Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems

Pan, Feng, Li, Bo, Zhang, Yao-Zhong and Draayer, Jerry P. (2013) Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems. Physical Review C, 88 3: 034305.1-034305.11. doi:10.1103/PhysRevC.88.034305

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Author Pan, Feng
Li, Bo
Zhang, Yao-Zhong
Draayer, Jerry P.
Title Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
Journal name Physical Review C   Check publisher's open access policy
ISSN 0556-2813
Publication date 2013-09-04
Year available 2013
Sub-type Article (original research)
DOI 10.1103/PhysRevC.88.034305
Open Access Status File (Publisher version)
Volume 88
Issue 3
Start page 034305.1
End page 034305.11
Total pages 11
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field-plus -pairing model in the strong-pairing interaction G → ∞ limit. Properties of the Stieltjes zeros of the extended Heine-Stieltjes polynomials, whose roots determine the projected states, and the related Van Vleck zeros are discussed. An electrostatic interpretation of these zeros is presented. As examples, applications to nonidentical particles of spin 1/2 and to identical bosons or fermions are made to elucidate the procedure and properties of the Stieltjes zeros and the related Van Vleck zeros. It is shown that the new angular momentum projection for identical bosons or fermions can be simplified with the branching multiplicity formula of U(N) ↓ O(3) and the special choices of the parameters used in the projection. Especially, it is shown that the solutions for identical bosons can always be expressed in terms of zeros of Jacobi polynomials. However, unlike nonidentical particle systems, the -coupled states of identical particles are nonorthogonal with respect to the multiplicity label after the projection.
Keyword Shell-model
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID OCI-0904874
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
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Citation counts: TR Web of Science Citation Count  Cited 11 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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