Prog. Theor. Phys. Vol. 70 No. 3 (1983) pp. 809-826

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Generator Coordinate Theory of Normalization Kernels of Cluster Systems. IV

— Application of Double Gel'fand Polynomials to SU₄ Symmetry of Cluster Wave Functions —

Yoshikazu Fujiwara, Y. C. Tang and Hisashi Horiuchi^*

School of Physics, University of Minnesota, Minneapolis, Minnesota 55455
^*Department of Physics, Kyoto University, Kyoto 606

(Received January 18, 1983)

Abstract:

The theory of double Gel'fand polynomials is applied to describe the irreducible representation of SU₄ group with respect to spin-isospin wave functions of many-cluster systems. Utilizing an expansion formula of the determinant associated with a matrix tensor product, it is shown that generator coordinate normalization kernels classified by SU₄ symmetry are compactly represented by double Gel'fand polynomials and their expansion coefficients in a power series. Combining the explicit expressions of generator coordinate kernels thus obtained with SU₃ classification technique of spatial wave functions, we can solve the eigenvalue problem of normalization kernels for a very wide class of cluster systems described by SU₃-shell-model wave functions having a common harmonic oscillator parameter. Numerical examples are given for 3N+3N+3N, α+2N+N, α+3N+N, ¹⁶O+3N+N and ¹²C+3N+N systems, where N represents a nucleon.

URL : http://ptp.ipap.jp/link?PTP/70/809/
DOI : 10.1143/PTP.70.809

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Citing Article(s) :

Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1277-1281 :
Pauli-Forbidden Region in the Phase-Space of Coupled-Channel System in the Framework of the Time-Dependent Variational Theory

Hisashi Horiuchi and Kazuhiro Yabana
Progress of Theoretical Physics Vol. 80 No. 4 (1988) pp. 663-677 :
Systematic Construction Method of Multi-Cluster Pauli-Allowed States

Kiyoshi Katō, Kimikatsu Fukatsu and Hajime Tanaka
Progress of Theoretical Physics Vol. 81 No. 4 (1989) pp. 841-857 :
A New Truncation Method for Multi-Cluster Orthogonality Condition Model

Kiyoshi Katō and Hajime Tanaka

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