HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 64 (1980) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 64 No. 1 (1980) pp. 184-203

[ Full Text PDF : FREE ACCESS (1511K) ]

A Semi-Classical Treatment of Non-Local Potentials

Hisashi Horiuchi

Department of Physics, Kyoto University, Kyoto 606

(Received February 14, 1980)

Abstract:

A semi-classical treatment of the three-dimensional Schrödinger equation containing a non-local potential is discussed by the use of the WKB method. An equivalent local potential is derived and the Perey effect is investigated. In deriving the equivalent local potential, it is shown that the concept of the parity-dependence should be introduced for the proper use of the WKB method. By using the equivalent local potential we discuss properties of the non-local potential, namely, its spatial, energy and angular-momentum dependence including the parity-dependence.


URL : http://ptp.ipap.jp/link?PTP/64/184/
DOI : 10.1143/PTP.64.184

[ Full Text PDF : FREE ACCESS (1511K) ] Citation:

References:

  1. K. Ikeda, R. Tamagaki, S. Saito, H. Horiuchi, A. Toshiaki-Suzuki and M. Kamimura, Prog. Theor. Phys. Suppl. No. 62 (1977).
  2. K. Wildermuth and Y. C. Tang, A Unified Theory of the Nucleus (Vieweg, Braunschweig, 1977).
  3. Proceedings of the International Symposium on Nuclear Collisions and Their Microscopic Description, Bled, 1977, Fizika 9, Suppl. 3 and 4.
  4. Proceedings of the International Conference on Clustering Aspects of Nuclear Structure and Nuclear Reactions, Winnipeg, 1978.
  5. D. Baye, J. Deenen and Y. Salmon, Nucl. Phys. A 289 (1977), 511[CrossRef].
  6. M. LeMere and Y. C. Tang, Phys. Rev. C 19 (1979), 391[APS].
  7. G. W. Greenless and Y. C. Tang, Phys. Lett. B 34 (1971), 359[CrossRef].
  8. M. LeMere, D. J. Stubeda, H. Horiuchi and Y. C. Tang, Nucl. Phys. A 320 (1979), 449[CrossRef].
  9. F. Perey and B. Buck, Nucl. Phys. 32 (1962), 353[CrossRef].
  10. F. G. Perey, Direct Interactions and Nuclear Reaction Mechanism, eds. E. Clementel and C. Villi (Gordon and Breach, Science Publishers, Inc., New York, 1963), p. 125.
  11. H. Horiuchi, Prog. Theor. Phys. 63 (1980), 725[PTP].
  12. N. Austern, Phys. Rev. 137 (1965), B752[APS].
  13. H. Fiedeldey, Nucl. Phys. A 96 (1967), 463[CrossRef].
  14. W. E. Frahn and R. H. Lemmer, Nuovo Cim. 5 (1957), 523; ibid. 5 (1957), 1564.
  15. R. E. Langer, Phys. Rev. 51 (1937), 669[APS].
  16. J. H. Van Vleck, Proc. Nat. Acad. Sci. 14 (1928), 178.
  17. L. S. Brown, Am. J. Phys. 40 (1972), 371.
  18. N. Takigawa and K. Hara, Z. Phys. A 276 (1976), 79.
  19. M. Coz, L. G. Arnold and A. D. MacKeller, Ann. of Phys. 59 (1970), 219[CrossRef]; ibid. 59 (1970), 504.
  20. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, New York, 1958), sect. III.
  21. A. B. Migdal and V. P. Krainov, Approximation Methods in Quantum Mechanics (W. A. Benjamin, Inc., New York, 1969).
  22. P. A. M. Dirac, The Principle of Quantum Mechanics (Oxford U. P., Oxford, Eng., 1947), 3rd ed., sect. 31.
  23. N. Austern, Direct Nuclear Reaction Theories (Wiley-Interscience, John Wiley & Sons, Inc., New York, 1970), sect. 5.2.
  24. H. Horiuchi, Prog. Theor. Phys. Suppl. No. 62 (1977), chap. 3.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1508-1510 :
    WKB Derivation of Equivalent Local Potentials from RGM Non-Local Potentials of the Systems of 0s-Shell-Nucleus + 16O
    Kaoru Aoki and Hisashi Horiuchi
  2. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1903-1905 :
    WKB Derivation of Equivalent Local Potentials from RGM Non-Local Potentials of the Systems of 0s-Shell-Nucleus+4He
    Kaoru Aoki and Hisashi Horiuchi
  3. Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1236-1239 :
    Equivalent Local Potentials for RGM Non-Local Potentials of the Systems of 0s-Shell-Nucleus+40Ca
    Kaoru Aoki and Hisashi Horiuchi
  4. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1658-1687 :
    Study of Local Inter-Nucleus Potential on the Basis of the Resonating Group Method. I
    Kaoru Aoki and Hisashi Horiuchi
  5. 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
  6. Progress of Theoretical Physics Vol. 69 No. 2 (1983) pp. 516-534 :
    Equivalent Local Potentials and Perey Factors for Various Kinds of Relative Wave Functions of RGM. I
    Hisashi Horiuchi
  7. Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 857-885 :
