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Beyond the first order of the hyperspherical harmonic expansion method

Journal Article · · Ann. Phys. (N.Y.); (United States)
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In this paper we demonstrate the inadequacy of the first order of the Hyperspherical Harmonic Expansion Method, the L/sub m/ approximation, for the calculation of the binding energies, charge form factors and charge densities of doubly magic nuclei like /sup 16/O and /sup 40/Ca. We then extend the Hyperspherical Expansion Method to many-fermion systems, consisting of an arbitrary number of fermions, and develop an exact formalism capable of generating the complete optimal subset of the hyperspherical harmonic basis functions. This optimal subset consists of those hyperspherical harmonic basis functions directly connected to the dominant first term in the expansion, the hyperspherical harmonic of minimal order L/sub m/, through the total interaction between the particles. The required many-body coefficients are given using either the Gogny or Talmi-Moshinsky coefficients for the two-body operators. Using the two-body coefficients the weight function generating the orthogonal polynomials associated with the optimal subset is constructed.

Research Organization:
Institut de Physique Nucleaire, Division de Physique Theorique, 91406 Orsay Cedex, France
OSTI ID:
5523893
Journal Information:
Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 138:2; ISSN APNYA
Country of Publication:
United States
Language:
English

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Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALKALINE EARTH ISOTOPES
BINDING ENERGY
CALCIUM 40
CALCIUM ISOTOPES
CHARGE DENSITY
CORRELATION FUNCTIONS
COULOMB FIELD
ELECTRIC FIELDS
ELECTROMAGNETIC FORM FACTORS
ENERGY
EVEN-EVEN NUCLEI
FERMIONS
FORM FACTORS
FUNCTIONS
HARMONIC OSCILLATOR MODELS
ISOTOPES
LIGHT NUCLEI
MANY-BODY PROBLEM
MATHEMATICAL MODELS
NUCLEI
OXYGEN 16
OXYGEN ISOTOPES
PARTICLE PROPERTIES
POLYNOMIALS
SERIES EXPANSION
STABLE ISOTOPES
WAVE FUNCTIONS