Quick Search:
Author: Title/Abstract: Vol./No: Page:

Prog. Theor. Phys. Vol. 15 No. 3 (1956) pp. 222-236

[ Full Text PDF : FREE ACCESS (1149K) ]

Effect of Hard Core on the Binding Energies of H3 and He3, I

Takashi Kikuta, Masato Morita* and Masami Yamada

Department of Physics, Faculty of Science, University of Tokyo
*Kobayasi Institute of Physical Research, Kokubunzi, Tokyo

(Received November 21, 1955)

Abstract:

The binding energies of H3 and He3 are calculated assuming two-body forces of exponential type with hard cores, radii of which are taken equal for both the spin singlet and the triplet states. The outside potentials are supposed charge-independent, and are chosen so as to fit the nuclear two-body data in the low energy region. The following results have been obtained concerning the effects of hard core: 1) it diminishes the binding energies of H3 and He3 considerably, and 2) the wave function is pushed out so that the Coulomb energy of He3, which is too large without hard core, is reasonably reduced to the experimental value for the difference between the binding energies of H3 and He3.


URL : http://ptp.ipap.jp/link?PTP/15/222/
DOI : 10.1143/PTP.15.222

[ Full Text PDF : FREE ACCESS (1149K) ] Citation:


References:

  1. E. Wigner, Phys. Rev. 43 (1933), 252[APS].
    E. Feenberg and J. K. Knipp, Phys. Rev. 48 (1935), 906[APS].
    E. Feenberg and S. S. Share, Phys. Rev. 50 (1936), 253[APS].
    S. Flugge, Zeits. f. Phys. 105 (1937), 522.
    W. Rarita and R. D. Present, Phys. Rev. 51 (1937), 788[APS].
    H. Margenau and D. T. Warren, Phys. Rev. 52 (1937), 790[APS].
    H. Margenau and W. A. Tyrrell, Jr., Phys. Rev. 54 (1938), 422[APS].
    F. W. Brown and M. S. Plesser, Phys. Rev. 56 (1939), 841[APS].
    F. W. Brown, Phys. Rev. 56 (1939), 1107[APS].
    E. Hylleraas and V. Risberg, Avhandl. Norske. Vid. Akad. (mat.-naturv. Kl.) No. 3 (1941).
    E. Gerjuoy and J. S. Schwinger, Phys. Rev. 61 (1942), 138[APS].
    H. Fröhlich, W. Ramsey and I. Sneddon, Cambr. Conf., (1946), 166.
    H. Fröhlich, K. Huang and I. Sneddon, Proc. R. Soc. A 191 (1947), 61.
    N. Svartholm, Arkiv Mat. Astron. Fysik A 35 Nos. 7 and 8 (1948).
    S. E. Clapp, Phys. Rev. 76 (1949), 873[APS].
    H. Feshbach and W. Rarita, Phys. Rev. 75 (1949), 1384[APS].
  2. C. W. Li, Ward Whaling, W. A. Fowler and C. C. Lauritzen, Phys. Rev. 83 (1951), 512[APS].
  3. N. Svartholm, Thesis, Lund University, (1945).
    J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics, (1952), 201.
  4. R. L. Pease, Thesis, M. I. T., (1950).
    R. L. Pease and H. Feshback, Phys. Rev. 81 (1951), 142[APS]; ibid. 88 (1952), 945[APS].
    See also, T. M. Hu and K. N. Hsu, Phys. Rev. 78 (1950), 633[APS].
  5. R. Jastrow, Phys. Rev. 81 (1951), 165[APS].
  6. For example, K. A. Brueckner et al., Phys. Rev. 95 (1954), 217[APS]; ibid. 96 (1954), 508[APS]; ibid. 97 (1955), 1353[APS].
  7. H. Feshbach and S. I. Rubinow, Phys. Rev. 98 (1955), 188[APS].
  8. J. M. Blatt and J. D. Jackson, Phys. Rev. 76 (1949), 18[APS].
  9. N. Svartholm, see reference 3).
  10. W. Rarita and R. D. Present, see reference 1).
  11. E. Gerjuoy and J. S. Schwinger, see reference 1).
  12. J. D. Jackson and J. M. Blatt, Rev. Mod. Phys. 22 (1950), 77[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 17 No. 3 (1957) pp. 326-330 :
    Effect of Hard Cores on the Binding Energies of H3 and He3, II
    Takashi Ohmura, Masato Morita and Masami Yamada
  2. Progress of Theoretical Physics Vol. 17 No. 4 (1957) pp. 543-555 :
    Cluster Development Method in the Quantum Mechanics of Many Particle System, I
    Fumiaki Iwamoto and Masami Yamada
  3. Progress of Theoretical Physics Vol. 18 No. 4 (1957) pp. 345-356 :
