Prog. Theor. Phys. Vol. 65 No. 6 (1981) pp. 1901-1927

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Generator Coordinate Theory of Normalization Kernels of Cluster Systems. III

— Application of Double Gel'fand Polynomials to General Cluster Systems —

Yoshikazu Fujiwara and Hisashi Horiuchi^*

Cyclotron Laboratory, Department of Physics, The University of Manitoba, Winnipeg R3T 2N2, Canada
and
Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
^*Department of Physics, Kyoto University, Kyoto 606

(Received September 5, 1980)

Abstract:

SU₃-scalar properties of normalization kernels of many-cluster systems are investigated by transforming the kernels into the generator coordinate space. We expand the kernel by the double Gel'fand polynomials which embody the canonical SU₃-coupling scheme of the harmonic oscillator wave functions in the complex generator coordinate space. By this procedure we can easily calculate the matrix elements of the antisymmetrization operator with respect to the SU₃-coupled basis states of the total system. Cluster systems involving non-SU₃-scalar clusters are also treated by constructing the SU₃ coherent states of the shell-model wave functions, which is another application of the double Gel'fand polynomials. Numerical examples are given with respect to 4α, 2α+²⁰Ne, ⁸Be+⁸Be and ²⁴Mg+α systems.

URL : http://ptp.ipap.jp/link?PTP/65/1901/
DOI : 10.1143/PTP.65.1901

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Citing Article(s) :

Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 809-826 :
Generator Coordinate Theory of Normalization Kernels of Cluster Systems. IV

Yoshikazu Fujiwara, Y. C. Tang and Hisashi Horiuchi
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

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Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1377-1387 :
Overlaps of Sp(6,R) States with Multi-Cluster States

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Progress of Theoretical Physics Vol. 80 No. 3 (1988) pp. 477-487 :
An Sp(6,R) Approach to Costructing Multi-Cluster Pauli-Allowed States

Shigehiro Hara and Yasuyuki Suzuki
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. 87 No. 1 (1992) pp. 151-167 :
The 4α Orthogonality Condition Model for Low-Lying 0⁺ States of ¹⁶O

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