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Title: Low-momentum nucleon-nucleon interactions and shell-model calculations

Abstract

In the last few years, the low-momentum nucleon-nucleon (NN) interaction V{sub low-k} derived from free-space NN potentials has been successfully used in shell-model calculations. V{sub low-k} is a smooth potential which preserves the deuteron binding energy as well as the half-on-shell T matrix of the original NN potential up to a momentum cutoff {lambda}. In this paper, we test a new low-momentum NN potential derived from chiral perturbation theory at next-to-next-to-next-to-leading order with a sharp low-momentum cutoff at 2.1 fm{sup -1}. Shell-model calculations for the oxygen isotopes using effective Hamiltonians derived from both types of low-momentum potential are performed. We find that the two potentials show the same perturbative behavior and yield very similar results.

Authors:
; ; ;  [1];  [2];  [3];  [4]
  1. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II, and Istituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, Via Cintia-I-80126 Napoli (Italy)
  2. Grupo de Fisica Nuclear, IUFFyM, Universidad de Salamanca, E-37008 Salamanca (Spain)
  3. Department of Physics, SUNY, Stony Brook, New York 11794 (United States)
  4. Department of Physics, University of Idaho, Moscow, Idaho 83844 (United States)
Publication Date:
OSTI Identifier:
20991012
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevC.75.024311; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BINDING ENERGY; CHIRALITY; DEUTERONS; HAMILTONIANS; NUCLEON-NUCLEON INTERACTIONS; NUCLEON-NUCLEON POTENTIAL; NUCLEONS; OXYGEN ISOTOPES; PERTURBATION THEORY; S MATRIX; SHELL MODELS

Citation Formats

Coraggio, L., Covello, A., Gargano, A., Itaco, N., Entem, D. R., Kuo, T. T. S., and Machleidt, R. Low-momentum nucleon-nucleon interactions and shell-model calculations. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.024311.
Coraggio, L., Covello, A., Gargano, A., Itaco, N., Entem, D. R., Kuo, T. T. S., & Machleidt, R. Low-momentum nucleon-nucleon interactions and shell-model calculations. United States. doi:10.1103/PHYSREVC.75.024311.
Coraggio, L., Covello, A., Gargano, A., Itaco, N., Entem, D. R., Kuo, T. T. S., and Machleidt, R. Thu . "Low-momentum nucleon-nucleon interactions and shell-model calculations". United States. doi:10.1103/PHYSREVC.75.024311.
@article{osti_20991012,
title = {Low-momentum nucleon-nucleon interactions and shell-model calculations},
author = {Coraggio, L. and Covello, A. and Gargano, A. and Itaco, N. and Entem, D. R. and Kuo, T. T. S. and Machleidt, R.},
abstractNote = {In the last few years, the low-momentum nucleon-nucleon (NN) interaction V{sub low-k} derived from free-space NN potentials has been successfully used in shell-model calculations. V{sub low-k} is a smooth potential which preserves the deuteron binding energy as well as the half-on-shell T matrix of the original NN potential up to a momentum cutoff {lambda}. In this paper, we test a new low-momentum NN potential derived from chiral perturbation theory at next-to-next-to-next-to-leading order with a sharp low-momentum cutoff at 2.1 fm{sup -1}. Shell-model calculations for the oxygen isotopes using effective Hamiltonians derived from both types of low-momentum potential are performed. We find that the two potentials show the same perturbative behavior and yield very similar results.},
doi = {10.1103/PHYSREVC.75.024311},
journal = {Physical Review. C, Nuclear Physics},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • Hyperon-nucleons interactions constructed by two frameworks, the Kyoto-Niigata SU{sub 6} quark model and the chiral effective field theory, are compared by investigating equivalent interactions in a low-momentum space and, in addition, by calculating hyperon single-particle potentials in the lowest-order Brueckner theory in symmetric nuclear matter. Two descriptions are shown to give similar matrix elements in most channels after renormalizing high momentum components. Although the range of the {Lambda}N interaction is different in two potentials, the {Lambda} single-particle potential in nuclear matter is very similar. The {Sigma}-nucleus and XI-nucleus potentials are also found to be similar. These predictions are to bemore » confronted with forthcoming experimental data.« less
  • An all-order summation of core-polarization diagrams using the low-momentum nucleon-nucleon interaction V{sub low-k} is presented. The summation is based on the Kirson-Babu-Brown (KBB) induced interaction approach in which the vertex functions are obtained self-consistently by solving a set of nonlinear coupled equations. It is found that the solution of these equations is simplified using V{sub low-k}, which is energy independent, and using the Green's functions in the particle-particle and particle-hole channels. We have applied this approach to the sd-shell effective interactions and find that the results we calculated to all orders by using the KBB summation technique are remarkably similarmore » to those of second-order perturbation theory, the average differences being less than 10%.« less
  • The first detailed comparison of the low-momentum interaction V{sub lowk} with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies. Over a wide range, all sets of V{sub lowk} matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V{sub lowk} reproduces satisfactorily many features of the single-particle and single-hole spectra on closed-shell nuclei, in particular through remarkably good splittings between spin-orbit partners on top of harmonic oscillator closures. The main deficiencies of pure two-nucleon interactions are associatedmore » with binding energies and with the failure to ensure magicity for the extruder-intruder closures. Here, calculations including three-nucleon interactions are most needed. V{sub lowk} makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.« less
  • The residual interaction responsible for the occurrence of certain closely spaced doublets in nuclei with a p/sub 1/2/, nucleon coupled to a core of spin j is sought to be represented by an effective nucleon-nucleon potential. After justifying the dropping of the hard core and the noncentral terms, the two- body potential is chosen to be static, nonsingular and central in character. The radial dependence is chosen to be of the Gaussian form. The relation between the parameters of an explicitly spin-dependent potential and those of the general exchange mixture is pointed out. The potential parameters are fixed by comparisonmore » of the observed splitting for p/sub 1/2/, -doublets with the theoretical results. The splittings for doublets in the T = 1 isobaric state occurring in the neutron-neutron or proton-proton system are satisfactorily explained assuming a Serber exchange mixture although a sizable triplet odd force is not ruled out. The results obtained from such systems are compared with those from the neutron-proton system to fix the parameters for the spin-dependent potential. Several levels or doublets in the nuclei Y/sup 88/, Zr/sup 90/, Nb/ sup 90/, N/sup 1 xtension of the treatment to three-particle doublets is discussed for the levels of Nb/sup 91/. (auth)« less