    Cluster Development Method in the Quantum Mechanics of Many Particle System, II
    Fumiaki Iwamoto and Masami Yamada
  4. Progress of Theoretical Physics Vol. 20 No. 2 (1958) pp. 163-170 :
    On the Exchange Magnetic Moments
    Eiichi Kuroboshi and Yasuo Hara
  5. Progress of Theoretical Physics Vol. 21 No. 4 (1959) pp. 533-561 :
    Quasi-Deuteron Model of Atomic Nuclei. I
    Takashi Tagami
  6. Progress of Theoretical Physics Vol. 22 No. 1 (1959) pp. 34-40 :
    Effect of Hard Cores on the Binding Energies of H3 and He3
    Takashi Ohmura
  7. Progress of Theoretical Physics Vol. 22 No. 1 (1959) pp. 148-150 :
    Effect of the Finite Size of the Proton on the Coulomb Energy of He3
    Takashi Ohmura
  8. Progress of Theoretical Physics Vol. 22 No. 2 (1959) pp. 274-298 :
    Tensor Force of the Pion-Theoretical Potential and the Doublet Splitting in n-He4 Scattering
    Sinobu Nagata, Tatuya Sasakawa, Tatsuro Sawada and Ryozo Tamagaki
  9. Progress of Theoretical Physics Vol. 31 No. 1 (1964) pp. 107-114 :
    Muon Capture in He3
    Akihiko Fujii and Yoshio Yamaguchi
  10. Progress of Theoretical Physics Vol. 34 No. 5 (1965) pp. 776-813 :
    Dynamical Correlations and the Nuclear Photoeffect
    Tso-Pin Wang and John W. Clark
  11. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 419-441 :
    Isobaric-Spin-3/2 States and Intermediate Symmetry States in Three-Body Nuclei
    Takashi Ohmura
  12. Progress of Theoretical Physics Vol. 42 No. 1 (1969) pp. 36-49 :
    Variational Calculation of Neutron-Proton Scattering
    Kenji Hasegawa
  13. Progress of Theoretical Physics Vol. 51 No. 1 (1974) pp. 134-154 :
    A New Variational Method and Binding Energy of the Triton with Realistic Potentials
    Yoshinori Akaishi, Motoki Sakai, Jun Hiura and Hajime Tanaka
  14. Progress of Theoretical Physics Vol. 51 No. 1 (1974) pp. 155-172 :
    Variational Calculations of the Alpha Particle with Realistic Nucleon-Nucleon Potentials
    Motoki Sakai, Ichiro Shimodaya, Yoshinori Akaishi, Jun Hiura and Hajime Tanaka
  15. Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 95-110 :
    Spin Condition in the Cluster Variation Method and Its Application to the Neutron Matter
    Hiroshi Mimura, Ichiro Homma and Masami Yamada
  16. Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 162-183 :
    A Variational Calculation on the n-d System
    Kenji Hasegawa and Ichirō Shimodaya
  17. Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1483-1494 :
    Particle-Nucleus Scattering Theory with Realistic Two-Body Interactions
    Yukio Kurihara, Yoshinori Akaishi and Hajime Tanaka
  18. Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 894-905 :
    Momentum Distribution Condition in the Cluster Variation Method
    Hiroshi Mimura and Masami Yamada
  19. Progress of Theoretical Physics Vol. 79 No. 2 (1988) pp. 493-501 :
    Cluster Variation Method for Finite-Temperature Systems. II
    Toshiro Yoshikoshi, Kazuhiro Oyamatsu and Masami Yamada
  20. Progress of Theoretical Physics Vol. 84 No. 4 (1990) pp. 641-657 :
    Improvement of the Gross Theory of β-Decay. II
    Takahiro Tachibana, Masami Yamada and Yukihisa Yoshida
  21. Progress of Theoretical Physics Vol. 91 No. 6 (1994) pp. 1149-1172 :
    A Variational Method for Infinite Fermion Systems with Central Forces
    Masatoshi Takano and Masami Yamada
  22. Progress of Theoretical Physics Vol. 93 No. 4 (1995) pp. 745-756 :
    Approximate Energy Expression for Symmetric Nuclear Matter with Central Forces
    Masatoshi Takano
  23. Progress of Theoretical Physics Supplement No.56 (1974) pp. 32-53 :
    Chapter III. Binding Energy of the Alpha Particle
    Motoki Sakai, Ichirô Shimodaya, Yoshinori Akaishi, Jun Hiura and Hajime Tanaka