    Study of Local Inter-Nucleus Potential on the Basis of the Resonating Group Method. III
    Kaoru Aoki and Hisashi Horiuchi
  8. Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 886-917 :
    Local Inter-Nucleus Potential and Pauli-Forbidden States
    Hisashi Horiuchi
  9. Progress of Theoretical Physics Vol. 69 No. 4 (1983) pp. 1154-1183 :
    Study of Local Inter-Nucleus Potential on the Basis of the Resonating Group Method. IV
    Kaoru Aoki and Hisashi Horiuchi
  10. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 609-612 :
    Study of Flux Conservation in the Presence of Non-Local Potential
    Kaoru Aoki
  11. Progress of Theoretical Physics Vol. 70 No. 6 (1983) pp. 1599-1623 :
    WKB Treatment of Boson Hamiltonian of Inter-Nucleus Interaction
    Hisashi Horiuchi, Kaoru Aoki, Takahiro Wada and Kazuhiro Yabana
  12. Progress of Theoretical Physics Vol. 71 No. 3 (1984) pp. 535-545 :
    Equivalent Local Potentials and Perey Factors for Various Kinds of Relative Wave Functions of RGM. II
    Hisashi Horiuchi
  13. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1275-1292 :
    A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. I
    Kazuhiro Yabana and Hisashi Horiuchi
  14. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 100-127 :
    A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. II
    Kazuhiro Yabana and Hisashi Horiuchi
  15. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 128-142 :
    A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. III
    Kazuhiro Yabana and Hisashi Horiuchi
  16. Progress of Theoretical Physics Vol. 73 No. 5 (1985) pp. 1172-1190 :
    Microscopic Study of the Dependence of the Light Ion Potential on the Projectile Mass Number
    Hisashi Horiuchi
  17. Progress of Theoretical Physics Vol. 75 No. 2 (1986) pp. 458-460 :
    Study of 16O+40Ca Potential by the Resonating Group Method
    Takahiro Wada
  18. Progress of Theoretical Physics Vol. 75 No. 3 (1986) pp. 619-638 :
    Microscopic Derivation of the Spin-Orbit Potential of Mass-Three Nucleus
    Takahiro Wada, Yukio Takahashi and Hisashi Horiuchi
  19. Progress of Theoretical Physics Vol. 75 No. 3 (1986) pp. 754-756 :
    Effect of Coulomb Force on the Volume Integral of Light-Ion Nuclear Potential
    Takahiro Wada and Hisashi Horiuchi
  20. Progress of Theoretical Physics Vol. 76 No. 5 (1986) pp. 1071-1088 :
    Microscopic Analysis of Inelastic Coupling Potential Based on the Coupled Channel Resonating Group Method. I
    Kazuhiro Yabana and Hisashi Horiuchi
  21. Progress of Theoretical Physics Vol. 78 No. 1 (1987) pp. 123-129 :
    Λ and Σ Single-Particle Potentials with Density-Dependent Effective Interactions
    Michio Kohno
  22. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 19-23 :
    Microscopic Derivation of the Nucleus-Nucleus Potential by the Use of the Density-Dependent Effective Interaction
    Kazuhiro Yabana, Takahiro Wada and Hisashi Horiuchi
  23. Progress of Theoretical Physics Vol. 80 No. 3 (1988) pp. 488-501 :
    Study of 16O-16O Potential by the Resonating Group Method. I
    Takahiro Wada and Hisashi Horiuchi
  24. Progress of Theoretical Physics Vol. 80 No. 3 (1988) pp. 502-516 :
    Study of 16O-16O Potntial by the Resonating Group Method. II
    Takahiro Wada and Hisashi Horiuchi
  25. Progress of Theoretical Physics Vol. 82 No. 6 (1989) pp. 1106-1124 :
    Microscopic Analysis of the Nucleus-Nucleus Optical Potential Based on the Feshbach Projection Operator Formalism. I
    Kazuhiro Yabana
  26. Progress of Theoretical Physics Vol. 91 No. 4 (1994) pp. 631-676 :
    Multiconfiguration Resonating-Group Study of Nuclear Reaction Mechanisms
    Yoshikazu Fujiwara and Y.C. Tang
  27. Progress of Theoretical Physics Vol. 94 No. 1 (1995) pp. 65-90 :
    Central Force of the Hyperon-Nucleon Interaction in the SU6 Quark Model
    Choki Nakamoto, Yasuyuki Suzuki and Yoshikazu Fujiwara
  28. Progress of Theoretical Physics Vol. 97 No. 4 (1997) pp. 587-616 :
    Extended Time-Reversal Operator and the Symmetries of the Hyperon-Nucleon Interaction
    Yoshikazu Fujiwara, Choki Nakamoto, Yasuyuki Suzuki and Zhang Zong-ye
  29. Progress of Theoretical Physics Vol. 101 No. 3 (1999) pp. 591-606 :
    Study of α + Nucleus Scattering with a Simplified Resonating-Group Method
    Tsuneo Kaneko and Y. C. Tang

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.