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Prog. Theor. Phys. Vol. 51 No. 3 (1974) pp. 745-759

[ Full Text PDF : FREE ACCESS (1203K) ]

On 12C + α Scattering by the Coupled Channel Resonating Group Method

— Solution of the Redundancy and Non-Orthogonality Problem —

Hisashi Horiuchi

Department of Physics, Kyoto University, Kyoto

(Received August 31, 1973)

Abstract:

A microscopic treatment of 12C + α scattering is formulated in the framework of the coupled channel resonating group method (CCRGM), using Feshbach's formulation for nucleon scattering.
The ground rotational band states of 12C of spins L = 0, 2 and 4 adopted in the channel coupling, and the wave functions of these three states are assumed to be described by the SU3 model wave functions of (0,4) representation. Since in the interaction region three channels which are based on the three states L = 0, 2, 4 of 12C are not orthogonal and even not independent of each other, we need to classify the states which are independent and orthogonal. The answer to this problem of the classification of the states is given systematically by solving the eigenvalue problem of the overlap kernel, whose eigenfunctions are classified entirely by the irreducible representation of the SU3 group.
In order to clarify the meaning of the CCRGM approach, we classify some important shell model states of a few-particle-hole excitation by means of our CCRGM scheme and give α-spectroscopic factors of these states, by using the solutions of the eigenvalue problem of the overlap kernel.
As an approximation of the CCRGM equation the equation of the coupled channel orthogonality condition model is formulated.


URL : http://ptp.ipap.jp/link?PTP/51/745/
DOI : 10.1143/PTP.51.745

[ Full Text PDF : FREE ACCESS (1203K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 447-460 :
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  3. Progress of Theoretical Physics Vol. 53 No. 4 (1975) pp. 1022-1041 :
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  4. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1448-1461 :
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  5. Progress of Theoretical Physics Vol. 55 No. 6 (1976) pp. 1751-1768 :
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  6. Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 204-222 :
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  7. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 774-789 :
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  8. Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1629-1648 :
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  9. Progress of Theoretical Physics Vol. 62 No. 5 (1979) pp. 1274-1292 :
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  10. Progress of Theoretical Physics Vol. 63 No. 3 (1980) pp. 895-918 :
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  11. Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 508-521 :
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  12. Progress of Theoretical Physics Vol. 120 No. 6 (2008) pp. 1139-1167 :
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  13. Progress of Theoretical Physics Supplement No.62 (1977) pp. 11-89 :
    Chapter II. Theory of Resonating Group Method and Generator Coordinate Method, and Orthogonality Condition Model
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  14. Progress of Theoretical Physics Supplement No.62 (1977) pp. 90-190 :
    Chapter III. Kernels of GCM, RGM and OCM and Their Calculation Methods
    Hisashi Horiuchi
  15. Progress of Theoretical Physics Supplement No.68 (1980) pp. 29-192 :
    Chapter II. Comprehensive Study of Alpha-Nuclei
    Yoshikazu Fujiwara, Hisashi Horiuchi, Kiyomi Ikeda, Masayasu Kamimura, Kiyoshi Katō, Yasuyuki Suzuki and Eiji Uegaki
  16. Progress of Theoretical Physics Supplement No.81 (1985) pp. 147-180 :
    Chapter V. Multi-Strange Hypernuclei
    Kiyomi Ikeda, Hiroharu Bandō and Toshio Motoba
  17. Progress of Theoretical Physics Supplement No.192 (2012) pp. 1-238 :
    Recent Developments in Nuclear Cluster Physics
    Hisashi Horiuchi, Kiyomi Ikeda and Kiyoshi Katō

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