# MANY-BODY PROBLEMS. Lecture Given by G.E. Brown at Universitetets Institut for Teoretisk Fysik and NORDITA Copenhagen

## Abstract

The Hartree method and the Hartree-Fock method for calculating wave functions in self-consistent fields are discussed, and use of occupation number representation is explained. Hartree-Fock equations are used in calculations of matrix elements using a Yukawa force in a liquid drop model nucleus. Perturbation theory is developed, particularly the Brillouin-Wigner and Rayleigh- Schrodinger perturbation expansions. Graphical techniques introduced into field theory by Goldstone and Hugenholtz as well as use of Wick's theorem in graphically analyzing series are examined. Various graphs are considered, and the effect of the Hartree-Fock self-consistent potential on graphs is explored. Brueckner's theory taking into account strong short-range nucleon repulsions is treated, and the oneparticle Green's function described and calculated by graphical perturbation methods is extended to quasiparticles. Particle-hole excitations are examined, and the twobodyGreen's Function is introduced to describe particlehole propagation. Particle-hole theory is then applied to liquid helium-3, and examination of collective motion in nuclei is undertaken with vibrations of the closed shells in spherical nuclei receiving particular attention. An extended schematic model for vibrations is described as is a time- dependent Hartree-Fock treatment for ground state solutions. Stability conditions in wave functions, moment of inertia considerations, and quantization of translational and rotational motion aremore »

- Publication Date:

- Research Org.:
- Nordisk Institut for Teoretisk Atomfysik, Copenhagen

- OSTI Identifier:
- 4708688

- Report Number(s):
- NP-12435(Pt.I)

- NSA Number:
- NSA-17-011481

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-63

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; ATOMS; BRUECKNER METHOD; ELECTRONS; ELEMENTARY PARTICLES; ENERGY LEVELS; EXCITATION; FIELD THEORY; GOLDSTONE DIAGRAMS; GREEN FUNCTION; HARTREE APPROXIMATION; HARTREE-FOCK METHOD; HELIUM 3; HOLES; INTERACTIONS; LIQUIDS; MANY BODY PROBLEM; MATRICES; MOMENT OF INERTIA; MOMENTUM; MOTION; NUCLEAR MODELS; NUCLEAR POTENTIAL; NUCLEONS; NUMERICALS; PERTURBATION THEORY; QUANTUM MECHANICS; ROTATION; SELF-CONSISTENT FIELD; VIBRATIONS; WICK THEOREM

### Citation Formats

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```*MANY-BODY PROBLEMS. Lecture Given by G.E. Brown at Universitetets Institut for Teoretisk Fysik and NORDITA Copenhagen*. Country unknown/Code not available: N. p., 1961.
Web.

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```*MANY-BODY PROBLEMS. Lecture Given by G.E. Brown at Universitetets Institut for Teoretisk Fysik and NORDITA Copenhagen*. Country unknown/Code not available.

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"MANY-BODY PROBLEMS. Lecture Given by G.E. Brown at Universitetets Institut for Teoretisk Fysik and NORDITA Copenhagen". Country unknown/Code not available.
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@article{osti_4708688,
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title = {MANY-BODY PROBLEMS. Lecture Given by G.E. Brown at Universitetets Institut for Teoretisk Fysik and NORDITA Copenhagen},

author = {},

abstractNote = {The Hartree method and the Hartree-Fock method for calculating wave functions in self-consistent fields are discussed, and use of occupation number representation is explained. Hartree-Fock equations are used in calculations of matrix elements using a Yukawa force in a liquid drop model nucleus. Perturbation theory is developed, particularly the Brillouin-Wigner and Rayleigh- Schrodinger perturbation expansions. Graphical techniques introduced into field theory by Goldstone and Hugenholtz as well as use of Wick's theorem in graphically analyzing series are examined. Various graphs are considered, and the effect of the Hartree-Fock self-consistent potential on graphs is explored. Brueckner's theory taking into account strong short-range nucleon repulsions is treated, and the oneparticle Green's function described and calculated by graphical perturbation methods is extended to quasiparticles. Particle-hole excitations are examined, and the twobodyGreen's Function is introduced to describe particlehole propagation. Particle-hole theory is then applied to liquid helium-3, and examination of collective motion in nuclei is undertaken with vibrations of the closed shells in spherical nuclei receiving particular attention. An extended schematic model for vibrations is described as is a time- dependent Hartree-Fock treatment for ground state solutions. Stability conditions in wave functions, moment of inertia considerations, and quantization of translational and rotational motion are other aspects discussed. (D.C.W.)},

doi = {},

journal = {},

number = ,

volume = ,

place = {Country unknown/Code not available},

year = {1961},

month = {11}

}