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Prog. Theor. Phys. Supplement No.62 (1977) pp. 191-235

[ Full Text PDF : FREE ACCESS (2785K) ]

Chapter IV. New Computational Methods of Analytical Derivation of Exchange Kernels

Akihiro Tohsaki-Suzuki

Faculty of Textile Science and Technology, Shinshu University, Ueda 386

(Received December 28, 1977)

Abstract:

The exchange kernels due to the antisymmetrization are derived in an analytical way with the symbolical use of computer memory by taking the α + 16O system as a typical example. Starting with the harmonic oscillator shell model wave functions around the centres as internal states of nuclei, we present new algorisms of deriving analytically the generator coordinate kernel (GCM kernel). We have developed two different algorisms for this purpose; one is named the UFPN and the other the “Rendez-Vous”. Contents of such algorisms are explained in detail. Transformation from the GCM kernel to the resonating group one (RGM one) is also analytically carried out by the aid of computer memory through differential formulas of the GCM kernel. Here, we make use of explicit form Bell's polynomials for performing complex differentiation. A new GCM kernel free from the spurious c.m. component is presented for cases with different oscillator parameters. An algorism of procedure to eliminate the c.m. component is the same as that of deriving the RGM kernel from the GCM one. Considerations are given to a simple method of calculating the direct potential, decomposition method of the kernel and a method of expanding the GCM kernel. The methods mentioned in this report will extend applicability of microscopic study of nucleus-nucleus interactions.


URL : http://ptp.ipap.jp/link?PTPS/62/191/
DOI : 10.1143/PTPS.62.191

[ Full Text PDF : FREE ACCESS (2785K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 61 No. 1 (1979) pp. 101-116 :
    Microscopic Study of 16O+16O Interaction
    Tomoaki Ando, Kiyomi Ikeda and Akihiro Tohsaki-Suzuki
  2. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 644-661 :
    A Study of 24Mg by 16O+ α+ α Cluster Model
    Kiyoshi Katō and Hiroharu Bandō
  3. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1608-1626 :
    Nucleus-Nucleus Interaction and Nuclear Saturation Property
    Tomoaki Ando, Kiyomi Ikeda and Akihiro Tohsaki-Suzuki
  4. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 2028-2059 :
    Study of Local Inter-Nucleus Potential on the Basis of the Resonating Group Method. II
    Kaoru Aoki and Hisashi Horiuchi
  5. Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 985-1004 :
    A Spectroscopic Study of the 21ΛNe Hypernucleus
    Taiichi Yamada, Kiyomi Ikeda, Hiroharu Bandō and Toshio Motoba
  6. Progress of Theoretical Physics Supplement No.62 (1977) pp. 1-10 :
    Chapter I. Introduction
    Kiyomi Ikeda and Ryozo Tamagaki
  7. Progress of Theoretical Physics Supplement No.81 (1985) pp. 104-146 :
    Chapter IV. Structure Study of Typical Light Hypernuclei
    Taiichi Yamada, Toshio Motoba, Kiyomi Ikeda and Hiroharu Bandō
  8. 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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