Prog. Theor. Phys. Vol. 54 No. 1 (1975) pp. 134-142
Quasiparticle Approximations in an Exactly Solvable Model
Department of Physics, Tohoku University, Sendai
(Received December 13, 1974)
The properties of two Hartree-Fock ground states of the well-known Lipkin model which are given by the fermion quasiparticle approximation and the boson quasiparticle approximation are studied. Similarity between the two approximations is pointed out. Using the boson quasiparticle approximation, we show that there exists a stable Hartree-Fock ground state of the approximated boson Hamiltonian for any strength of the anharmonic term. The Hartree-Fock energies given by the two approximation are calculated and are compared with the exact ground state energy.
DOI : 10.1143/PTP.54.134
S. T. Belyaev and V. G. Zelevinsky, Nucl. Phys. 39 (1962), 582[CrossRef].
- T. Marumori, M. Yamamura and A. Tokunaga, Prog. Theor. Phys. 31 (1964), 1009[PTP]; ibid. 37 (1967), 336[PTP].
H. J. Lipkin, N. Meshkov and A. J. Glick, Nucl. Phys. 62 (1965), 188[CrossRef].
N. Meshkov, A. J. Glick and H. J. Lipkin, Nucl. Phys. 62 (1965), 199[CrossRef].
A. J. Glick, H. J. Lipkin and N. Meshkov, Nucl. Phys. 62 (1965), 211[CrossRef].
D. Agassi, H. J. Lipkin and N. Meshkov, Nucl. Phys. 86 (1966), 321[CrossRef].
- A. Klein, “Theory of Collective Motion” in Dynamic Structure of Nuclear State, Proceedings of the 1971 Mont Tremblant International Summer School, ed. by D. J. Rowe et al. (University of Tront Press, 1972), p. 38.
See also A. Klein, R. M. Dreizler and R. E. Johnson, Phys. Rev. 171 (1968), 1216[APS].
T. Holstein and Primakoff, Phys. Rev. 58 (1940), 1098[APS].
S. C. Pang, A. Klein and R. M. Dreizler, Ann. of Phys. 49 (1968), 477[CrossRef].
H. Ui, Ann. of Phys. 49 (1968), 69[CrossRef].
- H. Ui, Prog. Theor. Phys. 44 (1970), 703[PTP].
- R. Y. Cusson, “The Deformed Harmonic Oscillator Shell Model for Medium-Light Nuclei” Chalk River preprint (not for publication) (1968).
- Y. Takahashi, Prog. Theor. Phys. 53 (1975), 461[PTP].