Abstract
The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.
Similar content being viewed by others
References
Arima, A., Iachello, F.: Phys. Lett. B53, 309 (1974), B57, 39 (1975); Phys. Rev. Lett.35, 1069 (1975); Ann. Phys. NY 99, 253 (1976);111, 201 (1979);123, 468 (1979)
Arima, A., Iachello, F., Scholten, O.: Ann. Phys. NY115, 325 (1978)
Bohr, A.: Kgl. Dan. Vid. Selsk. Mat. Fys. Medd.26, 14 (1952)
Bohr, A., Mottelson, B.R.: Mat.-Fys. Medd.27, 16 (1953)
Dieperink, A.E.L., Iachello, F., Scholten, O.: Phys. Rev. Lett.44, 1747 (1980)
Moshinsky, M.: Nucl. Phys. A338, 156 (1980)
Castanos, O., Chacon, E., Frank, A., Moshinsky, M.: J. Math. Phys.20, 35 (1979)
Ginocchio. J.N., Kirson, M.W.: Phys. Rev. Lett.44, 1744 (1980); Nucl. Phys. A350, 31 (1980)
Klein, A., Vallieres, M.: Phys. Lett.98 B, 5 (1981)
Klein, A., Li, C.T., Vallieres, M.: Phys. Rev. C25, 2733 (1982); Phys. Scr.25, 452 (1982)
Gilmore, R.: J. Math. Phys.20, 891 (1979)
Weiguny, A.: Z. Phys. A — Atoms and Nuclei301, 335 (1981)
Assenbaum, H.J., Weiguny, A.: Lecture Notes in Physics. Vol. 161, p. 192. Berlin, Heidelberg, New York: Springer 1982
Arima, A.: Lecture Notes in Physics. Vol. 161, p. 46. Berlin, Heidelberg, New York: Springer 1982
Ring, P., Gambhir, Y.K., Iwasaki, S., Schuck, P.: Lecture Notes in Physics. Vol. 161, p. 174. Berlin, Heidelberg, New York: Springer 1982
Iachello, F.: Lecture Notes in Physics Vol. 161, p. 1. Berlin, Heidelberg, New York: Springer 1982
Gilmore, R., Bowden, C.M., Narducci, L.M.: Phys. Rev. A12, 1019 (1975)
Brink, D.M., Weiguny, A.: Nucl. Phys. A120, 59 (1968)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Assenbaum, H.J., Weiguny, A. On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II. Z Physik A 310, 75–85 (1983). https://doi.org/10.1007/BF01433613
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01433613