Prog. Theor. Phys. Vol. 47 No. 2 (1972) pp. 484-497

[ Full Text PDF : FREE ACCESS (870K) ]

Interaction between Nucleon-Clusters with Full Exchange Effects

— An Equivalent Local Potential in a Soluble Model —

Sueji Okai, Sakae Saito^* and Ryozo Tamagaki^**

Physics Department, The College of General Education, Niigata University, Niigata
^*Department of Physics, Nagoya University, Nagoya
^**Research Institute for Fundamental Physics, Kyoto University, Kyoto

(Received September 3, 1971)

Abstract:

In order to shed light on the seeming conflict between the repulsive core of the phenomenological α-α potentials and the almost stationary inner oscillations of the wave functions obtained by the resonating group method, the phase-equivalent local potential preserving the inner oscillations is investigated for an exactly soluble model. In this model, the s-wave relative wave function has the inner oscillation at short distances due to the orthogonality condition to one forbidden state which embodies an essential role of the Pauli principle. Based on the model calculation, it is concluded that the equivalent local potential accompanying considerable energy dependence is mainly attractive at positive energy but loses physical meaning at negative energy because of the absence of bound states. A strong repulsive core with a large radius as found in the phenomenological analysis has no literal meaning, and should be regarded as an aspect of a model interaction without energy dependence that implies the non-existence of bound states located inside despite of the existence of the inner radial nodes.

URL : http://ptp.ipap.jp/link?PTP/47/484/
DOI : 10.1143/PTP.47.484

References:

O. Endo, I. Shimodaya and J. Hiura, Prog. Theor. Phys. 31 (1964), 1157[PTP].
P. Darriulat, G. Igo, H. G. Pugh and H. D. Holmgren, Phys. Lett. 11 (1964), 326[CrossRef]; Phys. Rev. 137 (1964), B315[APS].
S. Ali and A. R. Bodmer, Nucl. Phys. 80 (1966), 99[CrossRef].
For the review article on the α-α interaction, see for example, S. A. Afzal, A. A. Z. Ahmad and S. Ali, Rev. Mod. Phys. 41 (1969), 247[APS].
For the applications of the resonating group method to nuclei, see K. Wildermuth and W. McClure, Cluster Representations of Nuclei (Springer, Berlin, 1966).
R. Tamagaki and H. Tanaka, Prog. Theor. Phys. 34 (1965), 191[PTP].
S. Okai and S. C. Park, Phys. Rev. 145 (1966), 787[APS].
R. Tamagaki, Prog. Theor. Phys. Suppl. Extra Number (1968), 242[PTP].
S. Saito, Prog. Theor. Phys. 40 (1968), 893[PTP]; ibid. 41 (1969), 705[PTP].
H. Fiedeldey, Nucl. Phys. A 96 (1967), 463[CrossRef].
M. Coz, L. G. Arnold and A. D. MacKeller, Ann. of Phys. 59 (1970), 219[CrossRef]; ibid. 59 (1970), 504.
M. Bertero, G. Talenti and G. A. Viano, Nuovo Cim. 46 (1966), 337; Commun. Math. Phys. 6 (1967), 128[CrossRef]; Nucl. Phys. A 113 (1968), 635; ibid. 115 (1968), 395[CrossRef].
Equation (15) is the same equation as Eq. (2·30) in Ref. 8). See Ref. 8) for the detailed description about Eq. (15).
F. Smithies, Integral Equations (Cambridge University Press, New York, 1958).

Citing Article(s) :

Progress of Theoretical Physics Vol. 50 No. 1 (1973) pp. 111-120 :
Non-Local Effects in the Nucleon-Nucleus Effective Interaction

Marcel Coz
Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1561-1578 :
On the Inner Repulsive Effect Due to the Pauli Principle between Nuclear Composite Particles

Sakae Saito, Sueji Okai, Ryozo Tamagaki and Masaru Yasuno
Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1554-1566 :
Properties of the Saito Nonlocal Potential

M. J. Englefield and H. S. M. Shoukry
Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 447-460 :
Many-Cluster Problem by the Orthogonality Condition Model

Hisashi Horiuchi
Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 765-771 :
The Zero-Energy Continuum Bound State of the Saito Potential

B. Bagchi, B. Mulligan and S. B. Qadri
Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 839-841 :
Off-Energy-Shell Unitarity for the Saito Potential

B. Talukdar, U. Das and S. Chakravarty
Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 886-917 :
Local Inter-Nucleus Potential and Pauli-Forbidden States

Hisashi Horiuchi
Progress of Theoretical Physics Vol. 104 No. 5 (2000) pp. 1025-1040 :
G-Matrix Equation in the Quark-Model Resonating-Group Method for Baryon-Baryon Interaction

Yoshikazu Fujiwara, Michio Kohno, Choki Nakamoto and Yasuyuki Suzuki
Progress of Theoretical Physics Vol. 120 No. 6 (2008) pp. 1193-1205 :
Effective α-α t-Matrix Interaction at Medium Energies

Arun K. Jain and Bhushan N. Joshi
Progress of Theoretical Physics Supplement No.52 (1972) pp. 25-88 :
Chapter II. Typical Realization of Alpha-Particle Model Aspects in Beryllium Region

Jun Hiura and Ryozo Tamagaki
Progress of Theoretical Physics Supplement No.62 (1977) pp. 11-89 :
Chapter II. Theory of Resonating Group Method and Generator Coordinate Method, and Orthogonality Condition Model

Sakae Saito