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Prog. Theor. Phys. Supplement Extra Number (1968) pp. 242-258

Repulsive Core of Effective α-α Potential and the Pauli Principle

Ryozo Tamagaki

Research Institute for Fundamental Physics, Kyoto University, Kyoto

(Received October 5, 1968)

Abstract:

The α-α interaction is a typical one as the interaction between composite particles. The origin of the repulsive core employed in phenomenological α-α potentials is investigated in connection with the characteristic inner oscillation of the relative wave function which is attributed to the Pauli principle and the hard internal structure of the α-particle. It is shown that the elimination of the redundant solutions in the S and D waves leads to a unique description of the inner oscillation and the outer-most energy-independent node plays the role equivalent to the hard core radius. Arguments are developed so that the logical consequences obtained here is applicable to the interaction between the other composite particles. Validity of the effective α-α potential and connection with two nucleon potentials are also discussed. The importance of the angular momentum dependence of the effective potential should be emphasized, because the structural repulsive core disappears beyond some critical value of angular momentum.

URL : http://ptp.ipap.jp/link?PTPS/E68/242/
DOI : 10.1143/PTPS.E68.242

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References:

1. R. Tamagaki and H. Tanaka, Prog. Theor. Phys. 34 (1965), 191[PTP].
2. H. Morinaga, Phys. Rev. 101 (1956), 254[APS].
   H. Horiuchi and K. Ikeda, Prog. Theor. Phys. 40 (1968), 277[PTP].
3. J. Hiura and I. Shimodaya, Prog. Theor. Phys. 30 (1963), 585[PTP].
   A. Arima, H. Horiuchi and T. Sebe, Phys. Lett. B 24 (1967), 129[CrossRef].
   Y. Abe, S. Saito, O. Endo and J. Hiura, Contribution No. 4.16 to the 1967 International Conference on Nuclear Structure at Tokyo.
   J. Eichler, T. Marumori and K. Takada, Prog. Theor. Phys. 40 (1968), 60[PTP].
4. I. Shimodaya, R. Tamagaki and H. Tanaka, Prog. Theor. Phys. 27 (1962), 793[PTP].
5. E. Almqvist, D. A. Bromley and J. A. Kuehner, Phys. Rev. Lett. 4 (1960), 515[APS].
6. J. Maher, A. Weidinger, R. H. Siemssen and D. A. Bromley, Phys. Rev. Lett. 19 (1967), 369[APS].
7. S. Sakata, Prog. Theor. Phys. 16 (1955), 686[PTP].
8. a) S. Otsuki, R. Tamagaki and M. Wada, Prog. Theor. Phys. 32 (1964), 220[PTP].
   b) S. Machida and M. Namiki, Prog. Theor. Phys. 33 (1965), 125[PTP].
   c) S. Otsuki, R. Tamagaki and M. Yasuno, Prog. Theor. Phys. Suppl. Extra Number (1965), 578[PTP].
   d) M. Sato and R. Tamagaki, Prog. Theor. Phys. 37 (1967), 1147[PTP].
9. Y. Fujimoto and M. Taketani, Prog. Theor. Phys. Suppl. Extra Number (1965), 651[PTP].
10. R. Tamagaki, Rev. Mod. Phys. 39 (1967), 629[APS]; Proceedings of the 1967 International Conference on Nuclear Structure at Tokyo (Physical Society of Japan, 1968), p. 27.
11. R. J. Munn, B. Block and F. B. Malik, Phys. Rev. Lett. 21 (1968), 159[APS].
12. a) Haefner, Rev. Mod. Phys. 23 (1951), 228[APS].
    b) Sekine, Taketani, Toyoda and Inoue, Soryushiron Kenkyu (mimeographed circular in Japanese) 11 (1956), 195.
    c) E. van der Spuy and H. J. Pienaar, Nucl. Phys. 7 (1958), 397[CrossRef].
    d) O. Endo, I. Shimodaya and J. Hiura, Prog. Theor. Phys. 31 (1964), 1157[PTP].
    e) P. Darrinlat, G. Igo, H. G. Pugh and H. D. Holmgren, Phys. Lett. 11 (1964), 326[CrossRef]; Phys. Rev. 137 (1964), B315[APS].
13. a) E. van der Spuy, Nucl. Phys. 11 (1959), 615[CrossRef].
    b) A. C. Butcher and J. M. McNamee, Proc. Phys. Soc. 74 (1959), 529.
    c) E. W. Schmid and K. Wildermuth, Nucl. Phys. 26 (1961), 463[CrossRef].
14. S. Okai and S. C. Park, Phys. Rev. 145 (1966), 787[APS].
15. S. Okai, Genshikaku Kenkyu (mimeographed circular in Japanese) 10 (1965), 455.
16. A. Herzenberg and A. S. Roberts, Nucl. Phys. 3 (1957), 314[CrossRef].
17. S. Hochberg, H. S. W. Massey and L. H. Underhill, Proc. Phys. Soc. A 67 (1954), 957.
18. P. Swan, Proc. R. Soc. A 228 (1955), 10.
19. H. Tanaka, Proceedings of the 1967 International Conference on Nuclear Structure at Tokyo (Physical Society of Japan, 1968), p. 51.
    Y. Abe, O. Endo, R. Tamagaki and H. Tanaka, Contribution No. 3.45 to the 1967 International Conference on Nuclear Structure at Tokyo.
20. S. Okai and R. Tamagaki, Soryusiron Kenkyu (mimeographed circular in Japanese) 37 (1968), 441.
21. The similar argument has been developed for nucleon-nucleus interaction by
    H. Feshbach, Ann. of Phys. 19 (1962), 287[CrossRef].
22. S. Saito, Prog. Theor. Phys. 40 (1968), 893[PTP]; ibid. 41 (1969), 705[PTP].
23. R. Tamagaki, Prog. Theor. Phys. 39 (1968), 91[PTP].
24. S. Okai, Prog. Theor. Phys. 38 (1967), 1413[PTP].
25. A. Hasegawa and S. Nagata, Prog. Theor. Phys. 38 (1967), 1188[PTP].
26. R. A. Arndt and M. H. MacGregor, Phys. Rev. 141 (1966), 873[APS].
27. D. R. Thompson and Y. C. Tang, Phys. Rev. 159 (1967), 806[APS]; Nucl. Phys. A 106 (1968), 591[CrossRef].

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