Prog. Theor. Phys. Vol. 65 No. 5 (1981) pp. 1632-1666

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Generator Coordinate Theory of Normalization Kernels of Cluster Systems. II

— Systems Described by Three Generator Coordinate Vectors Involving Complex Conjugate One(s) —

Yoshikazu Fujiwara and Hisashi Horiuchi^*

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

(Received September 5, 1980)

Abstract:

SU₃-scalar property of nomalization kernels of cluster sysytems is investigated by transforming the kernel into the complex-generator-coordinate space. The eigenvalue problem of the normalization kernel is easily solved by diagonalizing the matrix elements of the antisymmetrization operator with respect to the vector-coupling basis set of the SU₃ algebra.
General explicit formulas giving the matrix elements are presented for the systems which are described by three generator coordinate vectors involving complex conjugate one(s). Numerical examples are given with respect to 2α+¹²C, ⁸Be+¹²C and ¹²C+¹²C systems.

URL : http://ptp.ipap.jp/link?PTP/65/1632/
DOI : 10.1143/PTP.65.1632

References:

H. Horiuchi, Prog. Theor. Phys. Suppl. No. 62 (1977), 90[PTP].
Y. Fujiwara and H. Horiuchi. Prog. Theor. Phys. 63 (1980), 895[PTP].
K. T. Hecht and W. Zahn, Nucl. Phys. A 313 (1979), 77[CrossRef].
Y. Fujiwara and H. Horiuchi, preprint RIFP 393 (1980).
D. M. Brink, Proceedings of the International School of Physics, Enrico Fermi, (Academic Press, New York and London, 1966), vol, 36, p. 247.
K. T. Hecht, Nucl. Phys. A 170 (1971), 34[CrossRef].
J. P. Elliott and M. Harvey, Proc. R. Soc. A 272 (1963), 557.

Citing Article(s) :

Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 1901-1927 :
Generator Coordinate Theory of Normalization Kernels of Cluster Systems. III

Yoshikazu Fujiwara and Hisashi Horiuchi
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

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

Yasuyuki Suzuki
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