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PTP Online Top > Volume 56 (1976) > Number 2
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Prog. Theor. Phys. Vol. 56 No. 2 (1976) pp. 583-598

[ Full Text PDF : FREE ACCESS (1462K) ]

The Generator Coordinate Method for Composite-Particle Scattering Based on the Kohn-Hulthén Variational Principle

— Application to α-α, 16O-α and 16O-16O scattering —

Yoshihide Mito and Masayasu Kamimura

Department of Physics, Kyushu University, Fukuoka

(Received February 21, 1976)

Abstract:

The Kohn-Hulthén variational principle is applied to the composite-particle scattering on the basis of the generator coordinate method (GCM) with proposing a new treatment of the external part of the trial function. In the proposed GC treatment, it is not necessary at all to construct the Hill-Wheeler weight functions which reproduce the regular and irregular Coulomb functions outside the nuclear-interaction region of the physical space ; a calculation of the GCM kernel only in the nuclear-interaction region is enough. In the application to α-α, 16O-α and 16O-16O scattering, it is shown that 8×8, 14×14 and 16×16 GC matrix elements respectively are enough to obtain sufficiently accurate phase shifts and wave functions up to about 60 MeV of c.m. energy for each case; for lower energies, the number of the matrix elements can be reduced more. It is much discussed how to examine the accuracy of the calculation within the framework of the present method.


URL : http://ptp.ipap.jp/link?PTP/56/583/
DOI : 10.1143/PTP.56.583

[ Full Text PDF : FREE ACCESS (1462K) ] Citation:

References:

  1. For example, Proceedings of the INS-IPCR Symmposium on Cluster Structure of Nuclei and Transfer Reactions Induced by Heavy-Ions, Tokyo, 1975.
  2. D. L. Hill and J. A. Wheeler, Phys. Rev. 89 (1953), 1102[APS].
    J. J. Griffin and J. A. Wheeler, Phys. Rev. 108 (1957), 311[APS].
  3. K. Wildermuth and W. McClure, Springer Tracts in Mod. Phys. 41 (1966).
  4. a) W. Kohn, Phys. Rev. 74 (1948), 1763[APS].
    b) L. Hulthén, Ark. Mat., Astr. Fys. A 35 (1948), No. 25.
    c) N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, 1965, the third edition), Chaps. VI and XIII.
  5. P. Heiss and H. H. Hackenbroich, Z. Phys. 235 (1970), 422.
    H. H. Hackenbroich, P. Heiss and Le-Chi-Niem, Nucl. Phys. A 221 (1974), 461[CrossRef].
  6. T. Matsuse, M. Kamimura and Y. Fukushima, Prog. Theor. Phys. 53 (1974), 706[PTP].
  7. M. Kamimura and T. Matsuse, Soryusiron Kenkyu (mimeographed circular in Japanese) 50 (1974), C27.
  8. M. Kamimura and T. Matsuse, Prog. Theor. Phys. 51 (1974), 438[PTP].
  9. H. Horiuchi, Prog. Theor. Phys. 43 (1970), 375[PTP].
  10. N. de Takacsy, Phys. Rev. C 5 (1972), 1883[APS].
  11. F. Tanabe, A. Tohsaki and R. Tamagaki, Prog. Theor. Phys. 50 (1973), 1774[PTP].
  12. H. Friedrich, H. Hüsken and A. Weiguny, Nucl. Phys. A 220 (1974), 45[CrossRef].
  13. F. Tanabe and F. Nemoto, Prog. Theor. Phys. 51 (1974), 2009[PTP].
  14. D. Baye and P.-H. Heensen, Nucl. Phys. A 233 (1974), 304[CrossRef].
  15. a) R. Beck, J. Borysowicz, D. M. Brink and M. V. Mihailovi'c, Nucl. Phys. A 244 (1975), 45[CrossRef];
    b) R. Beck, J. Borysowicz, D. M. Brink and M. V. Mihailovi'c, Nucl. Phys. A 244 (1975), 58[CrossRef].
  16. M. Kamimura, Proceedings of the INS-IPCR Symposium on Cluster Structure of Nuclei and Transfer Reactions induced by Heavy-Ions, Tokyo, 1975, p. 166.
  17. Y. Kondo, T. Matsuse and Y. Abe, to be published.
  18. A. B. Volkov, Nucl. Phys. 74 (1965), 33[CrossRef].
  19. R. H. Siemssen, J. K. Maher, A. Weidinger and D. A. Bromley, Phys. Rev. Lett. 19 (1967), 369[APS].
  20. R. A. Chatwin, J. S. Eck, A. Richter and D. Robson, Phys. Rev. 180 (1969), 1049[APS].
  21. S. Saito, Prog. Theor. Phys. 41 (1969), 705[PTP].
  22. A. Tohsaki, F. Tanabe and R. Tamagaki, Prog. Theor. Phys. 53 (1974), 1022[PTP].

Citing Article(s) :

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  8. Progress of Theoretical Physics Vol. 61 No. 1 (1979) pp. 101-116 :
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  12. Progress of Theoretical Physics Vol. 63 No. 5 (1980) pp. 1638-1653 :
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  14. Progress of Theoretical Physics Vol. 65 No. 2 (1981) pp. 586-612 :
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  16. Progress of Theoretical Physics Vol. 73 No. 2 (1985) pp. 397-413 :
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  17. Progress of Theoretical Physics Supplement No.62 (1977) pp. 1-10 :
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  18. Progress of Theoretical Physics Supplement No.62 (1977) pp. 11-89 :
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  19. Progress of Theoretical Physics Supplement No.62 (1977) pp. 90-190 :
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  20. Progress of Theoretical Physics Supplement No.62 (1977) pp. 191-235 :
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  21. Progress of Theoretical Physics Supplement No.62 (1977) pp. 236-294 :
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  22. Progress of Theoretical Physics Supplement No.65 (1979) pp. 173-199 :
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  23. Progress of Theoretical Physics Supplement No.68 (1980) pp. 29-192 :
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  24. Progress of Theoretical Physics Supplement No.68 (1980) pp. 193-302 :
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  25. Progress of Theoretical Physics Supplement No.68 (1980) pp. 303-358 :
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  26. Progress of Theoretical Physics Supplement No.81 (1985) pp. 42-103 :
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