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Morphing the shell model into an effective theory

Haxton1, Song

  • 1Institute for Nuclear Theory, Box 351550, and Department of Physics, University of Washington, Seattle, Washington 98195, USA.

Physical Review Letters
|September 16, 2000
PubMed
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This study presents a novel strategy for nuclear structure calculations, utilizing an expansion for high-momentum nucleons. This method offers an exact solution for bound-state properties, demonstrated for light nuclei.

Area of Science:

  • Nuclear Physics
  • Quantum Mechanics
  • Computational Physics

Background:

  • The nuclear structure problem, specifically determining bound-state properties of nucleons interacting via potentials, remains a significant challenge.
  • Traditional models often face limitations in accurately describing these complex systems.

Purpose of the Study:

  • To develop and present an exact strategy for solving the canonical nuclear structure problem.
  • To explore the reformulation of the nuclear shell model as a controlled effective theory.

Main Methods:

  • An expansion in the number of particles scattering at high momenta is employed.
  • Self-consistent solutions of the Bloch-Horowitz equation are obtained using an efficient Green's function method.
  • The Lanczos algorithm is utilized for computational efficiency.

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Main Results:

  • The proposed strategy is applied to the simplest nuclei, deuterium (d) and Helium-3 (3He).
  • The method provides a pathway to exact solutions for nuclear bound-state properties.

Conclusions:

  • The study demonstrates the feasibility and effectiveness of the developed strategy for nuclear structure calculations.
  • Reformulating the shell model as a controlled effective theory shows promising results for understanding nuclear properties.