Prog. Theor. Phys. Vol. 17 No. 1 (1957) pp. 43-62
Relation between the Nuclear Collective Model and the Individual Particle Model with Configurational Mixing
Research Institute for Fundamental Physics, Kyoto University, Kyoto
(Received September 10, 1956)
By using the method of the quantum mechanical description of collective motion, the relation between the collective model and the individual particle model with configuration mixing is discussed on the basis of the following postulates: (I) The wave function of the nucleus, as a system composed of actual nucleons, implies strong correlations, so that the Hartree approximation makes little sense. Consequently, the method of configurational mixing currently employed as well as the shell model may not be usable without altering the representation: (II) The strong correlation gives rise to collective motion, chiefly the surface oscillation at low energies. The individual motion of nucleons which remains after subtraction of the collective motion is only weakly correlated, so that the shell model is a good approximation to the individual motion.
Leaving aside the essential problem of proving this statement, we reach the following conclusions concerning the relationship between the collective and the shell models of nuclei. i) The individual particle model with configurational mixing does in fact hold in the case of small nuclear deformation, provided that the individual particle motion in the “collective representation” can be treated by means of the adiabatic approximation. ii) The effective inter-particle force responsible for the configurational mixing consists of the following two parts, one arising from the exchange of surfons between an extra-particle and a particle in the core and the other arising from a direct inter-particle interaction. iii) As far as the quadrupole moment is concerned, the collective model and the method of configurational mixing do not show any essential difference. However, there exists an essential difference in these two methods for the interpretation of the magnetic moments.
DOI : 10.1143/PTP.17.43
M. G. Mayer, Phys. Rev. 78 (1950), 16[APS];
ibid. 78 (1950), 22[APS].
- O. Haxel, J. H. D. Jensen and H. E. Suess, ZS. f. Phys. 128 (1950), 295.
R. J. Blin-Stoyle, Rev. Mod. Phys. 28 (1956), 75[APS].
- R. J. Blin-Stoyle, Proc. Phys. Soc. A 66, (1953), 1158.
R. J. Blin-Stoyle, and M. A. Perks, Proc. Phys. Soc. A 67 (1954), 885.
M. A. Perks, Proc. Phys. Soc. A 68 (1955), 1083.
- A. Arima and H. Horie, Prog. Theor. Phys. 12 (1954), 623[PTP].
H. Horie and A. Arima, Phys. Rev. 99 (1955), 778[APS].
- T. Marumori, S. Suekane and A. Yamamoto, Prog. Theor. Phys. 16 (1956), 320[PTP]; cited as M-S-Y.
- V. F. Weisskopf, Helv. Phys. Acta, 23 (1951), 187.
- C. C. Morrison, H. Muirhead and W. G. V. Rosser, Phil. Mag. 44 (1953), 1326.
- S. Hayakawa, M. Kawai and K. Kikuchi, Prog. Theor. Phys. 13 (1955), 415[PTP].
A. M. Lane and C. F. Wandel, Phys. Rev. 98 (1955), 1524[APS].
E. Clementel and C. Villi, Nuovo Cim. 2 (1955), 176.
E. Vogt, Phys. Rev. 101 (1956), 1792[APS].
A. M. Lane, R. G. Thomas and E. P. Wigner, Phys. Rev. 98 (1955), 693[APS].
H. Feshbach, C. E. Porter and V. F. Weisskopf, Phys. Rev. 96 (1954), 448[APS].
- M. G. Mayer and J. H. D. Jersen, Elementary Theory of Nuclear Shell Structure (1955).
R. J. Eden and N. C. Francis, Phys. Rev. 99 (1955), 1326[APS].
- S. Tomonaga, Prog. Theor. Phys. 13 (1955), 467, [PTP]especially §6.
- A. Bohr and B. R. Mottelson, Dan. Mat. -fys. Medd. 27 (1953), No. 16.
D. Inglis, Phys. Rev. 96 (1954), 1059[APS].
D. Inglis, Phys. Rev. 97 (1955), 701[APS].
- A. Bohr and B. R. Mottelson, Dan. Mat. -fys. Medd. 30 (1955), No. 1.
J. M. Araújo, Nucl. Phys. 1 (1956), 259[Elsevier].
- S. Tomonaga, Lecture at the annual meeting of the Physical Society of Japan, July (1956).
Citing Article(s) :
Progress of Theoretical Physics Vol. 18 No. 3 (1957) pp. 223-234
The Electric-Octupole Transitions of Nuclei