808, California 94551 (United States)
  3. (United States)
Publication Date:
OSTI Identifier:
20798342
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 819; Journal Issue: 1; Conference: 12. international symposium on capture gamma-ray spectroscopy and related topics, Notre Dame, IN (United States), 4-9 Sep 2005; Other Information: DOI: 10.1063/1.2187907; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ABSORPTION SPECTRA; APPROXIMATIONS; BINDING ENERGY; CORRELATIONS; EXCITATION; LIGHT NUCLEI; NUCLEON-NUCLEON POTENTIAL; QUADRUPOLE MOMENTS; RENORMALIZATION; REVIEWS; SHELL MODELS; SPACE; TRANSFORMATIONS; TWO-BODY PROBLEM

Citation Formats

Barrett, Bruce R., Stetcu, Ionel, Navratil, Petr, Vary, James P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, and SLAC, MS 81, 2575 Sand Hill Rd, Menlo Park, California 94025. Effective Interactions and Operators in Nuclei within the No-Core Shell Model. United States: N. p., 2006. Web. doi:10.1063/1.2187907.
Barrett, Bruce R., Stetcu, Ionel, Navratil, Petr, Vary, James P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, & SLAC, MS 81, 2575 Sand Hill Rd, Menlo Park, California 94025. Effective Interactions and Operators in Nuclei within the No-Core Shell Model. United States. doi:10.1063/1.2187907.
Barrett, Bruce R., Stetcu, Ionel, Navratil, Petr, Vary, James P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, and SLAC, MS 81, 2575 Sand Hill Rd, Menlo Park, California 94025. Mon . "Effective Interactions and Operators in Nuclei within the No-Core Shell Model". United States. doi:10.1063/1.2187907.
@article{osti_20798342,
title = {Effective Interactions and Operators in Nuclei within the No-Core Shell Model},
author = {Barrett, Bruce R. and Stetcu, Ionel and Navratil, Petr and Vary, James P. and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 and SLAC, MS 81, 2575 Sand Hill Rd, Menlo Park, California 94025},
abstractNote = {We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short-range operators, such as the nucleon-nucleon potential, the unitary-transformation method works extremely well at the two-body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A {<=} 16). However, for long-range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two-body cluster level does not include the higher-order correlations needed to renormalize these long-range operators adequately. Usually, such correlations can be obtained either by increasing the order of the cluster approximation or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher-order correlations in small model spaces.},
doi = {10.1063/1.2187907},
journal = {AIP Conference Proceedings},
number = 1,
volume = 819,
place = {United States},
year = {Mon Mar 13 00:00:00 EST 2006},
month = {Mon Mar 13 00:00:00 EST 2006}
}
  • We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short-range operators, such as the nucleon-nucleon potential, the unitary-transformation method works extremely well at the two-body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A {<=} 16). However, for long-range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two-body cluster level, does not include the higher-order correlations needed to renormalize these long-range operators adequately. Usually, such correlations can be obtained either by increasing the order ofmore » the cluster approximation, or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher-order correlations in small model spaces.« less
  • We implement an effective operator formalism for general one- and two-body operators, obtaining results consistent with the no-core shell model (NCSM) wave functions. The Argonne V8' nucleon-nucleon potential was used in order to obtain realistic wave functions for {sup 4}He, {sup 6}Li and {sup 12}C. In the NCSM formalism, we compute electromagnetic properties using the two-body cluster approximation for the effective operators and obtain results which are sensitive to the range of the bare operator. To illuminate the dependence on the range, we employ a Gaussian two-body operator of variable range, finding weak renormalization of long range operators (e.g., quadrupole)more » in a fixed model space. This is understood in terms of the two-body cluster approximation which accounts mainly for short-range correlations. Consequently, short range operators, such as the relative kinetic energy, will be well renormalized in the two-body cluster approximation.« less
  • We implement an effective operator formalism for general one- and two-body operators, obtaining results consistent with the no-core shell model (NCSM) wave functions. The Argonne V8' nucleon-nucleon potential was used in order to obtain realistic wave functions for {sup 4}He,{sup 6}Li, and {sup 12}C. In the NCSM formalism, we compute electromagnetic properties using the two-body cluster approximation for the effective operators and obtain results which are sensitive to the range of the bare operator. To illuminate the dependence on the range, we employ a Gaussian two-body operator of variable range, finding weak renormalization of long range operators (e.g., quadrupole) inmore » a fixed model space. This is understood in terms of the two-body cluster approximation which accounts mainly for short-range correlations. Consequently, short-range operators, such as the relative kinetic energy, will be well renormalized in the two-body cluster approximation.« less
  • A shell model calculation in an enlarged space spanned by two particles in the (2s, 1d) shell and three-particle-one-hole 2h omega excitations is performed using the bare'' G-matrix. An effective interaction for the (2s, 1d) shell is generated and its convergence properties are investigated. It is maintained that the series converges reasonably fast in G and that the single- particle energies used in the calculation are instrumental in this respect. This conclusion is corroborated by the E2 effective charges and B(E2) strengths that are computed for A = 17 and A = 18 nuclei respectively. (auth)